WO2025240751A1 - Adaptive 3d printing nozzle - Google Patents

Adaptive 3d printing nozzle

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Publication number
WO2025240751A1
WO2025240751A1 PCT/US2025/029573 US2025029573W WO2025240751A1 WO 2025240751 A1 WO2025240751 A1 WO 2025240751A1 US 2025029573 W US2025029573 W US 2025029573W WO 2025240751 A1 WO2025240751 A1 WO 2025240751A1
Authority
WO
WIPO (PCT)
Prior art keywords
nozzle
illustrates
printing
pins
cross
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
PCT/US2025/029573
Other languages
French (fr)
Inventor
Jochen Mueller
Seok Won Kang
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Johns Hopkins University
Original Assignee
Johns Hopkins University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Johns Hopkins University filed Critical Johns Hopkins University
Publication of WO2025240751A1 publication Critical patent/WO2025240751A1/en
Pending legal-status Critical Current
Anticipated expiration legal-status Critical

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Classifications

    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B33—ADDITIVE MANUFACTURING TECHNOLOGY
    • B33Y—ADDITIVE MANUFACTURING, i.e. MANUFACTURING OF THREE-DIMENSIONAL [3D] OBJECTS BY ADDITIVE DEPOSITION, ADDITIVE AGGLOMERATION OR ADDITIVE LAYERING, e.g. BY 3D PRINTING, STEREOLITHOGRAPHY OR SELECTIVE LASER SINTERING
    • B33Y30/00—Apparatus for additive manufacturing; Details thereof or accessories therefor
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B29—WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
    • B29C—SHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING
    • B29C64/00—Additive manufacturing, i.e. manufacturing of three-dimensional [3D] objects by additive deposition, additive agglomeration or additive layering, e.g. by 3D printing, stereolithography or selective laser sintering
    • B29C64/10—Processes of additive manufacturing
    • B29C64/106—Processes of additive manufacturing using only liquids or viscous materials, e.g. depositing a continuous bead of viscous material
    • B29C64/118—Processes of additive manufacturing using only liquids or viscous materials, e.g. depositing a continuous bead of viscous material using filamentary material being melted, e.g. fused deposition modelling [FDM]
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B29—WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
    • B29C—SHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING
    • B29C64/00—Additive manufacturing, i.e. manufacturing of three-dimensional [3D] objects by additive deposition, additive agglomeration or additive layering, e.g. by 3D printing, stereolithography or selective laser sintering
    • B29C64/20—Apparatus for additive manufacturing; Details thereof or accessories therefor
    • B29C64/205—Means for applying layers
    • B29C64/209—Heads; Nozzles
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B22—CASTING; POWDER METALLURGY
    • B22F—WORKING METALLIC POWDER; MANUFACTURE OF ARTICLES FROM METALLIC POWDER; MAKING METALLIC POWDER; APPARATUS OR DEVICES SPECIALLY ADAPTED FOR METALLIC POWDER
    • B22F10/00—Additive manufacturing of workpieces or articles from metallic powder
    • B22F10/10—Formation of a green body
    • B22F10/18—Formation of a green body by mixing binder with metal in filament form, e.g. fused filament fabrication [FFF]
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B22—CASTING; POWDER METALLURGY
    • B22F—WORKING METALLIC POWDER; MANUFACTURE OF ARTICLES FROM METALLIC POWDER; MAKING METALLIC POWDER; APPARATUS OR DEVICES SPECIALLY ADAPTED FOR METALLIC POWDER
    • B22F12/00—Apparatus or devices specially adapted for additive manufacturing; Auxiliary means for additive manufacturing; Combinations of additive manufacturing apparatus or devices with other processing apparatus or devices
    • B22F12/50—Means for feeding of material, e.g. heads
    • B22F12/53—Nozzles
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B22—CASTING; POWDER METALLURGY
    • B22F—WORKING METALLIC POWDER; MANUFACTURE OF ARTICLES FROM METALLIC POWDER; MAKING METALLIC POWDER; APPARATUS OR DEVICES SPECIALLY ADAPTED FOR METALLIC POWDER
    • B22F12/00—Apparatus or devices specially adapted for additive manufacturing; Auxiliary means for additive manufacturing; Combinations of additive manufacturing apparatus or devices with other processing apparatus or devices
    • B22F12/50—Means for feeding of material, e.g. heads
    • B22F12/57—Metering means
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B33—ADDITIVE MANUFACTURING TECHNOLOGY
    • B33Y—ADDITIVE MANUFACTURING, i.e. MANUFACTURING OF THREE-DIMENSIONAL [3D] OBJECTS BY ADDITIVE DEPOSITION, ADDITIVE AGGLOMERATION OR ADDITIVE LAYERING, e.g. BY 3D PRINTING, STEREOLITHOGRAPHY OR SELECTIVE LASER SINTERING
    • B33Y10/00—Processes of additive manufacturing
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B33—ADDITIVE MANUFACTURING TECHNOLOGY
    • B33Y—ADDITIVE MANUFACTURING, i.e. MANUFACTURING OF THREE-DIMENSIONAL [3D] OBJECTS BY ADDITIVE DEPOSITION, ADDITIVE AGGLOMERATION OR ADDITIVE LAYERING, e.g. BY 3D PRINTING, STEREOLITHOGRAPHY OR SELECTIVE LASER SINTERING
    • B33Y50/00—Data acquisition or data processing for additive manufacturing
    • B33Y50/02—Data acquisition or data processing for additive manufacturing for controlling or regulating additive manufacturing processes

Definitions

  • the present invention relates generally to three-dimensional (3D) printing. More particularly, the present invention relates to a shape-changing adaptive 3D printing nozzle. BACKGROUND OF THE INVENTION [0003] 3D printers extruding filaments through a fixed nozzle can encounter a conflict between high resolution, requiring small diameters, and high speed, requiring large diameters.
  • Extrusion-based 3D printing primarily employs nozzles with fixed exit shapes. This imposes a trade-off between resolution and speed: high resolution requires a small nozzle diameter, while high material deposition rate necessitates a larger diameter. The inverse- cubic relationship exacerbates design limitations in objects with varying feature sizes, confining complexity to multiples of the nozzle diameter. Achieving continuous gradients is unfeasible, and sloped surfaces result in undesirable “stair-stepping” artifacts.
  • shape fixed nozzles typically adopt a circular cross-section to facilitate printhead movement in any direction within a layer.
  • Multiscale features which are common in numerous engineered systems, particularly in biologically relevant applications like artificial vascular networks and bone grafts, and in other areas such as heat sinks and graded lattices, would benefit substantially from an adaptive extrusion nozzle in both performance and printing speed.
  • size-variable filaments can address the inherent discrepancies between intended and actual shapes caused by fixed-size, cylindrical filaments, by eliminating inter-filament voids and facilitating smoother surfaces. This approach could also resolve the resolution-speed tradeoff in 3D printing.
  • filament cross-sections and their spatial arrangement By varying filament cross-sections and their spatial arrangement, more complex structures with a wider design space can be printed within the same timeframe, compared to structures composed of uniform cross- sections.
  • filament diameter modulation is achievable through over- and under-extrusion, yet this method is constrained to size changes within -30 % and +35 % of the nozzle diameter.
  • a device for three-dimensional (3D) printing including a base plate.
  • the device includes a nozzle.
  • the nozzle includes a nozzle membrane and pins.
  • the nozzle is coupled to the base plate.
  • the nozzle comprises an exit and is configured to allow precise control of a cross-sectional shape of the exit.
  • the device also includes stepper motors.
  • the pins are coupled to the stepper motors to actuate changes in the cross-sectional shape of the exit.
  • the device includes cables connecting the pins to the stepper motors.
  • the cables can take the form of high strength inextensible fibers.
  • the device can include springs for returning the pins to their original positions.
  • the nozzle is further configured with a tapered internal channel shape suitable for shear-thinning ink.
  • the device can also include an ink inlet module.
  • FIGS.1A-1I illustrate image and diagrammatic views of an adaptive nozzle 3D printing (AN3DP) platform according to an embodiment of the present invention.
  • FIG.1A illustrates an overview and components of the AN3DP.
  • FIG.1B illustrates a schematic of the AN3DP print head.
  • FIG.1C illustrates a schematic of the adaptive nozzle actuation mechanism (left) and photos of the adaptive nozzle.
  • FIG.1D illustrates a schematic of an adaptive nozzle used for printing a size/shape-changing filament, accompanied by a photo of the implementation (top-left).
  • the schematic shows the size change of a circle (1-2), the shape changes from a circle to a rectangle (2-3), and the size change of a rectangle (3-4).
  • FIG. 1E illustrates photos of a bottom view of the adaptive nozzle (top) and corresponding target size (bottom) for small (left), medium (middle), and large exit mode (right).
  • FIG.1F illustrates photos showing the bottom view of the adaptive nozzle (top) and the corresponding target sizes (bottom) for the small (left), medium (middle), and large exit modes (right).
  • FIGS.2A-2I illustrate image and diagrammatic views of a design and implementation of an AN3DP platform according to an embodiment of the present invention.
  • FIG.2A illustrates an exploded view of the AN3D printhead consisting of a printhead assembly (I), an adaptive nozzle (II), and pin modules (III).
  • FIGS.2B-2D illustrate a pin module actuation mechanism for controlling nozzle exit size/shape: starting from the initial state, as illustrated in FIG.2B, tip-widening with a distance-increasing actuation, as illustrated in FIG.2C, via motor actuation, and then returning to the initial state, as illustrated in FIG.2D, due to the restoring moment from the spring and silicone cover after the motor actuation is released.
  • FIGS.2E and 2F illustrate a flexible silicone cover.
  • FIG.2F illustrates a cover fabricated from 3D-printed molds, shown in FIG.2E.
  • FIGS.2G and 2H illustrate metal pins and silicone cover integrated structure.
  • FIG.2H illustrates a tip-fastening mechanism, illustrated in FIG.2G.
  • FIG.2I illustrates that the metal pins and silicone cover integrated structure can be easily interchanged from the nozzle base via screws, allowing for simple replacement and cleaning after every print.
  • FIGS.3A-3D illustrate diagrammatic and graphical views of control for an AN3DP platform according to an embodiment of the present invention.
  • FIG.3A illustrates available nozzle size/shape depending on the number of actuators (1 (i), 2 (ii) and (iii), 4 (iv), and 8 (v))
  • FIGS.3B illustrate actuators, print height, and feed rate operation strategy for an exemplary filament having constant circle cross section ( ), diameter-increasing circle cross section ( , diameter-decreasing circle cross section ( , shape-changing from circle to square section ( ), and constant square cross section ( ).
  • FIGS.3B illustrate actuators, print height, and feed rate operation strategy for an exemplary filament having constant circle cross section ( ), diameter-increasing circle cross section ( , diameter-decreasing circle cross section ( , shape-changing from circle to square section ( ), and constant square cross section ( ).
  • FIGS.4A-4E illustrate diagrammatic and graphical views of an AN3DP platform according to an embodiment of the present invention. Typical objects consist of solid inner features, as illustrated in FIG.4B and surfaces, as illustrated in FIG.4C.
  • FIG.4B illustrates cross-sectional photos of solid inner features additively manufactured from circular filaments via a fixed nozzle (i) and square filaments via the adaptive nozzle (ii) (top) with a comparison of their volume solid fractions (bottom).
  • FIG.4C illustrates cross-sectional photos of surfaces additively manufactured from circular (iii) and square (iv) filaments via fixed nozzles, and a mix of square and triangle filaments from the adaptive nozzle (v), with a comparison of surface roughness and ; scale bars in (B) and (C), 5 mm.
  • FIG.4D illustrates multi-scale structures consisting of bulky solid parts and thin functional features (top) can be manufactured more quickly with AN3DP than with a fixed nozzle by filling up the solid parts with its maximum diameter ( ⁇ l) and thin features with its minimum diameter mode (l) (bottom).
  • the purple sections are the parts that are printed in maximum diameter mode ( ⁇ l) and the green ones in minimum diameter mode (l) when using AN3DP.
  • FIGS.5A-5E illustrate image, diagrammatic, and graphical views of AN3DP platform printing of structures resembling vascular networks according to an embodiment of the present invention.
  • FIG.5A illustrates a design of a structure resembling a vascular network having both continuously decreasing gradients, diameter of 8 mm (i), 6 mm to 4 mm (ii), and continuously-increasing gradients, 4 mm, 6 mm to 8 mm (top), AN3DP printing process with corresponding zoomed-in adaptive nozzles (middle), and printed structures (bottom) (scale bar: 10 mm)
  • FIG.5B illustrates a design of a vascular network-like structure having branches with five-fold difference in diameter, 2 mm (iii) to 10 mm (iv), and bifurcation points (top), AN3DP printing process with corresponding zoomed-in adaptive nozzles (middle), and printed structures (bottom); scale bars in (A) and (B), 10 mm.
  • FIG.5C illustrates a comparison of achievable cross-sectional areas of filaments extruded from AN3DP to those using fixed nozzles with diameters of 3 mm, 4 mm, 5 mm, 8 mm, and 10 mm, where thick lines represent equidimensional modes and thin lines represent under/over-extrusion modes, respectively.
  • FIG.5D is an illustration of a theoretical vascular network with 4 levels of hierarchy (left), showing the relationship of diameters ( , ) and lengths ( , ) at every branching point (right).
  • FIG. 5E is a theoretical print time comparison ( ) for vascular networks having total m-levels. All photos in FIGS.5A and 5B were modified to reduce color saturation to 33 % in PowerPoint (Microsoft).
  • FIG.6 illustrates schematic views of available sizes and shapes of the nozzle exit vary depending on the number of actuators. Pins indicated by dots of the same color are controlled by the same actuator. As the number of actuators increases, a greater variety of nozzle shapes becomes available, which is depicted with a denser background.
  • FIGS.7A and 7B illustrates graphical views of nozzle volumes depending on dimensions.
  • FIG.7A illustrates a rhombus-shape exit with dimensions of and .
  • FIG.7B illustrates a star-shape exit with dimensions of and , which are calculated from Eq.14.
  • FIGS.8A-8C illustrate schematic and graphical views of a volume calculation for arbitrary adaptive nozzle with n pins.
  • FIG.8A illustrates that the nozzle is shaped as a ‘twisted prism’ with a total height of . It has a cross-section at the base ( ) in the form of a regular n-gon, where the perpendicular distance from the center ( to each side is (i), as illustrated in FIG. 8B. At the exit ( ), the shape is an n-gon formed by controlled pin distances of (ii). The corresponding cross-sectional shape at h (ii) forms.
  • FIG.8C illustrates a 2n-gon, each vertex at a distance of and from the origin , and each line connecting a vertex to the origin forms an interval angle of with one another.
  • FIGS.10A and 10B illustrate graphical views of size/shape-varying filament extrusion by AN3DP.
  • FIG.10A illustrates an analytical model for the cross-sectional dimension of the filament, d'', along the extruded length, x, incorporating the nozzle exit dimension over time, d(t), ink input volumetric flow rate, F, nozzle volume as a function of exit dimension, V(d).
  • FIG.10B illustrates an example photo of a filament with varying dimensions.
  • FIGS.9A-9I illustrate image and graphical views of numerical calculation of surface roughness for additively manufactured surface structures shown in FIG.4C.
  • FIG.9A illustrates a cross-sectional photo of the structure fabricated with a circle-shaped fixed nozzle.
  • FIG.9B illustrates an extracted wall lines of the printed (in light grey) and target (in dark grey) from, FIG.9A.
  • FIG.9C illustrates an error E, representing the difference between the target and printed wall of (B), plotted along the Y-coordinate.
  • FIG.9D illustrates a cross- sectional photo of the structure fabricated with a square-shaped fixed nozzle.
  • FIG.9E illustrates an extracted wall lines of the printed (in light grey) and target (in dark grey) from, FIG.9D.
  • FIG.9F illustrates an error E, representing the difference between the target and printed wall of (E), plotted along the Y-coordinate.
  • FIG.9G illustrates a cross-sectional photo of the structure fabricated with square and triangle modes of the adaptive nozzle.
  • FIG.9H illustrates an extracted wall lines of the printed (in light grey) and target (in dark grey) from FIG.9G.
  • FIG.9I illustrates an error E, representing the difference between the target and printed wall of (H), plotted along the Y-coordinate.
  • FIGS.11A -11D illustrate image, schematic, and perspective views of potential applicability of using AN3DP within a fluid bath that serves as a support material to create complex vascular networks, though the specific implementation would need additional refinement.
  • FIG.11A illustrates the setup for embedded printing with an adaptive nozzle in a fluid bath, along with the corresponding actuator setup used for the testing.
  • FIG.11B illustrates a printing process in the bath; time order: top, middle, bottom.
  • FIG.11C illustrates a structure resembling vascular network printed into the bath.
  • FIG.11D illustrates an example of further refinement: an elongated and more pointed nozzle tip designed to minimize the disturbance of the bath fluid by the nozzle.
  • FIGS.12A-12G illustrate perspective and sectional views of a nozzle and core design for minimizing Outlet Shape Errors in an Adaptive Core-Shell Nozzle.
  • FIGS.13A-13F illustrate image and diagrammatic views of adaptive core-shell nozzle extrusion of hollow inflatable fibers.
  • FIGS.14A-14G illustrate graphical and image views of characterization of Adaptive Core-Shell Extrusion Process.
  • FIGS.15A-15C illustrate perspective and schematic views of design of nozzle replicas for characterizing the adaptive core-shell nozzle extrusion process in FIGS.3A-3G.
  • FIGS.16A and 16B illustrate image and graphical views of a full set of cross- section images and thickness analysis results of hollow fibers printed with nozzle replicas.
  • FIGS.17A and 17B illustrate schematic views of repeatability of actuator cross- section production.
  • FIGS.18A-18K illustrate graphical and image views of characterization of inflatable fiber deformation.
  • FIGS.19A-19C illustrate image and graphical views of low-cycle fatigue tests of single-joint fibers.
  • FIGS.20A-20F illustrate image and graphical views of a customized hand- assistive device fabricated using ACS-3DP.
  • FIG.21 illustrates an image view of a hand-assistive device design overlay of deformable and non-deformable (’fixed’) sections, with dimensions in mm, for the target design of the hand-assistive device.
  • FIGS.22A-22C illustrate schematic and graphical views of actuation force measurement of inflatable fiber.
  • FIGS.23A-23H illustrate graphical and image views of an ACS-3DP of inflatable fibers for a crawling turtle robot.
  • FIGS.24A and 24B illustrate a turtle robot body design.
  • DETAILED DESCRIPTION [0035] The presently disclosed subject matter now will be described more fully hereinafter with reference to the accompanying Drawings, in which some, but not all embodiments of the inventions are shown. Like numbers refer to like elements throughout. The presently disclosed subject matter may be embodied in many different forms and should not be construed as limited to the embodiments set forth herein; rather, these embodiments are provided so that this disclosure will satisfy applicable legal requirements. Indeed, many modifications and other embodiments of the presently disclosed subject matter set forth herein will come to mind to one skilled in the art to which the presently disclosed subject matter pertains having the benefit of the teachings presented in the foregoing descriptions and the associated Drawings.
  • An “Adaptive Nozzle 3D Printing (AN3DP)” nozzle enables dynamic alteration of nozzle diameter and cross-sectional shape during printing.
  • the AN3DP nozzle includes eight independently controllable, tendon-driven pins arrayed around a flexible, pressure-resistant membrane.
  • the design incorporates a tapered angle optimized for extruding shear-thinning inks and a pointed tip suitable for constrained-space printing, such as conformal and embedded printing.
  • AN3DP's efficacy is demonstrated through the fabrication of components with continuous gradients, eliminating the need for discretization, and achieving enhanced density and contour precision compared to traditional 3D printing methods.
  • This platform significantly expands the scope of extrusion-based 3D printers, thus facilitating diverse applications, including bioprinting cell-laden and hierarchical implants with bone-like microarchitecture.
  • Adaptive Core-Shell Printing can include a nozzle that accommodates a core. The core enable monolithic fabrication of hollow fiber actuators with precise control over wall thickness.
  • the present invention combines the dynamic functionality of an adaptive nozzle, which adjusts its cross-sectional shape during printing, a solid core, and coaxial multi-material or multi-phase extrusion, previously used for creating composite core-shell materials or hollow filaments with uniform shell thickness AN3DP
  • the AN3DP platform is capable of actively controlling both the size and cross- sectional shape of filaments in situ during the printing process.
  • the nozzle features a conical internal design, making it particularly effective for handling shear-thinning fluids, a crucial aspect in fused deposition modeling (FDM) or Fused Filament Fabrication (FFM) and direct ink writing (DIW) techniques. This versatility enables AN3DP to accommodate a wide array of materials.
  • FDM fused deposition modeling
  • FFM Fused Filament Fabrication
  • DIW direct ink writing
  • the acuminate external shape of the nozzle enhances tool accessibility, facilitating the creation of geometrically complex structures that are unachievable with fixed nozzles while considerably speeding up 3D printing of parts with varying feature sizes.
  • Current extrusion-based 3D printers on the market extrude filaments through a fixed nozzle presenting a dilemma: high resolution requires small diameters, while high speed necessitates large diameters. This limitation is apparent in virtually all physical objects spanning different feature sizes, including those with both bulk and intricate elements.
  • Such objects are vital in various applications, such as fabricating artificial organs with multiscale vascular networks, creating bone implants with fine surface dimples, designing heat sinks that combine a solid base for heat absorption with thin fins for efficient dissipation, and constructing graded lattice structures.
  • the present invention promises to revolutionize this domain by enabling dozens of times faster printing of these multiscale structures—with significantly enhanced precision— compared to traditional 3D printers. This breakthrough greatly expands the capabilities of extrusion-based 3D printers, paving the way for diverse applications, including bioprinting cell-laden and hierarchical implants with bone-like microarchitecture.
  • fixed nozzles typically feature a circular cross-section to facilitate printhead movement in all directions within a layer.
  • the nozzle of the present invention not only adjusts its size but also its outlet shape to suit various 3D printing conditions as dictated by the extruded part, adopting square, triangular, or rectangular shapes. This adaptability effectively mitigates the ubiquitous “stair stepping” effect in 3D printing, responsible for the “Minecraft-like” appearance of extruded parts due to layering and extrusion filament width.
  • FIGS.1A-1I illustrate image and diagrammatic views of an adaptive nozzle 3D printing (AN3DP) platform according to an embodiment of the present invention.
  • FIG.1A illustrates an overview and components of the AN3DP.
  • FIG.1B illustrates a schematic of the AN3DP print head.
  • FIG.1C illustrates a schematic of the adaptive nozzle actuation mechanism (left) and photos of the adaptive nozzle.
  • FIG.1D illustrates a schematic of an adaptive nozzle used for printing a size/shape-changing filament, accompanied by a photo of the implementation (top-left). The schematic shows the size change of a circle (1-2), the shape changes from a circle to a rectangle (2-3), and the size change of a rectangle (3-4).
  • FIG. 1E illustrates photos of a bottom view of the adaptive nozzle (top) and corresponding target size (bottom) for small (left), medium (middle), and large exit mode (right).
  • FIG.1F illustrates photos showing the bottom view of the adaptive nozzle (top) and the corresponding target sizes (bottom) for the small (left), medium (middle), and large exit modes (right).
  • FIG. 1G illustrates photos of the adaptive nozzle exit changing into various shapes, including a circle, rectangle, square, rhombus, and star.
  • FIGS.1H and 1I illustrate photos of filaments having different sizes, as in FIG.1H, and shapes, as in FIG.1I.
  • the AN3DP printhead adaptive is mounted, for example, on a Cartesian gantry system that controls its spatial positioning above the substrate, as illustrated in FIG.1A.
  • FIGS.1A and 1B illustrates a system 10 that includes an adaptive nozzle 12, according to the present invention.
  • the system 10 includes stepper motors 14. While four stepper motors 14 are shown any number of stepper motors known to or conceivable by one of skill in the art for the functionality of the invention could be used.
  • the stepper motors 14 are coupled to the adaptive nozzle 12 via drive pulley 16, idler pulley 18, and cable 20.
  • Pins 22 of the adaptive nozzle 12 are arranged around a silicone rubber cover 24 that can expand and contract along with the movement of the pins 22. Movement of pins 22 is affected by the stepper motor, pulley, cable system.
  • the AN3DP could also be mounted on a different 3D printing system, such as a robotic arm with 6 degrees of freedom, a wire-driven printer, or a drone.
  • the adaptive nozzle is equipped with four stepper motors, each regulated by microchips linked to a computer. These motors actuate cables running through idler and drive pulleys, as illustrated in FIGS. 1A and 1B to move the nozzle pin tips outward, as illustrated in FIG.1C. Encasing the inner volume of the nozzle is a stretchable silicone rubber membrane, which moves in tandem with the pins to maintain a continuous surface.
  • the nozzle employs eight laser-cut metal pins, grouped into pairs, each pair controlled by a single motor. These pins form the vertices of the nozzle's exit polygon, allowing for varied exit shapes while retaining a conical internal configuration regardless of the size or shape adjustments.
  • AN3DP facilitates the deposition of filaments with continuously varying sizes and shapes in a single setup, as illustrated in FIG.1D. It enables extruded filament diameter alterations up to 3.33 times, for instance, varying from 3 mm to 10 mm, as illustrated in FIGS.1E and 1F.
  • the nozzle can produce a range of shapes, including circular, square, rectangular, and star-shaped, as illustrated in FIG.1G. Additionally, it can deposit these shapes with feature sizes between 4 mm and 10 mm onto substrates, as illustrated in FIGS. 1H and 1I.
  • FIGS.2A-2I illustrate image and diagrammatic views of a design and implementation of an AN3DP platform according to an embodiment of the present invention.
  • FIG.2A illustrates an exploded view of the AN3D printhead consisting of a printhead assembly (I), an adaptive nozzle (II), and pin modules (III).
  • FIGS.2B-2D illustrate a pin module actuation mechanism for controlling nozzle exit size/shape: starting from the initial state, as illustrated in FIG.2B, tip-widening with a distance-increasing actuation, as illustrated in FIG.2C, via motor actuation, and then returning to the initial state, as illustrated in FIG.2D, due to the restoring moment from the spring and silicone cover after the motor actuation is released.
  • FIGS.2E and 2F illustrate a flexible silicone cover.
  • FIG.2F illustrates a cover fabricated from 3D-printed molds, shown in FIG.2E.
  • FIGS.2G and 2H illustrate metal pins and silicone cover integrated structure.
  • FIG.2H illustrates a tip-fastening mechanism, illustrated in FIG.2G.
  • FIG.2I illustrates that the metal pins and silicone cover integrated structure can be easily interchanged from the nozzle base via screws, allowing for simple replacement and cleaning after every print.
  • FIG.2A illustrates a printhead assembly 26, an adaptive nozzle 12, and a pin module 22 according to an embodiment of the present invention.
  • the printhead assembly 26 includes the stepper motor array 14, a base plate 28, and a height adjustment plate 30.
  • the printhead assembly also includes drive pulleys 16, idler pulleys 18, and cable 20.
  • the adaptive nozzle 12 includes a nozzle base 32 that couples to the printhead assembly 26.
  • Inlet 34 allows for the flow of ink through the silicone rubber cover 24 that expands and contracts when the pins 22 are expanded and contracted.
  • Springs 36 allow for the movement of the pins 22.
  • Pins 22 include a pin base 38 and a pin-tip bundle 40.
  • the AN3DP system features a nozzle with adjustable exit size and shape, a rapid and robust mechanism for transitioning between these configurations, and a compact nozzle design for improved tool accessibility. Key components include (i) a printhead assembly, (ii) an adaptive nozzle, and (iii) pin modules, as illustrated in FIG.2A.
  • the adaptive nozzle (ii) is mounted on the base plate, and the pin modules (iii) are actuated by inextensible cables, which are connected to stepper motors through drive and idler pulleys. These motors are positioned on the base plate, separate from the nozzle (ii), using a cable-driven actuation system. This system is akin to those used in robotics to achieve compact, dynamic end- effectors.
  • Each of the eight pin modules in the AN3DP system is connected to the nozzle base via an articulated revolute joint, ensuring high precision and consistent actuation over numerous cycles.
  • the pin tip moves a distance along the X-axis, driven by rotation about its axis due to cable tension from motor actuation, as illustrated in FIG.2C.
  • the motor actuation angle is approximately linearly related to the motor actuation angle, , where (approximately 0.796 mm/rad) is a constant ratio, and is the motor actuation angle.
  • This linear relationship arises because the cable length pulled is the product of the actuation angle and the drive pulley radius , and the pulled cable length is proportionate to This simple kinematic relationship facilitates precise control of the pins.
  • AN3DP The design of AN3DP involves intricate interdependencies and trade-offs among various parameters, such as the bending stiffness of a pin module, the stiffness of the restoration spring, the Young's modulus of the silicone rubber membrane, and the geometrical aspects like the moment arms of the pin tip and cable connection point. These parameters were optimized heuristically. For example, a longer moment arm at the pin tip enhances the diameter change range and tool accessibility but may compromise the pin tip's movement precision due to reduced bending stiffness in the pin module.
  • High restoration spring stiffness is required to counteract deformation under ink pressure, but this increased stiffness can stress the pin module, affecting the precision at the pin tip. Consequently, SUS 304 (Young’s modulus of 193 GPa) was used for the pins to maintain high stiffness, crucial for precision.
  • the pin tip width (0.7 mm) is deliberately chosen to be wide enough to avoid tearing the membrane while being narrow enough for precise representation of the target filament shape.
  • a flexible and highly stretchable material was chosen with a Young’s modulus of 0.15 MPa and an elongation at break of 1000%. This allows for significant size/shape change while retaining enough stiffness to prevent bulging in the nozzle wall and distortion at the tip under ink pressure.
  • the silicone rubber membrane is fabricated by injecting liquid silicone rubber into molds, as illustrated in FIG.2E.
  • a digital light processing (DLP) 3D printer was used with high-resolution resin for mold fabrication. This method ensures high precision, repeatability, and a smooth membrane surface, as imperfections, particularly near the nozzle tip, could lead to structural failures and ink leakage.
  • the mold design includes a single-piece ‘cavity a’ for the nozzle tip and two separate parts, 'cavities b and c', for easier removal of the finished cover from the mold, as illustrated in FIG.2E.
  • 'cavities b and c' were covered with 'cavity d’ to prevent gaps formation due to injection pressure.
  • Another important design consideration is the integration of stainless-steel pins with the silicone rubber membrane, as illustrated in FIGS.2G and 2H.
  • FIG.2G A fully assembled unit with eight pins is shown in FIG.2H.
  • FIG.2I Another key design consideration is the ease of interchangeability of the nozzle, particularly if it is treated as a consumable to be replaced after each print. This is achieved by enabling the nozzle to be easily screwed and unscrewed from the base, as illustrated in FIG. 2I. In examples, the cover is replaced, and the pins are cleaned after each print.
  • FIGS.3A-3D illustrate diagrammatic and graphical views of control for an AN3DP platform according to an embodiment of the present invention.
  • FIG.3A illustrates available nozzle size/shape depending on the number of actuators (1 (i), 2 (ii) and (iii), 4 (iv), and 8 (v))
  • FIGS.3B illustrate actuators, print height, and feed rate operation strategy for an exemplary filament having constant circle cross section ( ), diameter-increasing circle cross section ( , diameter-decreasing circle cross section ( , shape-changing from circle to square section ( ), and constant square cross section ( ).
  • FIGS.3B illustrate actuators, print height, and feed rate operation strategy for an exemplary filament having constant circle cross section ( ), diameter-increasing circle cross section ( , diameter-decreasing circle cross section ( , shape-changing from circle to square section ( ), and constant square cross section ( ).
  • 3C and 3D illustrate cross sectional area, as illustrated in FIG.3C, of a nozzle exit (A) and nozzle volume (V), as illustrated in FIG.3D depending on nozzle dimension (d) for square ( ⁇ ), circle ( ⁇ ), rectangular ( ), rhombus ( ⁇ ), and star ( ).
  • AN3DP intricate control over pin movements, the gantry system's print path and feed rate, and the ink extruder's flow rate to achieve variable size and shape in filament printing.
  • FIG.6 illustrates schematic views of available sizes and shapes of the nozzle exit vary depending on the number of actuators. Pins indicated by dots of the same color are controlled by the same actuator. As the number of actuators increases, a greater variety of nozzle shapes becomes available, which is depicted with a denser background. [0058] For size-only changes, all pin tips (1–8) can be controlled by a single actuator (i), with cables connected to the pins looped over an idler pulley and linked to a drive pulley. Increasing the number of actuators enables more complex shapes. For instance, with four pins (1, 3, 5, 7) connected to one actuator and the remaining four (2, 4, 6, 8) to another, shapes like circles, squares, and stars are possible (ii).
  • Two actuators can also create asymmetric shapes, e.g., pins 3-6 linked to one actuator and pins 7, 8, 1, 2 to another (iii).
  • the most diverse shape variations are achievable with eight actuators, each controlling a corresponding pin (v), as shown in FIG.6.
  • Each shape offers distinct advantages: circles are versatile like conventional fixed nozzles, allowing printing in any direction; squares minimize inter-filament voids in solid structures; concave shapes like stars enhance bonding in applications such as bone grafts. Importantly, switching between operational modes is straightforward, requiring only changes in cable routing.
  • the filament comprises sections with a constant circular cross-section ( ), an enlarging circular cross-section ( ), a diminishing circular cross-section ( ), a shape-transitioning section (circular to square; ), and a constant square cross-section ( ), as illustrated in FIG. 3B.
  • Motors induce angular displacements of , dictating the nozzle exit size/shape.
  • the gantry system regulates the print height h and feed rate v.
  • a volumetric extruder is employed to feed ink through the nozzle, offering precise flow rate control, superior to pressure-driven extruders, even with the nozzle’s geometric alterations.
  • the flowrate F is modulated by adjusting v, according to the equation , (1) where A is the cross-sectional area of the nozzle exit, as illustrated in FIG.3C.
  • A is the cross-sectional area of the nozzle exit, as illustrated in FIG.3C.
  • angular displacements remain fixed, and the print height h is set to times the filament height (i.e., for and ), with in this study.
  • Precise control of F also mitigates common additive manufacturing issues, such as die-swelling in viscoelastic ink extrusion, where the filament's immediate post-extrusion cross-sectional area, , is larger than the nozzle's exit area, A.
  • FIGS.7A and 7B illustrates graphical views of nozzle volumes depending on dimensions.
  • FIG.7A illustrates a rhombus-shape exit with dimensions of and .
  • FIG.7B illustrates a star-shape exit with dimensions of and , which are calculated from Eq.14.
  • the feed rate is reduced relative to the filament’s standalone rate. This adjustment compensates for the increased nozzle volume, as illustrated in FIG.3D and FIGS. 7A and 7B, and helps prevent necking. Conversely, in the diameter-decreasing region ( - ) and during shape transitions that reduce nozzle volume, the feed rate is increased.
  • FIGS.4A-4E illustrate diagrammatic and graphical views of an AN3DP platform according to an embodiment of the present invention.
  • Typical objects consist of solid inner features, as illustrated in FIG.4B and surfaces, as illustrated in FIG.4C.
  • FIG.4B illustrates cross-sectional photos of solid inner features additively manufactured from circular filaments via a fixed nozzle (i) and square filaments via the adaptive nozzle (ii) (top) with a comparison of their volume solid fractions (bottom).
  • FIG.4C illustrates cross-sectional photos of surfaces additively manufactured from circular (iii) and square (iv) filaments via fixed nozzles, and a mix of square and triangle filaments from the adaptive nozzle (v), with a comparison of surface roughness and ; scale bars in (B) and (C), 5 mm.
  • FIG.4D illustrates multi-scale structures consisting of bulky solid parts and thin functional features (top) can be manufactured more quickly with AN3DP than with a fixed nozzle by filling up the solid parts with its maximum diameter ( ⁇ l) and thin features with its minimum diameter mode (l) (bottom).
  • the purple sections are the parts that are printed in maximum diameter mode ( ⁇ l) and the green ones in minimum diameter mode (l) when using AN3DP.
  • ⁇ l maximum diameter mode
  • l minimum diameter mode
  • the heat sinks HS1-HS3 are represented not as specific points but as individual lines.
  • FIGS.5A-5E illustrate image, diagrammatic, and graphical views of AN3DP platform printing of structures resembling vascular networks according to an embodiment of the present invention.
  • FIG.5A illustrates a design of a structure resembling a vascular network having both continuously decreasing gradients, diameter of 8 mm (i), 6 mm to 4 mm (ii), and continuously-increasing gradients, 4 mm, 6 mm to 8 mm (top), AN3DP printing process with corresponding zoomed-in adaptive nozzles (middle), and printed structures (bottom) (scale bar: 10 mm)
  • FIG.5B illustrates a design of a vascular network-like structure having branches with five-fold difference in diameter, 2 mm (iii) to 10 mm (iv), and bifurcation points (top), AN3DP printing process with corresponding zoomed-in adaptive nozzles (middle), and printed structures (bottom); scale bars in (A) and (B), 10 mm.
  • FIG.5C illustrates a comparison of achievable cross-sectional areas of filaments extruded from AN3DP to those using fixed nozzles with diameters of 3 mm, 4 mm, 5 mm, 8 mm, and 10 mm, where thick lines represent equidimensional modes and thin lines represent under/over-extrusion modes, respectively.
  • FIG.5D is an illustration of a theoretical vascular network with 4 levels of hierarchy (left), showing the relationship of diameters ( , ) and lengths ( , ) at every branching point (right).
  • FIG. 5E is a theoretical print time comparison ( ) for vascular networks having total m-levels. All photos in FIGS.5A and 5B were modified to reduce color saturation to 33 % in PowerPoint (Microsoft).
  • FIG.4A most objects feature solid inner structures, shown in FIG. 4B and functional surfaces, as shown in FIG.4C.
  • a common issue in additive manufacturing is structural imperfections, often stemming from inter-filament voids. These voids arise in traditional 3D printing processes like FDM because fixed circular cross-section filaments cannot entirely fill the print space, resulting in a volume solid fraction of about 85%, as illustrated in FIG.5B. Even when reducing filament size, this volume fraction typically does not improve. FDM printers attempt to mitigate the problem by using layers much thinner than the nozzle diameter, which, while addressing the void issue, limits throughput speed and can distort the filament shape.
  • AN3DP can substantially increase the relative density of the printed object to 95%, or higher in further-optimized systems, as illustrated in FIG.5B. This capability not only enhances the structural integrity of the printed parts but also optimizes printing efficiency by reducing the need for overly thin layers and allowing for more accurate filament deposition. [0070] AN3DP can also rapidly produce objects with smooth surfaces. Smoothness is crucial both aesthetically and functionally, as it can improve properties like wear resistance and reduce geometric stress concentrations. This was demonstrated by printing a 45° angled wall, as illustrated in FIG.4C, using a combination of square and triangular filaments (v).
  • Modulating the nozzle size in AN3DP also significantly enhances the print speed for structures containing multi-scale features of various shapes, as illustrated in FIGS.4D and 4E. Assuming an extruder capable of any flow rate, the primary constraint on printing speed becomes the gantry system’s feed rate. Therefore, the print time can be approximated as proportional to the print path length. [0072] In conventional 3D printing with a fixed nozzle, the entire structure must be printed using a nozzle diameter l that matches the thinnest features size, as illustrated in FIG.4E. AN3DP, on the other hand, dynamically adjusts the nozzle size from l to (where ) for larger volume sections, with representing the diameter expansion ratio.
  • AN3DP is superior to fixed nozzles in printing parts with features varying from the smallest size or from available fixed nozzle diameters. This advantage extends to parts with constant features that don’t align with fixed nozzle diameters, like discrete honeycombs and lattices.
  • a prime example is vascular networks, featuring channels spanning several multiples in diameter.
  • FIGS.5A-5E To showcase AN3DP's capabilities in addressing such intricate designs, structures resembling two different vascular networks were fabricated, as illustrated in FIGS.5A-5E. These structures exhibit continuous transitions from the smallest to the largest channel diameters. The first structure exhibits a diameter transition from 8 mm at its thickest (i) to 4 mm at its thinnest (ii), and then back to 8 mm, as illustrated in FIG.5A. The second structure presents a more pronounced diameter variation, changing fivefold from 2 mm (i) to 10 mm (iv), which translates to a 25-fold difference in cross-sectional area, as illustrated in FIG.5B.
  • vascular networks could be printed within a cellular bath using AN3DP to create hollow channels after removing the extruded sacrificial material; though, this specific application would require further refinement, as illustrated in FIGS. 11A-11D.
  • the print times for fractal structures were compared, including vascular networks and analogous systems like plant pipes, to those produced with conventional fixed nozzle 3D printing, as illustrated in FIG.5D.
  • the fractal structures are modeled to bifurcate into two identical branches at each branching point, following specific ratios: a constant radius decreasing ratio ( ) of , aligning with Murray’s law for minimizing flow resistance, and a length decreasing ratio ( ) of 0.5 (32).
  • the structure comprises a total of m levels, where and denote the diameter and length of the k th level branch, respectively.
  • the nozzle diameter is determined by the thinnest branch at the m th level, .
  • AN3DP with its ability to handle a range of diameters from the thinnest feature ( ) to the thickest ( ), can print each kth level branch with its corresponding diameter ( ).
  • the 3D printing platform of the present invention introduces an adaptive nozzle for extruding filaments of varying sizes and shapes.
  • the nozzle membrane, blending stretchable silicone rubber with stiff metal pins, allows precise control of the exit's cross-section in a compact design, enhancing tool accessibility.
  • the technology intrinsically optimizes flow, eliminates voids, and improves surface finish, thus elevating print quality.
  • this approach offers a novel size/shape-controlling nozzle with significant potential for advancements. Future developments may include enhancing the degrees of freedom of pin motion for more diverse shapes, minimizing nozzle size with advanced manufacturing, and expanding size variability with more elastic materials.
  • the technology could integrate with other printing methods like core-shell or embedded printing, as illustrated in FIGS.11A-11D.
  • this innovation holds promise for revolutionizing multi-material, multi- scale 3D printing, impacting various fields such as soft robotics, bioprinting, and construction, by enabling greater design complexity and faster production.
  • the ink materials were prepared as a pure viscoelastic ink (DOWSIL SE 1700; Dow Corp.) by centrifugal mixing (2,000 rpm, 2 min; Flak-Tek) of the ink and 10% w/w curing agent. Filaments of various sizes and shapes, illustrated in FIGS.1H and 1I, were printed without a curing agent, while solid structures for demonstration and vascular network-like structures used the agent. Their colors were modified by adding 0.24% w/w pigment (Silc- Pig; Smooth-On). [0083] All parts of adaptive nozzle printhead were designed by SolidWorks.
  • the adaptive nozzle was mounted on the base plate, which had been fabricated using a fused deposition modeling 3D printer (i3 MK3S+; Prusa) from PLA material (1.75 mm PLA trusilver; Hatchbox).
  • the nozzle base and eight pin bases were fabricated using a DLP 3D printer (Sonic Mini 8K; Phrozen) from high-resolution resin (Aqua Gray 8K; Phrozen). After printing, they were washed with isopropyl alcohol and underwent post-curing in a curing machine (Form Cure; Formlabs) to achieve maximum stiffness, crucial for high-precision nozzle exit control.
  • the eight pin bases were then assembled onto the nozzle base, each with a shortly cut steel wire (Diameter 0.047’’ Lubricated 1065 Spring Steel Wire; McMaster), acting as a revolute joint, and a compression spring (OD 6 mm Length 20 mm; CREEYA Compression springs assortment kit).
  • the silicone rubber membrane, integrated with eight pin-tip bundles, was attached to the assembly using nuts (part number: 90001A302; McMaster-Carr) and cup point set screws (part number: 91390a601; McMaster-Carr).
  • Each pin-tip bundle consists of two laser-cut metal pins, nuts (part number: 90001A302; McMaster-Carr), screws (part number: 91794a744; McMaster-Carr), and washers (or spacers) (part number: 92141A204; McMaster-Carr).
  • Each metal pin was manufactured using a laser cutter (TruLaser Fiber 5030-5kw; Trumpf) from stainless steel (0.8 T, SUS304), followed by refining using a grinder (Dremel 4300 with P60 sandpaper; DREMEL) to keep nozzle tip compact.
  • the ink inlet module which was fabricated using a DLP 3D printer (Sonic Mini 8K; Phrozen), inserted into the whole assembly.
  • Kevlar cable (Diameter 0.014’’; McMaster) connected a pin base to a stepper motor. This connection was made through a hole in the nozzle base, an idler pulley (Round- Belt Idler Pulley for 1/8’’ diameter round belt; 1’’ OD, McMaster), and a drive pulley, which was fabricated using a DLP 3D printer (Sonic Mini 8K; Phrozen). The idler pulleys were mounted to the base plate with a height adjustment component, which was also fabricated using the same 3D printer.
  • stepper motors (Nema 171.5A 400mN.m 2 Phase 4 Wires 1.8degree; Iverntech) were mounted on the base plate with motor mounts, which were fabricated with the same 3D printer. Each drive pulley was connected to each motor with a screw. The four stepper motors were controlled by four drivers (printhead controller board, HYREL), which were connected to the gantry system (Engine SR, HYREL). [0085] The nozzle head is before every print by observing the bottom view of the nozzle with a microscopic camera (AF4115ZTW 1.3MP Wide-Angle FLC Wireless Ready Polarizer; SunriseDino).
  • the molds for the injection molding of silicone rubber membranes were designed using SolidWorks and fabricated with a DLP 3D printer (Sonic Mini 8K; Phrozen). For high- resolution, aqua-gray 8K resin was used. Once printed, the molds were rinsed with isopropyl alcohol using an air blow gun. After cleaning, to prevent the inhibition of silicone rubber curing, which can occur due to the presence of uncured resin on the mold surfaces, the molds were completely cured for over 6 hours in a curing machine (Form Cure; Formlabs). To further prohibit inhibition, the molds were soaked in an inhibitor (Inhibit X; Smooth-On).
  • a release material was applied (Ease Release 200; Smooth-On) and assembled the molds.
  • the liquid silicone rubber mixture was prepared by centrifugally mixing two parts of dragon skin 10 slow (Smooth-On; 1800 rpm, 2 min; Flak-Tek) in a negative pressure container. Colors were modified by adding 0.99% w/w pigment (Silc-Pig; Smooth-On). After injecting the liquid silicone rubber into the molds, they were cured in an oven (heratherm; Thermo Scientific) at 80°C for 30 minutes. The defects were trimmed, such as sprue and flash, from the fabricated covers after fabrication.
  • FIGS.8A-8C illustrate schematic and graphical views of a volume calculation for arbitrary adaptive nozzle with n pins.
  • FIG.8A illustrates that the nozzle is shaped as a ‘twisted prism’ with a total height of . It has a cross-section at the base ( ) in the form of a regular n-gon, where the perpendicular distance from the center ( to each side is (i), as illustrated in FIG. 8B. At the exit ( ), the shape is an n-gon formed by controlled pin distances of (ii).
  • FIG.8C illustrates a 2n-gon, each vertex at a distance of and from the origin , and each line connecting a vertex to the origin forms an interval angle of with one another.
  • the nozzle has a total height of , as illustrated in FIG. 8A, the normal distance of every edge from the center on the base plane (i) is , and the distance of ith pin tip from center on exit plane (iii) is ( ), as illustrated in FIG.8B. Eight pins are used in the current implementation but will derive the volume for general number of pins, n, here.
  • values and are constant values given from the nozzle design are variables controlled by actuators, and are distances of middle point of each edge of exit polygon from .
  • the nozzle shapes as a ‘twisted prism’ consists of a cross-section of ‘2n-gon’ at height h each vertex of which has distance of and and every line connecting the vertex and the origin has interval angle of each other, as illustrated in FIG.5C.
  • FIGS.9A-9I illustrate the profile of the dimension of the extruded filament along the filament extrusion length (x) under the nozzle exit dimension varies over time. Extruded filament was assumed to have the same shape and size as the cross-section of the nozzle exit at the time of extrusion . If the compression of ink is ignored, the following volume conservation equation is satisfied: , (15) [0091] where is the flow rate of ink injected by the volumetric extruder, V the volume of the nozzle (FIG.3D, FIGS.7A and 7B and Eq.14), A the cross-sectional area of the nozzle (FIGS.3C, 10A, 10B and Eq.13).
  • FIG.9A-9I illustrate image and graphical views of numerical calculation of surface roughness for additively manufactured surface structures shown in FIG.4C.
  • FIG.9A illustrates a cross-sectional photo of the structure fabricated with a circle-shaped fixed nozzle.
  • FIG.9B illustrates an extracted wall lines of the printed (in light grey) and target (in dark grey) from, FIG.9A.
  • FIG.9C illustrates an error E, representing the difference between the target and printed wall of (B), plotted along the Y-coordinate.
  • FIG.9D illustrates a cross- sectional photo of the structure fabricated with a square-shaped fixed nozzle.
  • FIG.9E illustrates an extracted wall lines of the printed (in light grey) and target (in dark grey) from, FIG.9D.
  • FIG.9F illustrates an error E, representing the difference between the target and printed wall of (E), plotted along the Y-coordinate.
  • FIG.9G illustrates a cross-sectional photo of the structure fabricated with square and triangle modes of the adaptive nozzle.
  • FIG.9H illustrates an extracted wall lines of the printed (in light grey) and target (in dark grey) from FIG.9G.
  • FIG.9I illustrates an error E, representing the difference between the target and printed wall of (H), plotted along the Y-coordinate.
  • FIGS.10A and 10B illustrate graphical views of size/shape-varying filament extrusion by AN3DP.
  • FIG.10A illustrates an analytical model for the cross-sectional dimension of the filament, d'', along the extruded length, x, incorporating the nozzle exit dimension over time, d(t), ink input volumetric flow rate, F, nozzle volume as a function of exit dimension, V(d).
  • FIG.10B illustrates an example photo of a filament with varying dimensions.
  • FIGS.11A -11D illustrate image, schematic, and perspective views of potential applicability of using AN3DP within a fluid bath that serves as a support material to create complex vascular networks, though the specific implementation would need additional refinement.
  • FIG.11A illustrates the setup for embedded printing with an adaptive nozzle in a fluid bath, along with the corresponding actuator setup used for the testing.
  • FIG.11B illustrates a printing process in the bath; time order: top, middle, bottom.
  • FIG.11C illustrates a structure resembling vascular network printed into the bath.
  • FIG.11D illustrates an example of further refinement: an elongated and more pointed nozzle tip designed to minimize the disturbance of the bath fluid by the nozzle.
  • the various sizes and shapes of filaments illustrated in FIGS.1I and 1H, were printed at a feed rate of 1 mm s -1 with corresponding flow rate from Eq.1.
  • the print height h was set to twice the filament's height for each specific size and shape to preserve their cross-sectional shapes as much as possible.
  • the solid structures for demonstration were printed at a feed rate of 1 mm s -1 .
  • the initial layers were printed at a height of 5 mm, with each subsequent layer increasing in height by 5 mm.
  • a flow rate of 1.5 ml min -1 was used, while 0.95 ml min -1 for the triangle mode.
  • the flow rate for the triangle mode was set slightly higher than the ideal rate of 0.75 ml min -1 after several tests. This adjustment was necessary because the three pins, which were supposed to be placed at the center of the nozzle exit to create a perfect straight slope of the triangle, could not reach it due to the minimum distance ( >0) from the center. Also, the three pins were manually further pushed towards the nozzle center to achieve as straight the slope as possible.
  • the vascular network-like structures were printed at a constant flow rate of 1 ml min -1 .
  • the feed rate for each constant diameter printing section was set per Eq.1. However, for the diameter-transition sections, the rates were determined experimentally (Tables 1 and 2) but still set as constant for each section.
  • the print height was set to 1.1 times the height (or diameter) of the filament for constant-diameter printing sections and was set to linearly vary for diameter-transition sections over time.
  • the motor's rotation was adjusted to reach a diameter of 2 mm, while the realized diameter was the minimum diameter of the adaptive nozzle, 3 mm.
  • the nozzle height was further lowered by 1 mm. This height adjustment made the under-extrusion process relatively successful, which is highly sensitive to the print height.
  • the relative print time is calculated from the Eqs.22 and 23 as , (24) [00102] Meanwhile, for the multi-level vascular network in FIGS.5D and 5E, the print time t is approximated as a part with volume with a nozzle diameter of L as . (25) [00103]
  • the printed filament as it is printed given by , since tree-like structures have a circular cross-sectional shape, which is the same as the circular filament. It allows the print time to be calculated more precisely on this specific example than the rough result in Eq.21.
  • the total volume of m-level of vascular network is given as , (26) Where , (27) , (28) .
  • the soft actuator Central to these systems is the soft actuator, which enables complex object manipulation with simple control schemes.
  • inflatable actuators are often favored due to their capacity to generate large forces, achieve rapid actuation, and provide high compliance, all while comprising relatively simple, often single-material structures.
  • These actuators operate by expanding internal voids or air channels with pressurized fluid or reducing volumes via vacuum.
  • Various mechanisms have been developed to control the deformation of inflatable actuators, such as via designing complex air channel structures, by integrating them with 3D knitted or kirigami structures, or combining them with rigid components.
  • extremely soft materials pose challenges to conventional subtractive manufacturing methods and many of these approaches still require manual assembly or multi-step molding, hindering complexity in shape and materials combinations, and scalability.
  • a core can be added to the adaptive nozzle to facilitate an Adaptive Core-Shell 3D Printing (ACS-3DP) method, which builds upon AN3DP.
  • ACS- 3DP adds a core to the actively controllable nozzle of AN3DP.
  • the added core allows for the 3D printing of hollow core tubing and actuators.
  • the present invention can be used for a direct ink writing process, known for its extensive material compatibility, including target materials for soft actuators, such as silicone rubbers.
  • ACS-3DP enables the monolithic fabrication of hollow fiber actuators with precise control over wall thickness.
  • the printhead of the present invention is lightweight, cost-effective, and compatible even with low-budget desktop 3D printers. It can be easily mounted on a gantry stage and connected to motor controllers via the operating software, making the system accessible to both hobbyists and professionals. Additionally, the ACS-3DP printhead enables rapid real-time adjustments, eliminating the need for manual setup changes.
  • a key feature is its ability to simultaneously modify both the outlet shape and internal taper angle, optimizing extrusion for non-Newtonian shear-thinning inks like silicones.
  • To achieve precise shell thickness control undesired printhead deformation is minimized through mechanical reinforcements, while a tapered solid core with a wide, robust attachment at the ink inlet, gradually narrowing toward the tip, enhances core stability, as illustrated in FIGS.12A-12G.
  • ACS-3DP precisely tunes wall thickness along the azimuthal angle within the cross-section, enabling accurate control of actuator deformation angles, actuation forces, and bending modes under pneumatic pressure, including targeted directional bending or largely undeformed states.
  • FIGS.12A-12G illustrate perspective and sectional views of a nozzle and core design for minimizing Outlet Shape Errors in an Adaptive Core-Shell Nozzle.
  • FIG.12A illustrates a perspective view of a solid core 42 attached to the ink inlet and the nozzle base 32.
  • the solid core 42 is inserted into the nozzle base 32 after the adaptive nozzle 12 is integrated with the nozzle base 32.
  • the pins 22 are actuated with cables, as shown in FIG. 12B the initial state to FIG.12C.
  • FIG.12D illustrates a sectional view of an actuated state.
  • the nozzle outlet shape may be distorted due to structural deformation caused by insufficient stiffness of the nozzle base. This distortion results in the nozzle outlet shape deviating from the ideal shape.
  • a structural stiffener with wide anchoring points, as illustrated in FIGS.12F and 12G are added to the base plate, ensuring maximized moment arms, is introduced.
  • the ACS-3DP printhead is based on an adaptive 3D printing nozzle and introduces an adaptive shell structure surrounding a circular solid core with a radius of r h , which creates hollow fiber cores, as illustrated in FIGS.13A and 13B.
  • Fibers are typically printed on a substrate, resembling conventional material extrusion 3D printing, which works particularly well for long fibers with fiber length L fiber diameter 2R f , as illustrated in FIG.13C.
  • short fibers such as L > 2Rf
  • short fibers can also be extruded in air, which is advantageous for fibers with extremely thin wall thicknesses, as illustrated in FIG.13D.
  • the precisely controlled variable thickness between the core and shell as illustrated in FIG.13E, enables the generation of hollow fibers with azimuthally varying wall thickness, which can be adjusted in real-time along the fiber’s length.
  • the printhead is mounted on a Cartesian gantry system that manages both printhead motion and the actuation of the printhead using microchips.
  • the extrusion process utilizes a volumetric extruder for precise flow rate control.
  • FIGS.13A-13F illustrate image and diagrammatic views of adaptive core- shell nozzle extrusion of hollow inflatable fibers.
  • FIG.13A illustrates a photograph of the adaptive core-shell nozzle printhead.
  • FIG.13B illustrates photos of the bottom view of the adaptive nozzle (left) and schematics of the corresponding target outlet modes (right) for extruding the ’fixed’ section (i) and deforming sections with four different directions (ii-v), where the arrows indicate the directions of the thinnest shell.
  • FIGS.13C and 13D illustrate perspective views of inflatable fibers that are printed on a substrate or extruded in the air.
  • FIG.13E illustrates a cross-sectional view of FIG.13C in the X-Z plane, showing how the solid core and adaptive shell create the thickness-varying inflatable fiber.
  • the outlet of the adaptive shell is octagonal, consisting of eight metal pin tips connected by a flexible silicone membrane forming the edges, as illustrated in FIG.13B. The membrane is designed to deform under actuated pin motion while resisting ink pressure.
  • the distance (r) from the center to each octagonal vertex is controlled by actuators linked to the pins via cables. Actuator rotation pulls the cables, moving the pins outward, while compression springs restore them to their original positions.
  • actuators are used, each controlling two neighboring pins, with control initially limited to two radii, r 1 and r 2 , or a constant r f , as illustrated in FIG.13B. This simplification reduces control parameters for analysis while maintaining the ability to produce a practical variety of fibers.
  • ACS-3DP can fabricate hollow fibers consisting of ’fixed’ sections (i) and deformable sections oriented in four directions (ii-v).
  • the ’fixed’ sections have a hollow radius of R h and an outer radius of R f , while the deformable sections have an outer radius varying between R 1 and R 2 , as illustrated in FIG.13E.
  • the region between the two pins closest to the fixed core achieves the smallest radius R 1 , while the opposite direction reaches the largest radius R 2 , as indicated by the arrow as illustrated in FIG.13E.
  • the air channel in the core structure prevents negative air pressure and suction within the hollow filament as it is extruded, mitigating the risk of cross-sectional deformations or hole formation in thin wall sections.
  • ⁇ y 500Pa
  • Each fiber is printed at room temperature within seconds to minutes, while the pot life of PDMS lasts over three hours before significant thickening occurs, ensuring that curing time does not interfere with the printing process.
  • the volumetric extruder automatically compensates for minor viscosity changes by adjusting pressure accordingly. After curing in an oven at 80°C, PDMS achieves a high elongation-at-break of approximately 500%, making it well-suited for inflatable fibers.
  • the hollow fibers Under pneumatic actuation (p > 0), the hollow fibers exhibit bending deflection towards the direction of R 2 in the deforming section (R 1 ⁇ R 2 ) (ii), while remaining straight in the ‘fixed’ sections with an outer radius of R f (i) as illustrated in FIG.13F.
  • materials with higher stretchability such as Ecoflex and Dragonskin, could also be used if greater deformation capability is needed.
  • a rheology modifier such as fumed silica, would be needed to ensure printability.
  • the non-axisymmetric outlet shape of the ACS-3DP nozzle results in non- uniform fluid flow velocity at the outlet, with the flow being faster in the wider gap, as illustrated in FIG.14A.
  • FIGS.14A-14G illustrate graphical and image views of characterization of Adaptive Core-Shell Extrusion Process.
  • FIG.14A illustrates a geometrical model of the adaptive core-shell nozzle for finite element simulation with a cross-sectional view (i).
  • FIG. 14A illustrates fluid flow speed ratio (V 2 / V 1 ) as a function of the degree of nozzle asymmetry (r 1 /r 2 ), where the color indicates the fluid flow speed at the nozzle exit.
  • FIG.14C illustrates nozzle exit shapes with flow speed illustrated by color (top) and cross-sections of the printed hollow filaments fabricated by nozzle replicas, as illustrated in FIG.15B.
  • FIG.14E illustrates a photo of the printing process of a hollow fiber using a nozzle replica, as illustrated in FIG.14B, the nozzle exit shape (ii), and cross-sections of the printed filaments (iii) depending on the orientations of the thinnest filament thickness relative to the substrate ( ⁇ , ⁇ , ⁇ , ⁇ ).
  • FIG.14F illustrates thickness ratios ( ⁇ ) of the printed filaments (T 1 /T 2 ) to that of the nozzle outlet (t 1 /t 2 ) depending on the nozzle shape (r 1 / r 2 ).
  • FIGS.15A-15C illustrate perspective and schematic views of design of nozzle replicas for characterizing the adaptive core-shell nozzle extrusion process in FIGS.14A- 14G.
  • FIG.15A illustrates an iso-view
  • FIG.15B illustrates a cross-sectional view of the nozzle design.
  • FIGS.16A and 16B illustrate image and graphical views of a full set of cross- section images and thickness analysis results of hollow fibers printed with nozzle replicas.
  • the coordinate systems are consistent with FIG.14E; scale bar, 5 mm.
  • FIG.16B illustrates thickness variations of the fibers in FIG.16A as a function of the azimuthal angle, depending on the nozzle shapes (r 2 ) and print directions. [00125]
  • the top views of the printed fibers demonstrate their continuity and surface quality, as illustrated in FIG.14G.
  • FIGS.17A and 17B illustrate schematic views of repeatability of actuator cross-section production.
  • a single-joint structure comprising a deformable section (II) sandwiched between two ’fixed’ sections (I), is assumed three parameters are selected for the sweeps, as illustrated in FIG.18A: the actuating joint length La, the degree of asymmetry ⁇ , and the cross-sectional area A ratio , defined as the ratio of the area of the hole to the area of the skin. [00130]
  • the degree of asymmetry ⁇ and the cross-sectional area A ratio are defined as follows: Where R 1 and R 2 are the distance from the center of the hole to the nearest vertex and the distance to the farthest vertex of the deformable section (II), respectively.
  • the value R h denotes the radius of the hollow hole.
  • the inflatable fiber is fixed at its base, with the other side remaining unconstrained, as illustrated in FIGS.18B and 18C. Input pressure p is applied along the side wall of the inner hole, causing the non-symmetric fibers to deflect with a bending angle ⁇ that increases as ⁇ , L a , or A ratio increases.
  • FIGS.18A-18K illustrate graphical and image views of characterization of inflatable fiber deformation.
  • FIG.18A illustrates a schematic of an inflatable hollow fiber consisting of a deformable section (II) surrounded by ’fixed’ sections (I). Bending angles ( ⁇ ) of the inflatable fibers obtained by finite element analysis:
  • FIG.18B illustrates a function of the degree of asymmetry ( ⁇ ) and joint length (L a ) under an actuation pressure (p) of 70 kPa.
  • FIG.18C illustrates as a function of area ratio (A ratio ) and joint length (L a ) under an actuation pressure (p) of 30 kPa.
  • FIG.18E illustrates a definition of actuation force (F act ) (top) and how it varies with ⁇ and L a (bottom), or f) with A ratio and L a under p of 50 kPa.
  • FIGS. 18I-18K illustrate a demonstration of an inflatable fiber deforming into a complex 3D shape:
  • FIG.18I illustrates a design of the fiber with seven sections (1-7)
  • FIG.18J illustrates a cross- sectional view in the X-Y plane (top), in the X-Z plane for each section where arrows indicate the orientation of the thinnest shell (center), and exterior view of the fabricated actuator from the X-Y direction (bottom)
  • FIG.18K illustrates a fabricated fiber before actuation (left) and after actuation (right).
  • FIGS.18I-18K a fiber following a complex 3D path is designed and fabricated, as illustrated in FIGS.18I-18K, where each section is designed to rotate by approximately 90 degrees from sections i to vii.
  • the fiber Upon applying input pressure, the fiber, initially straight, deforms into a 3D shape as each section bends in the direction of its thickest wall, as illustrated in FIG.18K.
  • the resulting shape aligns closely with the target design, as illustrated in FIG.18I, confirming the functionality of the fibers produced through the ACS- 3DP process.
  • a low-cycle fatigue test was conducted on the inflatable fibers, as illustrated in FIGS.19A-19C.
  • FIGS.19A-19C illustrate image and graphical views of low-cycle fatigue tests of single-joint fibers.
  • FIG.19A illustrates a single-joint fiber used in the fatigue test, consisting of a deformable section (ii) between two fixed sections (i and iii) (top), with scanned cross-sections of each section (i, ii, iii) (bottom).
  • FIG.19B illustrates a bending angle ( ⁇ ) over test time (s) for large-deformation actuation under an input air pressure of 24 psi (165.47 kPa). Maximum and minimum bending angles at each cycle are marked by blue and red circles, respectively. The actuator ruptured after 124 cycles, following the last cycle shown in the graph.
  • FIG.19C illustrates a smaller deformation actuation test under an input air pressure of 17 psi (117.21 kPa). Maximum and minimum bending angles at each cycle are marked by blue and red circles, respectively. The total cycle count is approximately 2000; scale bars, 10 mm.
  • FIGS.20A-20F illustrate image and graphical views of a customized hand- assistive device fabricated using ACS-3DP.
  • FIG.20A illustrates the design of five inflatable fibers for the assistive device and a photo of the wearer’s hand.
  • FIG.20B illustrates that each fiber is controlled by an individual pressure (p 1 to p 5 ), assisting each phalanx.
  • FIG.20C illustrates the device, whose cross-sectional views of the non-deform ’fixed’ section (I) and the deformable section (II) are shown on the right, enables various assistive modes, including FIG.20D, which illustrates a pincer grasp (p4, p5 > 0), FIG.20E illustrates a tripod grasp (p3, p 4 , p 5 > 0), and f) hook grasp (p 1 to p 5 > 0), showing before actuation (i) and after actuation (ii).
  • FIGS.20A-20F To demonstrate the suitability of ACS-3DP for functional robotic structures that adaptively and seamlessly interact with their environments, a customized hand-assistive device was fabricated, as illustrated in FIGS.20A-20F. Hand-assistive devices augment the grasping force of patients with impaired hand function or support rehabilitation to restore hand-manipulating abilities. To maximize efficiency and ensure safety while transmitting the required force, actuators were customized to align with the wearer’s hand anatomy. The device consists of five fibers, each featuring multiple segments corresponding to the fingers, as illustrated in FIG.20A.
  • FIG.21 illustrates an image view of a hand-assistive device design overlay of deformable and non-deformable (’fixed’) sections, with dimensions in mm, for the target design of the hand-assistive device.
  • the dimensions are aligned with the locations of the hand’s joints and phalanges.
  • the second and third fingers are replicated with added complexity to facilitate complex tasks.
  • All deformable sections are designed so that the thickest sides make contact with the hand, ensuring the inner, expandable side bends naturally along the fingers’ movement direction.
  • the fabricated hand-assistive device By attaching and controlling five independent compressed air sources (p 1 p 5 ), as illustrated in FIG.20B, the fabricated hand-assistive device, as illustrated in FIG.20C, performs various grasping modes required for daily tasks.
  • the device enables pincer grasping, as illustrated in FIG.20D, for manipulating small objects by actuating the thumb (p 5 > 0) and index finger (p 4 > 0), tripod grasping, as illustrated in FIG.
  • FIGS.22A-22C illustrate schematic and graphical views of actuation force measurement of inflatable fiber.
  • FIG.22A illustrates a schematic of single-joint fiber design with a deformable section (ii) between fixed sections (i and iii) (top), along with its cross- section (bottom). The right end of the fiber is clamped, while all other sides remain unconstrained.
  • FIG.22B illustrates that the fiber inflates, its left end contacts the ground, generating an actuation force f act .
  • FIG.22C illustrates a graphical view of actuation force (f act ) as a function of input air pressure (p), with corresponding images of the fiber at each pressure level; scale bars, 10 mm.
  • the ACS-3DP process is relatively faster than other manufacturing methods and can produce various customized fibers without requiring setup changes.
  • FIG.23A complex kinematic motions of a turtle’s fins enable adaptive maneuvering over challenging terrains, as illustrated in FIG.23A, serving as inspiration for mimicking such motions with advanced soft actuators.
  • complex kinematic motion can be achieved using only a single pressure source per fin by employing pre-programmed inflatable fibers, as illustrated in FIG.23B.
  • inflatable fibers consisting of five sections (i–v) are designed, as illustrated in FIG.23C. Sections i, iii, and v are structured to remain largely undeformed under actuation pressure, while sections ii and iv deform significantly.
  • Section ii has a thin wall in the Y+ direction, causing it to bend in the Y– direction when pressurized, whereas section iv has a thin wall in the X+ direction, resulting in bending in the X– direction. Additionally, the wall thickness difference between the thinnest and thickest sides in section ii is more pronounced than in section iv, ensuring that section ii bends before section iv as the input pressure increases.
  • FIGS.23A-23H illustrate graphical and image views of an ACS-3DP of inflatable fibers for a crawling turtle robot.
  • FIG.23A illustrates a sea turtle in nature that crawls using its fins
  • FIG.23B illustrates a turtle robot that mimics this locomotion mechanism using inflatable fibers
  • FIG.23C illustrates an exemplary actuator design for the right fin
  • FIG.23D illustrates a crawling mechanism of the turtle robot (top) with actuation schemes of the inflatable fibers (bottom) provided as the pressure (p) profile over a cycle
  • FIG.23E illustrates a sequence of the extrusion process.
  • FIG.23G illustrates a trajectory of a tracking point marked on the inflatable fiber for one cycle in the X-Y plane, showing sequential and hysteretic actuation even under a single pressure source.
  • FIG.23H illustrates snapshots of the turtle robot moving in the X+ direction during a single actuation cycle.
  • the turtle robot progresses in the X+ direction under cyclic pneumatic actuation, as illustrated in FIG.23D.
  • Inflation Phase I the inflatable fins lift the robot’s body as segment ii actuates while the other segments remain inactive.
  • the inflatable fibers are fabricated sequentially from section i to v, as illustrated in FIG.23E, using ACS-3DP.
  • the top view of the fabricated fiber highlights clear transitions from section ii to iii (I) and from sections iii and iv to v (II), with corresponding cross-sections shown on the right, as illustrated in FIG.12F.
  • the printed fiber exhibits hysteresis, as confirmed through video tracking analysis using a high-speed camera, as illustrated in FIG.23G, which enables sequential actuation: bending occurs in the Y– direction during Inflation Phase I, followed by bending in the X– direction during Inflation Phase II. Also, the sequence of actuation can vary depending on the design.
  • FIG.23H An Adaptive Core-Shell 3D printing process is presented herein for the direct and monolithic fabrication of anisotropic inflatable fiber actuators.
  • the fabricated fibers consist of ‘fixed’ and deformable sections, with the deformable sections designed to bend in various spatial directions under applied pressure. The degree of bending and the sequence of actuation for each segment are controlled through thickness variations along the azimuthal direction within the cross-section and through actuation speed, respectively.
  • ACS-3DP may be integrated with different 3D printing methods, such as multi-material or subvoxel printing, enabling fibers to achieve higher actuation forces by incorporating strain-constraining rigid material strips or functionalities like sensing. Further, applying a multi-core system to ACS-3DP could enable the fabrication of multi-DOF actuation fibers, whereas the current design is limited to one DOF, significantly expanding its potential applications.
  • Materials are prepared using a PDMS material (DOWSIL SE 1700; Dow Corp.) by mixing the material with 10% w/w curing agent in a centrifugal mixer (2000 rpm for 2 minutes; Flak-Tek).
  • Adaptive Core-Shell Printhead The printhead is modified from a previous design proposed in reference, which outlines the details of the printhead. A solid core structure is added to the ink inlet component, as illustrated in FIG. 12A. Since even minor deflection in the nozzle base significantly affects the precision of the extruded filament, as illustrated in FIGS.12B-12D, the nozzle is reinforced with a stiffener, as illustrated in FIG.12E.
  • the core structure is designed to protrude from the adaptive nozzle shell, as proposed in reference.
  • An air channel outlet is incorporated into the core’s center, preventing hollow core shrinkage caused by potential negative pressure.
  • Both the nozzle base and the ink inlet module with the solid core are fabricated using a Digital Light Processing (DLP) 3D printer (Sonic Mini 8K, Phrozen) and washed with isopropyl alcohol to prevent clogging.
  • DLP Digital Light Processing
  • Silicone rubber membranes and compression springs with different geometries are used depending on the diameter range of the inflatable fibers to be printed.
  • a longer compression spring free length 20 mm, OD 6 mm; CREEYA compression springs assortment kit
  • a membrane with an initial tip diameter of 2 mm are used.
  • a shorter compression spring free length 15 mm, OD 6 mm; CREEYA compression springs assortment kit
  • a membrane with an initial tip diameter of 5 mm are used. The latter configuration allows the adaptive nozzle to expand to larger diameters.
  • ACS-3DP and 3D Printing with Nozzle Replica All inflatable fibers are printed or extruded using a gantry system (Engine SR, HYREL).
  • the adaptive nozzle with a solid core structure is connected to a syringe filled with printing ink (Becton, Dickinson and Company), mounted on a syringe pump (FUSION 200-X, Chemyx).
  • the syringe is linked to the nozzle inlet via a PVC tube (1/8 inch x 1/4 inch) and an adapter (25x Male luer lock 1/8 inch 3.2- mm PP Hose Barb Adapter, RSN Lab).
  • the fiber designed to deform into a 3D shape for demonstration, as illustrated in FIGS.18J and 18K, is fabricated on a substrate with a core structure of r h 1mm.
  • the flow rate is set at 3.5 ml min ⁇ 1 , while the print height (a gap between the nozzle tip and the substrate) is maintained at 8 mm for all sections.
  • the length of the deformable section ii, la is set as 19 mm.
  • the nozzle outlet is adjusted to produce deformable section (ii) to be nearly identical to deformable section of the hand assistive device, as illustrated in FIGS.15D-15F and ’fixed’ sections (i and iii) to that of the device, as illustrated in FIGS.15D-15F.
  • the extrusion times are set as follows: 25 s for section (i), 35 s for section (ii), 50 s for sections (iii) and (iv), and 100 s for section (v).
  • the filaments fabricated on a substrate to characterize the extrusion process using the nozzle replicas, as illustrated in FIGS.13A-13G are printed at a constant flow rate of 2 ml min ⁇ 1 and a constant feed rate of 60 mm min ⁇ 1 with a print height of 10 mm.
  • the fiber shown in FIGS.18A-18K is cured in an oven (Heratherm, Thermo Fisher Scientific) for 1 hour at 80°C, while the other fibers, as illustrated in FIGS.13, 17, 19, 20, 22, and 23 are cured for 30 minutes at the same temperature.
  • Fluid Flow Simulation A commercial multiphysics simulation software (COMSOL Multiphysics 6.1, COMSOL) is used to numerically analyze fluid flow inside the adaptive core shell nozzle, as illustrated in FIGS.14A-14G. Since the extrusion process can be characterized as low-Reynolds number fluid flow, the Laminar Flow module is utilized. The ink’s non-Newtonian shear thinning behavior is modeled using the Herschel-Bulkley- Papanastasiou model, with the following assumed parameters: a fluid consistency coefficient (m) of 900 Pa ⁇ s, a flow behavior index (n) of 0.23, and a yield stress ( ⁇ y ) of 500 N/m 2 .
  • m fluid consistency coefficient
  • n flow behavior index
  • ⁇ y yield stress
  • a ’no- slip’ boundary condition is applied to the walls, while a mass flow rate of 0.1608 ⁇ 10 ⁇ 4 , kg/s (equivalent to 2, ml/min for the SE 1700 ink) is imposed at the inlet, effectively assuming a uniform positive pressure at the nozzle inlet.
  • the pressure then gradually decreases to a static pressure of 0 Pa (ambient conditions) at the outlet. Due to nozzle asymmetry and the ink’s rheological properties, the rate and distribution of the pressure drop vary around the outlet, leading to local deviations in flow rates.
  • the simulation employs the ’Physics-Controlled Mesh’ option with an element size set to ’Finer’ to ensure accurate resolution of flow characteristics.
  • Finite Element Analysis of Inflatable Fibers A commercial multiphysics simulation software (COMSOL Multiphysics 6.1, COMSOL) is used to numerically investigate the solid behavior of the inflatable fibers. A stationary analysis is conducted, taking into account geometrically nonlinear behavior. A Mooney-Rivlin hyperelastic model with nine parameters for rubber is used to model the cured SE 1700 material. Fixed constraints are imposed at the bottom of the fiber, while a pressure load is applied to the inner walls of the fiber to simulate air pressure. [00158] For the contact force simulations, as illustrated in FIGS.18E-18H, an aluminum plate is virtually placed parallel to the actuator with a gap of 0.1 mm.
  • a contact condition using the ‘Penalty’ method provided by the software is imposed between the fiber and the plate.
  • the ‘Physics- Controlled Mesh’ option with a ’Normal’ element size is used.
  • input pressure is employed as a continuation parameter.
  • An interval of 10000 Pa is used for deformation investigations, as illustrated in FIGS.18B and 18C, and an interval of 1000 Pa is used for contact force investigations, as illustrated in FIGS.18E and 18F, starting from 0Pa.
  • L a is varied from 5 mm to 30 mm in increments of 5 mm
  • a ratio 1.5
  • L a is varied from 5 mm to 30 mm in increments of 5 mm
  • R 2 is varied from R h + 0.1mm to 2 R h in increments of 0.2 mm, while ensuring that the hole radius R h remains smaller than the closest point to the center on the outer cross-section.
  • a microscopic camera (AF4115ZTW 1.3-MP wide-angle FLC wireless-ready polarizer, SunriseDino) is used to observe the bottom of the nozzle during calibration.
  • High-speed Video Analysis The sequential actuation with hysteresis of the inflatable fiber for the turtle robot is recorded using a high-speed camera (FASTCAM SA5, Photron). Tracking points are marked on the inflatable fiber and analyzed using the ’vision.PointTracker’ function in MATLAB, which employs the Kanade-Lucas-Tomasi (KLT) algorithm. A single tracking point showing the clearest path is selected for the tracking analysis.
  • KLT Kanade-Lucas-Tomasi
  • the seven curves are averaged and the root mean square (RMS) value of each curve is calculated with respect to the mean curve. Then, the RMS values are normalized by dividing them by the mean distance of the mean curve. Finally, the standard deviation of the seven curves is computed based on the mean RMS values. These values are obtained for each of the seven repeated tests for the first outlet shape, as illustrated in FIG. 17A, and the second outlet shape, as illustrated in FIG.17B.
  • RMS root mean square
  • Hand-assistive Device A nitrile glove (heavy-duty nitrile gloves, large size, Medprayer) is used as the orange glove for the hand-assistive device, with the inflatable fibers adhered to it using instant adhesion (Super glue, Loctite). Each fiber is connected to a syringe (Becton, Dickinson and Company) through silicone tubing (1/8” inner diameter ⁇ 3/16” outer diameter, uxcell) via adapters (male luer lock, 1/8 inch, MEETOOT). The fibers are actuated with air.
  • syringe Becton, Dickinson and Company
  • silicone tubing (1/8” inner diameter ⁇ 3/16” outer diameter, uxcell
  • adapters male luer lock, 1/8 inch, MEETOOT
  • Turtle Robot The turtle robot body is designed using SolidWorks, as illustrated in FIGS.14A and 14B, and fabricated with a DLP 3D printer (Sonic Mini 8K, Phrozen) using high-resolution resin (Aqua Gray 8K, Phrozen). For visual purposes, the body is coated with a liquid rubber material (Flex Seal, Flex Seal). The printed fibers and robot body are connected via adapters (male luer lock, 3/16 inch, MEETOOT) with additional sealing to prevent air leakage. A Kevlar cable (0.014 inch in diameter, McMaster) is routed for this purpose.
  • FIGS.14A and 14B illustrate a turtle robot body design.
  • FIG.14A illustrates an iso-view of the CAD design of the robot body.
  • FIG.14B illustrates a transparent top view of the body showing air channels that connect pressure inlets to the connections for inflatable actuators.
  • the actuation pressure (p) was supplied by a pressure pump (Digital Syringe Dispenser 98666, LOCTITE). Air was used as the pressure source. The right end of the fiber was clamped onto a positioning arm, while the left end was positioned above a scale (Precision Balance ME1002T/00, METTLER TOLEDO) with a 3 mm gap. The actuation forces were measured using the scale in grams and then converted to Newtons by assuming the gravitational acceleration in the lab to be 9.81 m/s 2 . [00172] It should be noted that the control of the print nozzles and 3D printing systems described herein can be executed with a program(s) fixed on one or more non-transitory computer readable medium.
  • the non-transitory computer readable medium can be loaded onto a computing device, server, 3D printer device processor, smartphone, tablet, phablet, or any other suitable device known to or conceivable by one of skill in the art.
  • a computing device server, 3D printer device processor, smartphone, tablet, phablet, or any other suitable device known to or conceivable by one of skill in the art.
  • steps of the method described can be carried out using a computer, non-transitory computer readable medium, or alternately a computing device, microprocessor, or other computer type device independent of or incorporated with an imaging or signal collection device.
  • An independent computing device can be networked together with the 3D printing hardware either with wires or wirelessly.
  • the computing device for executing the present invention can be a completely unique computer designed especially for the implementation of this method.
  • a non-transitory computer readable medium is understood to mean any article of manufacture that can be read by a computer.
  • non-transitory computer readable media includes, but is not limited to, magnetic media, such as a floppy disk, flexible disk, hard disk, reel-to-reel tape, cartridge tape, cassette tape or cards, optical media such as CD-ROM, writable compact disc, magneto-optical media in disc, tape or card form, and paper media, such as punched cards and paper tape.
  • magnetic media such as a floppy disk, flexible disk, hard disk, reel-to-reel tape, cartridge tape, cassette tape or cards
  • optical media such as CD-ROM, writable compact disc, magneto-optical media in disc, tape or card form
  • paper media such as punched cards and paper tape.
  • the non- transitory computer readable medium is understood to be any article of manufacture readable by a computer.
  • Such non-transitory computer readable media includes, but is not limited to, magnetic media, such as floppy disk, flexible disk, hard disk, reel-to-reel tape, cartridge tape, cassette tapes or cards, optical media such as CD-ROM, DVD, Blu-ray, writable compact discs, magneto-optical media in disc, tape, or card form, and paper media such as punch cards or paper tape.
  • the program for executing the method and algorithms of the present invention can reside on a remote server or other networked device.
  • Any databases associated with the present invention can be housed on a central computing device, server(s), in cloud storage, or any other suitable means known to or conceivable by one of skill in the art. All of the information associated with the application is transmitted either wired or wirelessly over a network, via the internet, cellular telephone network, RFID, or any other suitable data transmission means known to or conceivable by one of skill in the art.

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Abstract

An "Adaptive Nozzle 3D Printing (AN3DP)" nozzle, enables dynamic alteration of nozzle diameter and cross-sectional shape during printing. The AN3DP nozzle includes eight independently controllable, tendon-driven pins arrayed around a flexible, pressure-resistant membrane. The design incorporates a tapered angle optimized for extruding shear-thinning inks and a pointed tip suitable for constrained-space printing, such as conformal and embedded printing. The device can also include a core which enables the monolithic fabrication of hollow fiber actuators with precise control over wall thickness. In some embodiments, the present invention combines the dynamic functionality of an adaptive nozzle, which adjusts its cross-sectional shape during printing, a solid core, and coaxial multi-material or multi-phase extrusion, previously used for creating composite core-shell materials or hollow filaments with uniform shell thickness for lightweighting.

Description

ADAPTIVE 3D PRINTING NOZZLE CROSS REFERENCE TO RELATED APPLICATIONS [0001] This application claims the benefit of U.S. Provisional Patent Application No. 63/647,933 filed on May 15, 2024, which is incorporated by reference, herein, in its entirety. FIELD OF THE INVENTION [0002] The present invention relates generally to three-dimensional (3D) printing. More particularly, the present invention relates to a shape-changing adaptive 3D printing nozzle. BACKGROUND OF THE INVENTION [0003] 3D printers extruding filaments through a fixed nozzle can encounter a conflict between high resolution, requiring small diameters, and high speed, requiring large diameters. This limitation is especially pronounced in multiscale architectures featuring both bulk and intricate elements. [0004] Extrusion-based 3D printing primarily employs nozzles with fixed exit shapes. This imposes a trade-off between resolution and speed: high resolution requires a small nozzle diameter, while high material deposition rate necessitates a larger diameter. The inverse- cubic relationship exacerbates design limitations in objects with varying feature sizes, confining complexity to multiples of the nozzle diameter. Achieving continuous gradients is unfeasible, and sloped surfaces result in undesirable “stair-stepping” artifacts. Regarding shape, fixed nozzles typically adopt a circular cross-section to facilitate printhead movement in any direction within a layer. However, cylindrical filaments fail to produce fully dense parts unless they are severely deformed during extrusion. A square or rectangular nozzle could mitigate this issue. However, such cross-sections can only extrude material along the Cartesian axes that align with the faces of the cuboids, and they would intensify stair- stepping problems, even if directionality was addressed; for example, via rotating nozzles. [0005] These and other limitations significantly impede the broader adoption and advancement of additive manufacturing and its applications. Multiscale features, which are common in numerous engineered systems, particularly in biologically relevant applications like artificial vascular networks and bone grafts, and in other areas such as heat sinks and graded lattices, would benefit substantially from an adaptive extrusion nozzle in both performance and printing speed. Additionally, in the fabrication of standard 3D solid structures using extrusion-based printers, size-variable filaments can address the inherent discrepancies between intended and actual shapes caused by fixed-size, cylindrical filaments, by eliminating inter-filament voids and facilitating smoother surfaces. This approach could also resolve the resolution-speed tradeoff in 3D printing. By varying filament cross-sections and their spatial arrangement, more complex structures with a wider design space can be printed within the same timeframe, compared to structures composed of uniform cross- sections. [0006] In fixed-nozzle extrusion, filament diameter modulation is achievable through over- and under-extrusion, yet this method is constrained to size changes within -30 % and +35 % of the nozzle diameter. Different approaches adjust filament width by rotating their high- aspect ratio exit, directly modify nozzle size, or shape. However, most existing methods only allow for size variation, lacking the ability to control the filament's cross-sectional shape. Even with shape-changing nozzles, the focus is primarily on the outlet shape, neglecting the internal nozzle dynamics crucial for material flow, especially when extruding shear-thinning materials. These systems necessitate intricate mechatronic assemblies and often have large nozzle wall thicknesses at the tip, which can degrade print quality and limit their applicability. For instance, they are unsuitable for embedded printing, where material is extruded in three dimensions within a gel-like sacrificial support matrix, or for printing on conformal surfaces, and they cannot be used in applications like printing within narrow spaces for minimally invasive surgery. [0007] It would be advantageous to provide a high-speed, high-resolution 3D printing nozzle and in addition to provide adaptive core-shell 3D printing of hollow fiber actuators. SUMMARY OF THE INVENTION [0008] The foregoing needs are met, to a great extent, by the present invention, wherein one aspect is a device for three-dimensional (3D) printing including a base plate. The device includes a nozzle. The nozzle includes a nozzle membrane and pins. The nozzle is coupled to the base plate. The nozzle comprises an exit and is configured to allow precise control of a cross-sectional shape of the exit. The device also includes stepper motors. The pins are coupled to the stepper motors to actuate changes in the cross-sectional shape of the exit. [0009] In accordance with an aspect of the present invention, the device includes cables connecting the pins to the stepper motors. The cables can take the form of high strength inextensible fibers. The device can include springs for returning the pins to their original positions. The nozzle is further configured with a tapered internal channel shape suitable for shear-thinning ink. The device can also include an ink inlet module. BRIEF DESCRIPTION OF THE DRAWINGS [0010] The accompanying drawings provide visual representations, which will be used to more fully describe the representative embodiments disclosed herein and can be used by those skilled in the art to better understand them and their inherent advantages. In these drawings, like reference numerals identify corresponding elements and: [0011] FIGS.1A-1I illustrate image and diagrammatic views of an adaptive nozzle 3D printing (AN3DP) platform according to an embodiment of the present invention. FIG.1A illustrates an overview and components of the AN3DP. FIG.1B illustrates a schematic of the AN3DP print head. FIG.1C illustrates a schematic of the adaptive nozzle actuation mechanism (left) and photos of the adaptive nozzle. FIG.1D illustrates a schematic of an adaptive nozzle used for printing a size/shape-changing filament, accompanied by a photo of the implementation (top-left). The schematic shows the size change of a circle (1-2), the shape changes from a circle to a rectangle (2-3), and the size change of a rectangle (3-4). FIG. 1E illustrates photos of a bottom view of the adaptive nozzle (top) and corresponding target size (bottom) for small (left), medium (middle), and large exit mode (right). FIG.1F illustrates photos showing the bottom view of the adaptive nozzle (top) and the corresponding target sizes (bottom) for the small (left), medium (middle), and large exit modes (right). FIG. 1G illustrates photos of the adaptive nozzle exit changing into various shapes, including a circle, rectangle, square, rhombus, and star. FIGS.1H and 1I illustrate photos of filaments having different sizes, as in FIG.1H, and shapes, as in FIG.1I. [0012] FIGS.2A-2I illustrate image and diagrammatic views of a design and implementation of an AN3DP platform according to an embodiment of the present invention. FIG.2A illustrates an exploded view of the AN3D printhead consisting of a printhead assembly (I), an adaptive nozzle (II), and pin modules (III). FIGS.2B-2D illustrate a pin module actuation mechanism for controlling nozzle exit size/shape: starting from the initial state, as illustrated in FIG.2B, tip-widening with a distance-increasing actuation, as illustrated in FIG.2C, via motor actuation, and then returning to the initial state, as illustrated in FIG.2D, due to the restoring moment from the spring and silicone cover after the motor actuation is released. FIGS.2E and 2F illustrate a flexible silicone cover. FIG.2F illustrates a cover fabricated from 3D-printed molds, shown in FIG.2E. FIGS.2G and 2H illustrate metal pins and silicone cover integrated structure. FIG.2H illustrates a tip-fastening mechanism, illustrated in FIG.2G. FIG.2I illustrates that the metal pins and silicone cover integrated structure can be easily interchanged from the nozzle base via screws, allowing for simple replacement and cleaning after every print. [0013] FIGS.3A-3D illustrate diagrammatic and graphical views of control for an AN3DP platform according to an embodiment of the present invention. FIG.3A illustrates available nozzle size/shape depending on the number of actuators (1 (i), 2 (ii) and (iii), 4 (iv), and 8 (v)) FIGS.3B illustrate actuators, print height, and feed rate operation strategy for an exemplary filament having constant circle cross section ( ), diameter-increasing circle cross section ( , diameter-decreasing circle cross section ( , shape-changing from circle to square section ( ), and constant square cross section ( ). FIGS. 3C and 3D illustrate cross sectional area, as illustrated in FIG.3C, of a nozzle exit (A) and nozzle volume (V), as illustrated in FIG.3D depending on nozzle dimension (d) for square (☐), circle (○), rectangular ( ), rhombus (♢), and star ( ). [0014] FIGS.4A-4E illustrate diagrammatic and graphical views of an AN3DP platform according to an embodiment of the present invention. Typical objects consist of solid inner features, as illustrated in FIG.4B and surfaces, as illustrated in FIG.4C. FIG.4B illustrates cross-sectional photos of solid inner features additively manufactured from circular filaments via a fixed nozzle (i) and square filaments via the adaptive nozzle (ii) (top) with a comparison of their volume solid fractions (bottom). FIG.4C illustrates cross-sectional photos of surfaces additively manufactured from circular (iii) and square (iv) filaments via fixed nozzles, and a mix of square and triangle filaments from the adaptive nozzle (v), with a comparison of surface roughness and ; scale bars in (B) and (C), 5 mm. FIG.4D illustrates multi-scale structures consisting of bulky solid parts and thin functional features (top) can be manufactured more quickly with AN3DP than with a fixed nozzle by filling up the solid parts with its maximum diameter (λl) and thin features with its minimum diameter mode (l) (bottom). FIG.4E illustrates a theoretical evaluation of the advantage of using AN3DP over fixed nozzles in terms of print time ( = ) depending on volume ratio of thin parts ( ) and diameter change ratio of AN3DP (λ) for various practical parts, including heat sinks (HS1-HS3) and graded honeycomb lattices (HC1-HC8). The purple sections are the parts that are printed in maximum diameter mode (λl) and the green ones in minimum diameter mode (l) when using AN3DP. When using a fixed nozzle, all parts are printed with a nozzle with diameter l. In the graph, the heat sinks HS1-HS3 are represented not as specific points but as individual lines. This is because the feature size of the bulky base parts (in purple) is much larger than that of the pins (in green), allowing any ratio of λ to be used for printing the base parts. [0015] FIGS.5A-5E illustrate image, diagrammatic, and graphical views of AN3DP platform printing of structures resembling vascular networks according to an embodiment of the present invention. FIG.5A illustrates a design of a structure resembling a vascular network having both continuously decreasing gradients, diameter of 8 mm (i), 6 mm to 4 mm (ii), and continuously-increasing gradients, 4 mm, 6 mm to 8 mm (top), AN3DP printing process with corresponding zoomed-in adaptive nozzles (middle), and printed structures (bottom) (scale bar: 10 mm) FIG.5B illustrates a design of a vascular network-like structure having branches with five-fold difference in diameter, 2 mm (iii) to 10 mm (iv), and bifurcation points (top), AN3DP printing process with corresponding zoomed-in adaptive nozzles (middle), and printed structures (bottom); scale bars in (A) and (B), 10 mm. FIG.5C illustrates a comparison of achievable cross-sectional areas of filaments extruded from AN3DP to those using fixed nozzles with diameters of 3 mm, 4 mm, 5 mm, 8 mm, and 10 mm, where thick lines represent equidimensional modes and thin lines represent under/over-extrusion modes, respectively. FIG.5D is an illustration of a theoretical vascular network with 4 levels of hierarchy (left), showing the relationship of diameters ( , ) and lengths ( , ) at every branching point (right). FIG. 5E is a theoretical print time comparison ( ) for vascular networks having total m-levels. All photos in FIGS.5A and 5B were modified to reduce color saturation to 33 % in PowerPoint (Microsoft). [0016] FIG.6 illustrates schematic views of available sizes and shapes of the nozzle exit vary depending on the number of actuators. Pins indicated by dots of the same color are controlled by the same actuator. As the number of actuators increases, a greater variety of nozzle shapes becomes available, which is depicted with a denser background. [0017] FIGS.7A and 7B illustrates graphical views of nozzle volumes depending on dimensions. FIG.7A illustrates a rhombus-shape exit with dimensions of and . FIG.7B illustrates a star-shape exit with dimensions of and , which are calculated from Eq.14. [0018] FIGS.8A-8C illustrate schematic and graphical views of a volume calculation for arbitrary adaptive nozzle with n pins. FIG.8A illustrates that the nozzle is shaped as a ‘twisted prism’ with a total height of . It has a cross-section at the base ( ) in the form of a regular n-gon, where the perpendicular distance from the center ( to each side is (i), as illustrated in FIG. 8B. At the exit ( ), the shape is an n-gon formed by controlled pin distances of (ii). The corresponding cross-sectional shape at h (ii) forms. FIG.8C illustrates a 2n-gon, each vertex at a distance of and from the origin , and each line connecting a vertex to the origin forms an interval angle of with one another. [0019] FIGS.10A and 10B illustrate graphical views of size/shape-varying filament extrusion by AN3DP. FIG.10A illustrates an analytical model for the cross-sectional dimension of the filament, d'', along the extruded length, x, incorporating the nozzle exit dimension over time, d(t), ink input volumetric flow rate, F, nozzle volume as a function of exit dimension, V(d). FIG.10B illustrates an example photo of a filament with varying dimensions. [0020] FIGS.9A-9I illustrate image and graphical views of numerical calculation of surface roughness for additively manufactured surface structures shown in FIG.4C. FIG.9A illustrates a cross-sectional photo of the structure fabricated with a circle-shaped fixed nozzle. FIG.9B illustrates an extracted wall lines of the printed (in light grey) and target (in dark grey) from, FIG.9A. FIG.9C illustrates an error E, representing the difference between the target and printed wall of (B), plotted along the Y-coordinate. FIG.9D illustrates a cross- sectional photo of the structure fabricated with a square-shaped fixed nozzle. FIG.9E illustrates an extracted wall lines of the printed (in light grey) and target (in dark grey) from, FIG.9D. FIG.9F illustrates an error E, representing the difference between the target and printed wall of (E), plotted along the Y-coordinate. FIG.9G illustrates a cross-sectional photo of the structure fabricated with square and triangle modes of the adaptive nozzle. FIG.9H illustrates an extracted wall lines of the printed (in light grey) and target (in dark grey) from FIG.9G. FIG.9I illustrates an error E, representing the difference between the target and printed wall of (H), plotted along the Y-coordinate. [0021] FIGS.11A -11D illustrate image, schematic, and perspective views of potential applicability of using AN3DP within a fluid bath that serves as a support material to create complex vascular networks, though the specific implementation would need additional refinement. FIG.11A illustrates the setup for embedded printing with an adaptive nozzle in a fluid bath, along with the corresponding actuator setup used for the testing. FIG.11B illustrates a printing process in the bath; time order: top, middle, bottom. FIG.11C illustrates a structure resembling vascular network printed into the bath. FIG.11D illustrates an example of further refinement: an elongated and more pointed nozzle tip designed to minimize the disturbance of the bath fluid by the nozzle. [0022] FIGS.12A-12G illustrate perspective and sectional views of a nozzle and core design for minimizing Outlet Shape Errors in an Adaptive Core-Shell Nozzle. [0023] FIGS.13A-13F illustrate image and diagrammatic views of adaptive core-shell nozzle extrusion of hollow inflatable fibers. [0024] FIGS.14A-14G illustrate graphical and image views of characterization of Adaptive Core-Shell Extrusion Process. [0025] FIGS.15A-15C illustrate perspective and schematic views of design of nozzle replicas for characterizing the adaptive core-shell nozzle extrusion process in FIGS.3A-3G. [0026] FIGS.16A and 16B illustrate image and graphical views of a full set of cross- section images and thickness analysis results of hollow fibers printed with nozzle replicas. [0027] FIGS.17A and 17B illustrate schematic views of repeatability of actuator cross- section production. [0028] FIGS.18A-18K illustrate graphical and image views of characterization of inflatable fiber deformation. [0029] FIGS.19A-19C illustrate image and graphical views of low-cycle fatigue tests of single-joint fibers. [0030] FIGS.20A-20F illustrate image and graphical views of a customized hand- assistive device fabricated using ACS-3DP. [0031] FIG.21 illustrates an image view of a hand-assistive device design overlay of deformable and non-deformable (’fixed’) sections, with dimensions in mm, for the target design of the hand-assistive device. [0032] FIGS.22A-22C illustrate schematic and graphical views of actuation force measurement of inflatable fiber. [0033] FIGS.23A-23H illustrate graphical and image views of an ACS-3DP of inflatable fibers for a crawling turtle robot. [0034] FIGS.24A and 24B illustrate a turtle robot body design. DETAILED DESCRIPTION [0035] The presently disclosed subject matter now will be described more fully hereinafter with reference to the accompanying Drawings, in which some, but not all embodiments of the inventions are shown. Like numbers refer to like elements throughout. The presently disclosed subject matter may be embodied in many different forms and should not be construed as limited to the embodiments set forth herein; rather, these embodiments are provided so that this disclosure will satisfy applicable legal requirements. Indeed, many modifications and other embodiments of the presently disclosed subject matter set forth herein will come to mind to one skilled in the art to which the presently disclosed subject matter pertains having the benefit of the teachings presented in the foregoing descriptions and the associated Drawings. Therefore, it is to be understood that the presently disclosed subject matter is not to be limited to the specific embodiments disclosed and that modifications and other embodiments are intended to be included within the scope of the appended claims. [0036] An “Adaptive Nozzle 3D Printing (AN3DP)” nozzle, enables dynamic alteration of nozzle diameter and cross-sectional shape during printing. The AN3DP nozzle includes eight independently controllable, tendon-driven pins arrayed around a flexible, pressure-resistant membrane. The design incorporates a tapered angle optimized for extruding shear-thinning inks and a pointed tip suitable for constrained-space printing, such as conformal and embedded printing. AN3DP's efficacy is demonstrated through the fabrication of components with continuous gradients, eliminating the need for discretization, and achieving enhanced density and contour precision compared to traditional 3D printing methods. This platform significantly expands the scope of extrusion-based 3D printers, thus facilitating diverse applications, including bioprinting cell-laden and hierarchical implants with bone-like microarchitecture. [0037] In other embodiments described further herein, Adaptive Core-Shell Printing (ACS- 3DP) can include a nozzle that accommodates a core. The core enable monolithic fabrication of hollow fiber actuators with precise control over wall thickness. The present invention combines the dynamic functionality of an adaptive nozzle, which adjusts its cross-sectional shape during printing, a solid core, and coaxial multi-material or multi-phase extrusion, previously used for creating composite core-shell materials or hollow filaments with uniform shell thickness AN3DP [0038] The AN3DP platform is capable of actively controlling both the size and cross- sectional shape of filaments in situ during the printing process. The nozzle features a conical internal design, making it particularly effective for handling shear-thinning fluids, a crucial aspect in fused deposition modeling (FDM) or Fused Filament Fabrication (FFM) and direct ink writing (DIW) techniques. This versatility enables AN3DP to accommodate a wide array of materials. Additionally, the acuminate external shape of the nozzle enhances tool accessibility, facilitating the creation of geometrically complex structures that are unachievable with fixed nozzles while considerably speeding up 3D printing of parts with varying feature sizes. [0039] Current extrusion-based 3D printers on the market extrude filaments through a fixed nozzle, presenting a dilemma: high resolution requires small diameters, while high speed necessitates large diameters. This limitation is apparent in virtually all physical objects spanning different feature sizes, including those with both bulk and intricate elements. Such objects are vital in various applications, such as fabricating artificial organs with multiscale vascular networks, creating bone implants with fine surface dimples, designing heat sinks that combine a solid base for heat absorption with thin fins for efficient dissipation, and constructing graded lattice structures. [0040] The present invention promises to revolutionize this domain by enabling dozens of times faster printing of these multiscale structures—with significantly enhanced precision— compared to traditional 3D printers. This breakthrough greatly expands the capabilities of extrusion-based 3D printers, paving the way for diverse applications, including bioprinting cell-laden and hierarchical implants with bone-like microarchitecture. [0041] In addition to size limitations, fixed nozzles typically feature a circular cross-section to facilitate printhead movement in all directions within a layer. Any deviation from a circular shape would restrict the print directions, as the extruded material would not lay evenly, particularly on its sides. However, cylindrical filaments often fail to produce fully dense parts—akin to a jar full of marbles, where gaps inevitably remain—unless they undergo significant deformation during extrusion, which adversely affects print quality. The nozzle of the present invention not only adjusts its size but also its outlet shape to suit various 3D printing conditions as dictated by the extruded part, adopting square, triangular, or rectangular shapes. This adaptability effectively mitigates the ubiquitous “stair stepping” effect in 3D printing, responsible for the “Minecraft-like” appearance of extruded parts due to layering and extrusion filament width. [0042] The nozzle design of the present invention not only significantly enhances the speed of 3D printing but also unveils new opportunities for commercializing bioprinters for artificial organ fabrication, a milestone previously unattainable due to the prolonged duration of printing beyond cell survival. It also promises to transform the use of concrete printers for personalized construction, enabling rapid manufacturing that incorporates detailed individual preferences, and expediting the production of custom consumer products tailored to personal needs or preferences. [0043] FIGS.1A-1I illustrate image and diagrammatic views of an adaptive nozzle 3D printing (AN3DP) platform according to an embodiment of the present invention. FIG.1A illustrates an overview and components of the AN3DP. FIG.1B illustrates a schematic of the AN3DP print head. FIG.1C illustrates a schematic of the adaptive nozzle actuation mechanism (left) and photos of the adaptive nozzle. FIG.1D illustrates a schematic of an adaptive nozzle used for printing a size/shape-changing filament, accompanied by a photo of the implementation (top-left). The schematic shows the size change of a circle (1-2), the shape changes from a circle to a rectangle (2-3), and the size change of a rectangle (3-4). FIG. 1E illustrates photos of a bottom view of the adaptive nozzle (top) and corresponding target size (bottom) for small (left), medium (middle), and large exit mode (right). FIG.1F illustrates photos showing the bottom view of the adaptive nozzle (top) and the corresponding target sizes (bottom) for the small (left), medium (middle), and large exit modes (right). FIG. 1G illustrates photos of the adaptive nozzle exit changing into various shapes, including a circle, rectangle, square, rhombus, and star. FIGS.1H and 1I illustrate photos of filaments having different sizes, as in FIG.1H, and shapes, as in FIG.1I. [0044] The AN3DP printhead adaptive is mounted, for example, on a Cartesian gantry system that controls its spatial positioning above the substrate, as illustrated in FIG.1A. FIGS.1A and 1B illustrates a system 10 that includes an adaptive nozzle 12, according to the present invention. The system 10 includes stepper motors 14. While four stepper motors 14 are shown any number of stepper motors known to or conceivable by one of skill in the art for the functionality of the invention could be used. The stepper motors 14 are coupled to the adaptive nozzle 12 via drive pulley 16, idler pulley 18, and cable 20. Pins 22 of the adaptive nozzle 12 are arranged around a silicone rubber cover 24 that can expand and contract along with the movement of the pins 22. Movement of pins 22 is affected by the stepper motor, pulley, cable system. [0045] The AN3DP could also be mounted on a different 3D printing system, such as a robotic arm with 6 degrees of freedom, a wire-driven printer, or a drone. The adaptive nozzle is equipped with four stepper motors, each regulated by microchips linked to a computer. These motors actuate cables running through idler and drive pulleys, as illustrated in FIGS. 1A and 1B to move the nozzle pin tips outward, as illustrated in FIG.1C. Encasing the inner volume of the nozzle is a stretchable silicone rubber membrane, which moves in tandem with the pins to maintain a continuous surface. The nozzle employs eight laser-cut metal pins, grouped into pairs, each pair controlled by a single motor. These pins form the vertices of the nozzle's exit polygon, allowing for varied exit shapes while retaining a conical internal configuration regardless of the size or shape adjustments. [0046] AN3DP facilitates the deposition of filaments with continuously varying sizes and shapes in a single setup, as illustrated in FIG.1D. It enables extruded filament diameter alterations up to 3.33 times, for instance, varying from 3 mm to 10 mm, as illustrated in FIGS.1E and 1F. The nozzle can produce a range of shapes, including circular, square, rectangular, and star-shaped, as illustrated in FIG.1G. Additionally, it can deposit these shapes with feature sizes between 4 mm and 10 mm onto substrates, as illustrated in FIGS. 1H and 1I. [0047] FIGS.2A-2I illustrate image and diagrammatic views of a design and implementation of an AN3DP platform according to an embodiment of the present invention. FIG.2A illustrates an exploded view of the AN3D printhead consisting of a printhead assembly (I), an adaptive nozzle (II), and pin modules (III). FIGS.2B-2D illustrate a pin module actuation mechanism for controlling nozzle exit size/shape: starting from the initial state, as illustrated in FIG.2B, tip-widening with a distance-increasing actuation, as illustrated in FIG.2C, via motor actuation, and then returning to the initial state, as illustrated in FIG.2D, due to the restoring moment from the spring and silicone cover after the motor actuation is released. FIGS.2E and 2F illustrate a flexible silicone cover. FIG.2F illustrates a cover fabricated from 3D-printed molds, shown in FIG.2E. FIGS.2G and 2H illustrate metal pins and silicone cover integrated structure. FIG.2H illustrates a tip-fastening mechanism, illustrated in FIG.2G. FIG.2I illustrates that the metal pins and silicone cover integrated structure can be easily interchanged from the nozzle base via screws, allowing for simple replacement and cleaning after every print. [0048] FIG.2A illustrates a printhead assembly 26, an adaptive nozzle 12, and a pin module 22 according to an embodiment of the present invention. The printhead assembly 26 includes the stepper motor array 14, a base plate 28, and a height adjustment plate 30. The printhead assembly also includes drive pulleys 16, idler pulleys 18, and cable 20. The adaptive nozzle 12 includes a nozzle base 32 that couples to the printhead assembly 26. Inlet 34 allows for the flow of ink through the silicone rubber cover 24 that expands and contracts when the pins 22 are expanded and contracted. Springs 36 allow for the movement of the pins 22. Pins 22 include a pin base 38 and a pin-tip bundle 40. [0049] The AN3DP system features a nozzle with adjustable exit size and shape, a rapid and robust mechanism for transitioning between these configurations, and a compact nozzle design for improved tool accessibility. Key components include (i) a printhead assembly, (ii) an adaptive nozzle, and (iii) pin modules, as illustrated in FIG.2A. The adaptive nozzle (ii) is mounted on the base plate, and the pin modules (iii) are actuated by inextensible cables, which are connected to stepper motors through drive and idler pulleys. These motors are positioned on the base plate, separate from the nozzle (ii), using a cable-driven actuation system. This system is akin to those used in robotics to achieve compact, dynamic end- effectors. [0050] Each of the eight pin modules in the AN3DP system is connected to the nozzle base via an articulated revolute joint, ensuring high precision and consistent actuation over numerous cycles. Initially, as illustrated in FIG.2B, the pin tip moves a distance along the X-axis, driven by rotation about its axis due to cable tension from motor actuation, as illustrated in FIG.2C. Here, is approximately linearly related to the motor actuation angle, , where (approximately 0.796 mm/rad) is a constant ratio, and is the motor actuation angle. This linear relationship arises because the cable length pulled is the product of the actuation angle and the drive pulley radius , and the pulled cable length is proportionate to This simple kinematic relationship facilitates precise control of the pins. When the motor rotates back to its initial angle, the pin tip reverts to its starting position, aided by the restorative force of a spring and the contractile force of the silicone membrane, as illustrated in FIG.2D. [0051] The design of AN3DP involves intricate interdependencies and trade-offs among various parameters, such as the bending stiffness of a pin module, the stiffness of the restoration spring, the Young's modulus of the silicone rubber membrane, and the geometrical aspects like the moment arms of the pin tip and cable connection point. These parameters were optimized heuristically. For example, a longer moment arm at the pin tip enhances the diameter change range and tool accessibility but may compromise the pin tip's movement precision due to reduced bending stiffness in the pin module. High restoration spring stiffness is required to counteract deformation under ink pressure, but this increased stiffness can stress the pin module, affecting the precision at the pin tip. Consequently, SUS 304 (Young’s modulus of 193 GPa) was used for the pins to maintain high stiffness, crucial for precision. The pin tip width (0.7 mm) is deliberately chosen to be wide enough to avoid tearing the membrane while being narrow enough for precise representation of the target filament shape. [0052] For the membrane, a flexible and highly stretchable material was chosen with a Young’s modulus of 0.15 MPa and an elongation at break of 1000%. This allows for significant size/shape change while retaining enough stiffness to prevent bulging in the nozzle wall and distortion at the tip under ink pressure. The silicone rubber membrane is fabricated by injecting liquid silicone rubber into molds, as illustrated in FIG.2E. To achieve a thin membrane (0.5 mm thickness) with high manufacturing consistency, a digital light processing (DLP) 3D printer was used with high-resolution resin for mold fabrication. This method ensures high precision, repeatability, and a smooth membrane surface, as imperfections, particularly near the nozzle tip, could lead to structural failures and ink leakage. To mitigate this risk, the mold design includes a single-piece ‘cavity a’ for the nozzle tip and two separate parts, 'cavities b and c', for easier removal of the finished cover from the mold, as illustrated in FIG.2E. Further, 'cavities b and c' were covered with 'cavity d’ to prevent gaps formation due to injection pressure. The fabricated cover has a smooth surface and a tip hole (diameter l 0 = 2mm) without any imperfection, as illustrated in FIG.2F. The result is a smooth cover with a precise tip hole (diameter l 0 = 2 mm; FIG.2F). [0053] Another important design consideration is the integration of stainless-steel pins with the silicone rubber membrane, as illustrated in FIGS.2G and 2H. Ensuring a tight fit between these components avoids slippage of the cover from the pins, which could lead to imprecise control of the nozzle's exit size and shape, and potentially result in the cover being punctured by the pin tips. To concentrate their force on the pin tips, spacers are employed, as illustrated in FIG.2G. A fully assembled unit with eight pins is shown in FIG.2H. [0054] Another key design consideration is the ease of interchangeability of the nozzle, particularly if it is treated as a consumable to be replaced after each print. This is achieved by enabling the nozzle to be easily screwed and unscrewed from the base, as illustrated in FIG. 2I. In examples, the cover is replaced, and the pins are cleaned after each print. During assembly, the inlet part is inserted into the cover, which prevents ink leakage at the neck of the silicone membrane and shields the base part from ink, thus ensuring its reusability. This design balances the need for a secure and precise assembly with the practical requirements of maintenance and interchangeability in the AN3DP system. [0055] FIGS.3A-3D illustrate diagrammatic and graphical views of control for an AN3DP platform according to an embodiment of the present invention. FIG.3A illustrates available nozzle size/shape depending on the number of actuators (1 (i), 2 (ii) and (iii), 4 (iv), and 8 (v)) FIGS.3B illustrate actuators, print height, and feed rate operation strategy for an exemplary filament having constant circle cross section ( ), diameter-increasing circle cross section ( , diameter-decreasing circle cross section ( , shape-changing from circle to square section ( ), and constant square cross section ( ). FIGS. 3C and 3D illustrate cross sectional area, as illustrated in FIG.3C, of a nozzle exit (A) and nozzle volume (V), as illustrated in FIG.3D depending on nozzle dimension (d) for square (☐), circle (○), rectangular ( ), rhombus (♢), and star ( ). [0056] AN3DP intricate control over pin movements, the gantry system's print path and feed rate, and the ink extruder's flow rate to achieve variable size and shape in filament printing. The system's versatility is enhanced by various pins-actuators routing combinations, as illustrated in FIG.3A. Each pin tip (1–8) moves along a line from the center to its initial position within a distance range of ( ; =1.5 mm and =5 mm in the setup). [0057] FIG.6 illustrates schematic views of available sizes and shapes of the nozzle exit vary depending on the number of actuators. Pins indicated by dots of the same color are controlled by the same actuator. As the number of actuators increases, a greater variety of nozzle shapes becomes available, which is depicted with a denser background. [0058] For size-only changes, all pin tips (1–8) can be controlled by a single actuator (i), with cables connected to the pins looped over an idler pulley and linked to a drive pulley. Increasing the number of actuators enables more complex shapes. For instance, with four pins (1, 3, 5, 7) connected to one actuator and the remaining four (2, 4, 6, 8) to another, shapes like circles, squares, and stars are possible (ii). Two actuators can also create asymmetric shapes, e.g., pins 3-6 linked to one actuator and pins 7, 8, 1, 2 to another (iii). Using four actuators—the maximum in the setup—allows for an expanded array of shapes, including hexagons, rhombuses, squares, stars, and circles (iv). The most diverse shape variations are achievable with eight actuators, each controlling a corresponding pin (v), as shown in FIG.6. [0059] Each shape offers distinct advantages: circles are versatile like conventional fixed nozzles, allowing printing in any direction; squares minimize inter-filament voids in solid structures; concave shapes like stars enhance bonding in applications such as bone grafts. Importantly, switching between operational modes is straightforward, requiring only changes in cable routing. [0060] In an exemplary AN3DP setup, the filament comprises sections with a constant circular cross-section ( ), an enlarging circular cross-section ( ), a diminishing circular cross-section ( ), a shape-transitioning section (circular to square; ), and a constant square cross-section ( ), as illustrated in FIG. 3B. Motors induce angular displacements of , dictating the nozzle exit size/shape. The gantry system regulates the print height h and feed rate v. A volumetric extruder is employed to feed ink through the nozzle, offering precise flow rate control, superior to pressure-driven extruders, even with the nozzle’s geometric alterations. Due to the volumetric extrusion's slow response time, the flowrate F is modulated by adjusting v, according to the equation , (1) where A is the cross-sectional area of the nozzle exit, as illustrated in FIG.3C. For sections with constant cross-sections ( and ), angular displacements remain fixed, and the print height h is set to times the filament height (i.e., for and ), with in this study. [0061] Precise control of F also mitigates common additive manufacturing issues, such as die-swelling in viscoelastic ink extrusion, where the filament's immediate post-extrusion cross-sectional area, , is larger than the nozzle's exit area, A. By applying the flow rate from Eq.1, the deposited filament’s cross-sectional area can be fitted to the nozzle exit, resembling 'equidimensional' mode. Variations in F across different cross-sections and their impact on uniform flow will be examined further herein. [0062] In regions where filament size and shape change, actuators ( - ) and print height h are varier linearly over time. Correspondingly, feed rate v is adjusted to ensure a smooth transition. For simplicity, v is set constant within each transition zone; however, for optimal equidimensional printing, v should ideally be a nonlinear function, as illustrated in FIGS.9A-9I. [0063] FIGS.7A and 7B illustrates graphical views of nozzle volumes depending on dimensions. FIG.7A illustrates a rhombus-shape exit with dimensions of and . FIG.7B illustrates a star-shape exit with dimensions of and , which are calculated from Eq.14. [0064] During the diameter-increasing segment ( - ) and shape transitions that enlarge the nozzle volume ( - ), the feed rate is reduced relative to the filament’s standalone rate. This adjustment compensates for the increased nozzle volume, as illustrated in FIG.3D and FIGS. 7A and 7B, and helps prevent necking. Conversely, in the diameter-decreasing region ( - ) and during shape transitions that reduce nozzle volume, the feed rate is increased. This compensates for the excess ink emerging due to the reduced volume, as illustrated in FIG.3D and prevents over-extrusion. The specific feed rates are empirically determined, as shown in Table 1, below, and applied in the final application. [0065] When printing with discrete increments in nozzle diameter, a pause is needed to allow the nozzle to adapt to the increased volume. This waiting period depends on the volume difference (V) between the two states and the flow rate F. The pause durations used in the study were established through experimental trials, as shown in Table 2, below. [0066] To demonstrate the capabilities of AN3DP, several representative objects were fabricated and their properties and print time compared with comparable parts produced with a fixed nozzle. [0067] FIGS.4A-4E illustrate diagrammatic and graphical views of an AN3DP platform according to an embodiment of the present invention. Typical objects consist of solid inner features, as illustrated in FIG.4B and surfaces, as illustrated in FIG.4C. FIG.4B illustrates cross-sectional photos of solid inner features additively manufactured from circular filaments via a fixed nozzle (i) and square filaments via the adaptive nozzle (ii) (top) with a comparison of their volume solid fractions (bottom). FIG.4C illustrates cross-sectional photos of surfaces additively manufactured from circular (iii) and square (iv) filaments via fixed nozzles, and a mix of square and triangle filaments from the adaptive nozzle (v), with a comparison of surface roughness and ; scale bars in (B) and (C), 5 mm. FIG.4D illustrates multi-scale structures consisting of bulky solid parts and thin functional features (top) can be manufactured more quickly with AN3DP than with a fixed nozzle by filling up the solid parts with its maximum diameter (λl) and thin features with its minimum diameter mode (l) (bottom). FIG.4E illustrates a theoretical evaluation of the advantage of using AN3DP over fixed nozzles in terms of print time ( = ) depending on volume ratio of thin parts ( ) and diameter change ratio of AN3DP (λ) for various practical parts, including heat sinks (HS1-HS3) and graded honeycomb lattices (HC1-HC8). The purple sections are the parts that are printed in maximum diameter mode (λl) and the green ones in minimum diameter mode (l) when using AN3DP. When using a fixed nozzle, all parts are printed with a nozzle with diameter l. In the graph, the heat sinks HS1-HS3 are represented not as specific points but as individual lines. This is because the feature size of the bulky base parts (in purple) is much larger than that of the pins (in green), allowing any ratio of λ to be used for printing the base parts. [0068] FIGS.5A-5E illustrate image, diagrammatic, and graphical views of AN3DP platform printing of structures resembling vascular networks according to an embodiment of the present invention. FIG.5A illustrates a design of a structure resembling a vascular network having both continuously decreasing gradients, diameter of 8 mm (i), 6 mm to 4 mm (ii), and continuously-increasing gradients, 4 mm, 6 mm to 8 mm (top), AN3DP printing process with corresponding zoomed-in adaptive nozzles (middle), and printed structures (bottom) (scale bar: 10 mm) FIG.5B illustrates a design of a vascular network-like structure having branches with five-fold difference in diameter, 2 mm (iii) to 10 mm (iv), and bifurcation points (top), AN3DP printing process with corresponding zoomed-in adaptive nozzles (middle), and printed structures (bottom); scale bars in (A) and (B), 10 mm. FIG.5C illustrates a comparison of achievable cross-sectional areas of filaments extruded from AN3DP to those using fixed nozzles with diameters of 3 mm, 4 mm, 5 mm, 8 mm, and 10 mm, where thick lines represent equidimensional modes and thin lines represent under/over-extrusion modes, respectively. FIG.5D is an illustration of a theoretical vascular network with 4 levels of hierarchy (left), showing the relationship of diameters ( , ) and lengths ( , ) at every branching point (right). FIG. 5E is a theoretical print time comparison ( ) for vascular networks having total m-levels. All photos in FIGS.5A and 5B were modified to reduce color saturation to 33 % in PowerPoint (Microsoft). [0069] As illustrated in FIG.4A, most objects feature solid inner structures, shown in FIG. 4B and functional surfaces, as shown in FIG.4C. A common issue in additive manufacturing is structural imperfections, often stemming from inter-filament voids. These voids arise in traditional 3D printing processes like FDM because fixed circular cross-section filaments cannot entirely fill the print space, resulting in a volume solid fraction of about 85%, as illustrated in FIG.5B. Even when reducing filament size, this volume fraction typically does not improve. FDM printers attempt to mitigate the problem by using layers much thinner than the nozzle diameter, which, while addressing the void issue, limits throughput speed and can distort the filament shape. In contrast, AN3DP can substantially increase the relative density of the printed object to 95%, or higher in further-optimized systems, as illustrated in FIG.5B. This capability not only enhances the structural integrity of the printed parts but also optimizes printing efficiency by reducing the need for overly thin layers and allowing for more accurate filament deposition. [0070] AN3DP can also rapidly produce objects with smooth surfaces. Smoothness is crucial both aesthetically and functionally, as it can improve properties like wear resistance and reduce geometric stress concentrations. This was demonstrated by printing a 45° angled wall, as illustrated in FIG.4C, using a combination of square and triangular filaments (v). The result was a significantly smoother wall, with surface roughness factors of = 1.65 mm and = 4.14 mm, compared to those produced with a fixed circular nozzle (iii; = 3.37 mm and = 6.44 mm) and with a fixed square nozzle (iv; = 2.78 mm and = 4.67 mm). represents the maximum height difference between the highest peak and lowest valley on the wall's surface, while is the root mean square of surface deviations from the intended wall profile. These measurements indicate that AN3DP can achieve a superior surface finish, significantly reducing the roughness typically associated with 3D printed objects. This smoother finish enhances the visual appeal of the printed parts and potentially improves their functional performance, especially in applications where surface quality is a critical factor. [0071] Modulating the nozzle size in AN3DP also significantly enhances the print speed for structures containing multi-scale features of various shapes, as illustrated in FIGS.4D and 4E. Assuming an extruder capable of any flow rate, the primary constraint on printing speed becomes the gantry system’s feed rate. Therefore, the print time can be approximated as proportional to the print path length. [0072] In conventional 3D printing with a fixed nozzle, the entire structure must be printed using a nozzle diameter l that matches the thinnest features size, as illustrated in FIG.4E. AN3DP, on the other hand, dynamically adjusts the nozzle size from l to (where ) for larger volume sections, with representing the diameter expansion ratio. Two volumes are defined, for the smaller features and for the larger ones, with the total volume being . As either the volume of thin parts ( ) or the diameter ratio time ratio decreases significantly, as illustrated in FIG.4E, meaning AN3DP prints faster compared to traditional fixed nozzle printing. [0073] This approach is particularly advantageous for objects like heat sinks (HS1-HS3 in FIG.4E), which combine a solid base for heat absorption with thin fins for efficient heat dissipation, and for graded lattice structures (HC1-HC8, as illustrated in FIG.4E). For example, consider a honeycomb graded lattice structure, HC4, with of 0.0677, where the thickness of the thickest feature is five times that of the thinnest feature. In this structure, the size of the thinnest features, indicated in green, dictates the minimum nozzle diameter. This structure can be printed 9.53 times faster using AN3DP with λ = 5. AN3DP is superior to fixed nozzles in printing parts with features varying from the smallest size or from available fixed nozzle diameters. This advantage extends to parts with constant features that don’t align with fixed nozzle diameters, like discrete honeycombs and lattices. [0074] The growing complexity of natural and engineered structures, propelled by advances in topology optimization and data-driven design, often involves forms that deviate from traditional geometric norms—eschewing right angles, straight lines, flat surfaces, and constant feature sizes. A prime example is vascular networks, featuring channels spanning several multiples in diameter. [0075] To showcase AN3DP's capabilities in addressing such intricate designs, structures resembling two different vascular networks were fabricated, as illustrated in FIGS.5A-5E. These structures exhibit continuous transitions from the smallest to the largest channel diameters. The first structure exhibits a diameter transition from 8 mm at its thickest (i) to 4 mm at its thinnest (ii), and then back to 8 mm, as illustrated in FIG.5A. The second structure presents a more pronounced diameter variation, changing fivefold from 2 mm (i) to 10 mm (iv), which translates to a 25-fold difference in cross-sectional area, as illustrated in FIG.5B. [0076] This variability is achieved by combining AN3DP, which accommodates nozzle exit diameters from 3 mm to 10 mm, with under-extrusion. For under-extrusion, the print head's travel speed is set to be v faster than the equi-dimensional mode's rate specified in Eq.1, allowing to produce a filament (iv) thinner than AN3DP's minimum diameter. The theoretically achievable range of filament cross-sectional areas, along with those of the printed filaments (i – iv), is shown in FIG.5C. This range attainable with AN3DP surpasses that of conventional fixed nozzles, covering the entire spectrum of fixed-nozzle diameters of 3, 4, 5, 6, 8, and 10 mm. Further, the vascular networks could be printed within a cellular bath using AN3DP to create hollow channels after removing the extruded sacrificial material; though, this specific application would require further refinement, as illustrated in FIGS. 11A-11D. This demonstrates AN3DP's potential in fabricating complex, multiscale structures that are increasingly demanded in advanced engineering and biomedical applications. [0077] Next, the print times for fractal structures were compared, including vascular networks and analogous systems like plant pipes, to those produced with conventional fixed nozzle 3D printing, as illustrated in FIG.5D. The fractal structures are modeled to bifurcate into two identical branches at each branching point, following specific ratios: a constant radius decreasing ratio ( ) of , aligning with Murray’s law for minimizing flow resistance, and a length decreasing ratio ( ) of 0.5 (32). The structure comprises a total of m levels, where and denote the diameter and length of the kth level branch, respectively. [0078] In fixed nozzle 3D printing, the nozzle diameter is determined by the thinnest branch at the mth level, . AN3DP, with its ability to handle a range of diameters from the thinnest feature ( ) to the thickest ( ), can print each kth level branch with its corresponding diameter ( ). As the number of levels m increases, the relative print time between the two approaches ( ) grows exponentially, as illustrated in FIG. 5E. This relationship does not consider shape accuracy; the fixed nozzle would not be able to print each branch with the required diameter, leading to over- or under-estimation of branches deviating from multiples of the smallest branch. [0079] The 3D printing platform of the present invention introduces an adaptive nozzle for extruding filaments of varying sizes and shapes. The nozzle membrane, blending stretchable silicone rubber with stiff metal pins, allows precise control of the exit's cross-section in a compact design, enhancing tool accessibility. The technology intrinsically optimizes flow, eliminates voids, and improves surface finish, thus elevating print quality. It enables parts with continuous feature sizes, features deviating from nozzle multiples, and it accelerates the production of parts with non-uniform features by altering cross-sectional size. [0080] A first of its kind, this approach offers a novel size/shape-controlling nozzle with significant potential for advancements. Future developments may include enhancing the degrees of freedom of pin motion for more diverse shapes, minimizing nozzle size with advanced manufacturing, and expanding size variability with more elastic materials. The technology could integrate with other printing methods like core-shell or embedded printing, as illustrated in FIGS.11A-11D. [0081] Ultimately, this innovation holds promise for revolutionizing multi-material, multi- scale 3D printing, impacting various fields such as soft robotics, bioprinting, and construction, by enabling greater design complexity and faster production. [0082] The ink materials were prepared as a pure viscoelastic ink (DOWSIL SE 1700; Dow Corp.) by centrifugal mixing (2,000 rpm, 2 min; Flak-Tek) of the ink and 10% w/w curing agent. Filaments of various sizes and shapes, illustrated in FIGS.1H and 1I, were printed without a curing agent, while solid structures for demonstration and vascular network-like structures used the agent. Their colors were modified by adding 0.24% w/w pigment (Silc- Pig; Smooth-On). [0083] All parts of adaptive nozzle printhead were designed by SolidWorks. The adaptive nozzle was mounted on the base plate, which had been fabricated using a fused deposition modeling 3D printer (i3 MK3S+; Prusa) from PLA material (1.75 mm PLA trusilver; Hatchbox). The nozzle base and eight pin bases were fabricated using a DLP 3D printer (Sonic Mini 8K; Phrozen) from high-resolution resin (Aqua Gray 8K; Phrozen). After printing, they were washed with isopropyl alcohol and underwent post-curing in a curing machine (Form Cure; Formlabs) to achieve maximum stiffness, crucial for high-precision nozzle exit control. The eight pin bases were then assembled onto the nozzle base, each with a shortly cut steel wire (Diameter 0.047’’ Lubricated 1065 Spring Steel Wire; McMaster), acting as a revolute joint, and a compression spring (OD 6 mm Length 20 mm; CREEYA Compression springs assortment kit). The silicone rubber membrane, integrated with eight pin-tip bundles, was attached to the assembly using nuts (part number: 90001A302; McMaster-Carr) and cup point set screws (part number: 91390a601; McMaster-Carr). Each pin-tip bundle consists of two laser-cut metal pins, nuts (part number: 90001A302; McMaster-Carr), screws (part number: 91794a744; McMaster-Carr), and washers (or spacers) (part number: 92141A204; McMaster-Carr). Each metal pin was manufactured using a laser cutter (TruLaser Fiber 5030-5kw; Trumpf) from stainless steel (0.8 T, SUS304), followed by refining using a grinder (Dremel 4300 with P60 sandpaper; DREMEL) to keep nozzle tip compact. Finally, the ink inlet module, which was fabricated using a DLP 3D printer (Sonic Mini 8K; Phrozen), inserted into the whole assembly. [0084] Each Kevlar cable (Diameter 0.014’’; McMaster) connected a pin base to a stepper motor. This connection was made through a hole in the nozzle base, an idler pulley (Round- Belt Idler Pulley for 1/8’’ diameter round belt; 1’’ OD, McMaster), and a drive pulley, which was fabricated using a DLP 3D printer (Sonic Mini 8K; Phrozen). The idler pulleys were mounted to the base plate with a height adjustment component, which was also fabricated using the same 3D printer. Four stepper motors (Nema 171.5A 400mN.m 2 Phase 4 Wires 1.8degree; Iverntech) were mounted on the base plate with motor mounts, which were fabricated with the same 3D printer. Each drive pulley was connected to each motor with a screw. The four stepper motors were controlled by four drivers (printhead controller board, HYREL), which were connected to the gantry system (Engine SR, HYREL). [0085] The nozzle head is before every print by observing the bottom view of the nozzle with a microscopic camera (AF4115ZTW 1.3MP Wide-Angle FLC Wireless Ready Polarizer; SunriseDino). [0086] The molds for the injection molding of silicone rubber membranes were designed using SolidWorks and fabricated with a DLP 3D printer (Sonic Mini 8K; Phrozen). For high- resolution, aqua-gray 8K resin was used. Once printed, the molds were rinsed with isopropyl alcohol using an air blow gun. After cleaning, to prevent the inhibition of silicone rubber curing, which can occur due to the presence of uncured resin on the mold surfaces, the molds were completely cured for over 6 hours in a curing machine (Form Cure; Formlabs). To further prohibit inhibition, the molds were soaked in an inhibitor (Inhibit X; Smooth-On). Finally, to facilitate the separation of the cured silicone rubber membrane from the molds, a release material was applied (Ease Release 200; Smooth-On) and assembled the molds. The liquid silicone rubber mixture was prepared by centrifugally mixing two parts of dragon skin 10 slow (Smooth-On; 1800 rpm, 2 min; Flak-Tek) in a negative pressure container. Colors were modified by adding 0.99% w/w pigment (Silc-Pig; Smooth-On). After injecting the liquid silicone rubber into the molds, they were cured in an oven (heratherm; Thermo Scientific) at 80°C for 30 minutes. The defects were trimmed, such as sprue and flash, from the fabricated covers after fabrication. Finally, after assembly with metal pins, the gaps between the pins and the holes on the membrane were further sealed using the same liquid silicone rubber prepared earlier. This was followed by curing in the same oven at 80°C for 30 minutes. [0087] FIGS.8A-8C illustrate schematic and graphical views of a volume calculation for arbitrary adaptive nozzle with n pins. FIG.8A illustrates that the nozzle is shaped as a ‘twisted prism’ with a total height of . It has a cross-section at the base ( ) in the form of a regular n-gon, where the perpendicular distance from the center ( to each side is (i), as illustrated in FIG. 8B. At the exit ( ), the shape is an n-gon formed by controlled pin distances of (ii). The corresponding cross-sectional shape at h (ii) forms. FIG.8C illustrates a 2n-gon, each vertex at a distance of and from the origin , and each line connecting a vertex to the origin forms an interval angle of with one another. [0088] In an exemplary embodiment, the nozzle has a total height of , as illustrated in FIG. 8A, the normal distance of every edge from the center on the base plane (i) is , and the distance of ith pin tip from center on exit plane (iii) is ( ), as illustrated in FIG.8B. Eight pins are used in the current implementation but will derive the volume for general number of pins, n, here. In FIG.8B, values and are constant values given from the nozzle design, are variables controlled by actuators, and are distances of middle point of each edge of exit polygon from . By ignoring the small amount of local deformation of the elastic wall under ink pressure, the nozzle shapes as a ‘twisted prism’ consists of a cross-section of ‘2n-gon’ at height h each vertex of which has distance of and and every line connecting the vertex and the origin has interval angle of each other, as illustrated in FIG.5C. Here, the distances given as , (7)
. (10) + , (11) . (12) For the eight pins setup, n=8, in the current study, the nozzle exit area , as illustrated in FIG.5C) and volume V (FIGS.5D and FIGS.8A-8C) are derived as [0089] where For the calculations shown in FIGS.3C, 3D, and 7, the values = 10.21 mm and = 2+27.8 mm were used. The nozzle height was set to vary to the nozzle dimension. However, to simplify the calculation, the distance of the pin with the greatest distance was selected for calculating the height variation; for instance, for the square mode in FIG.3C. [0090] FIGS.9A-9I illustrate the profile of the dimension of the extruded filament along the filament extrusion length (x) under the nozzle exit dimension varies over time. Extruded filament was assumed to have the same shape and size as the cross-section of the nozzle exit at the time of extrusion . If the compression of ink is ignored, the following volume conservation equation is satisfied: , (15) [0091] where is the flow rate of ink injected by the volumetric extruder, V the volume of the nozzle (FIG.3D, FIGS.7A and 7B and Eq.14), A the cross-sectional area of the nozzle (FIGS.3C, 10A, 10B and Eq.13). Then, the filament extrusion speed is given by: . (16) Finally, the . (17) . (18) [0092] Since extruded filament in the air, rather than the deposited one, by moving the gantry system at a speed of v=dx/dt as specified in Eq.16, ultimately achieve a deposited filament that matches the dimension profile of the in Eq. 18 could be achieved. [0093] To calculate the volume solid fraction, as illustrated in FIG.4B, the number of pixels of filament areas were counted using a color range selection tool (funniness of 80; sampled the color from a specific point in the printed area) and divided by the total number of pixels of the examination window (10 mm × 10 mm; 1265 pixels × 1265 pixels) using a commercial software (Photoshop; Adobe Systems Inc.). The high-resolution images were acquired using a scanner (perfection v600 photo; Epson). [0094] FIGS.9A-9I illustrate image and graphical views of numerical calculation of surface roughness for additively manufactured surface structures shown in FIG.4C. FIG.9A illustrates a cross-sectional photo of the structure fabricated with a circle-shaped fixed nozzle. FIG.9B illustrates an extracted wall lines of the printed (in light grey) and target (in dark grey) from, FIG.9A. FIG.9C illustrates an error E, representing the difference between the target and printed wall of (B), plotted along the Y-coordinate. FIG.9D illustrates a cross- sectional photo of the structure fabricated with a square-shaped fixed nozzle. FIG.9E illustrates an extracted wall lines of the printed (in light grey) and target (in dark grey) from, FIG.9D. FIG.9F illustrates an error E, representing the difference between the target and printed wall of (E), plotted along the Y-coordinate. FIG.9G illustrates a cross-sectional photo of the structure fabricated with square and triangle modes of the adaptive nozzle. FIG.9H illustrates an extracted wall lines of the printed (in light grey) and target (in dark grey) from FIG.9G. FIG.9I illustrates an error E, representing the difference between the target and printed wall of (H), plotted along the Y-coordinate. [0095] FIGS.10A and 10B illustrate graphical views of size/shape-varying filament extrusion by AN3DP. FIG.10A illustrates an analytical model for the cross-sectional dimension of the filament, d'', along the extruded length, x, incorporating the nozzle exit dimension over time, d(t), ink input volumetric flow rate, F, nozzle volume as a function of exit dimension, V(d). FIG.10B illustrates an example photo of a filament with varying dimensions. [0096] FIGS.11A -11D illustrate image, schematic, and perspective views of potential applicability of using AN3DP within a fluid bath that serves as a support material to create complex vascular networks, though the specific implementation would need additional refinement. FIG.11A illustrates the setup for embedded printing with an adaptive nozzle in a fluid bath, along with the corresponding actuator setup used for the testing. FIG.11B illustrates a printing process in the bath; time order: top, middle, bottom. FIG.11C illustrates a structure resembling vascular network printed into the bath. FIG.11D illustrates an example of further refinement: an elongated and more pointed nozzle tip designed to minimize the disturbance of the bath fluid by the nozzle. [0097] For the surface smoothness calculation, as illustrated in FIG.4C, the background pixels were eliminated with a commercial software (Photoshop; Adobe Systems) from the photos obtained from a scanner (perfection v600 photo; Epson), as illustrated in FIGS.11A, 11D, and 11G, and then extracted border lines using a function ‘bwboundaries’ in the MATLAB (MathWorks) (FIGS.9B, 9E, and 9H). After calculating the error E between target walls and border lines of printed structures (FIGS.9C, 9F, and 9I), the roughness and are calculated as follows: , (19) , (20) where Y is an evaluation domain, as illustrated in FIGS.11C, 11F, and 11I. [0098] The various sizes and shapes of filaments, solid structures for demonstration, and vascular network-like structures were all fabricated on a gantry system (Engine SR, HYREL). The adaptive nozzle was attached to an ink-filled syringe (Becton, Dickinson and Company), which was loaded on a syringe pump (FUSION 200-X, Chemyx), to the nozzle inlet with a PVC tube (1/8’’ 1/4’’) and an adapter (25x Male luer lock 1/8" 3.2mm PP Hose Barb Adapter, RSN Lab). The various sizes and shapes of filaments, illustrated in FIGS.1I and 1H, were printed at a feed rate of 1 mm s-1 with corresponding flow rate from Eq.1. The print height h was set to twice the filament's height for each specific size and shape to preserve their cross-sectional shapes as much as possible. Both for fixed nozzles and adaptive nozzles, the solid structures for demonstration were printed at a feed rate of 1 mm s-1. The initial layers were printed at a height of 5 mm, with each subsequent layer increasing in height by 5 mm. For the square mode, a flow rate of 1.5 ml min-1 was used, while 0.95 ml min-1 for the triangle mode. The flow rate for the triangle mode was set slightly higher than the ideal rate of 0.75 ml min-1 after several tests. This adjustment was necessary because the three pins, which were supposed to be placed at the center of the nozzle exit to create a perfect straight slope of the triangle, could not reach it due to the minimum distance ( >0) from the center. Also, the three pins were manually further pushed towards the nozzle center to achieve as straight the slope as possible. The vascular network-like structures were printed at a constant flow rate of 1 ml min-1. The feed rate for each constant diameter printing section was set per Eq.1. However, for the diameter-transition sections, the rates were determined experimentally (Tables 1 and 2) but still set as constant for each section. The print height was set to 1.1 times the height (or diameter) of the filament for constant-diameter printing sections and was set to linearly vary for diameter-transition sections over time. In the under- extrusion printing process for the thinnest part with a diameter of 2 mm, the motor's rotation was adjusted to reach a diameter of 2 mm, while the realized diameter was the minimum diameter of the adaptive nozzle, 3 mm. To compensate for the parasitic height-change at the nozzle tip, the nozzle height was further lowered by 1 mm. This height adjustment made the under-extrusion process relatively successful, which is highly sensitive to the print height. Nevertheless, since 2 mm is a value smaller than the suggested radius to be achieved through the under-extrusion process from the physical diameter of 3 mm (10), it tended to show slightly inconsistent results. All prints were conducted using G-code, which was manually written. [0099] The circle and square-shaped fixed nozzles for comparison were fabricated with a 3D printer (Sonic Mini 8K, Phrozen) from high-resolution resin (Aqua Gray 8K, Phrozen), followed by being washed with isopropyl alcohol. The demonstration solid structures with the nozzles were conducted on the same gantry system (Engine SR, HYREL) and syringe pump (FUSION 200-X, Chemyx). [00100] All printed structures, except the filaments in FIGS.1H and 1I, were cured after the prints were done in an oven (heratherm, Thermo Scientific) at 80°C for 2 hours. [00101] The theoretical print time was evaluated for multi-scale structures given in FIGS.4D, 4E, 5D and 5E. For the functional solid parts in FIGS.4D and 4E, the print time t is approximated as of a part with volume with a nozzle diameter of L as , (21) where is a maximum feed rate achievable by the gantry system. The filaments are laid down such that their centerlines maintain a consistent distance L, thus, corresponding occupying cross-sectional area as .Then, print times with fixed nozzle with diameter of l, , and with AN3DP with diameter ranging from l to , , are given as , (22) , (23) where , , , l, and are total volume, volume of bulky solid parts, volume of detailed thin functional part, diameter of fixed nozzle exit (or the diameter of smallest mode of AN3DP), and diameter change range, respectively. The relative print time is calculated from the Eqs.22 and 23 as , (24) [00102] Meanwhile, for the multi-level vascular network in FIGS.5D and 5E, the print time t is approximated as a part with volume with a nozzle diameter of L as . (25) [00103] Here, the printed filament as it is printed, given by , since tree-like structures have a circular cross-sectional shape, which is the same as the circular filament. It allows the print time to be calculated more precisely on this specific example than the rough result in Eq.21. [00104] The total volume of m-level of vascular network is given as , (26) Where , (27) , (28) . (29) [00105] Here, , , and are the volume of a single branch of the mth-level, a constant length decreasing ratio at every bifurcation, and a constant radius decreasing ratio at every bifurcation, respectively. Then, the print time for the fixed nozzle with diameter of , , and AN3DP with diameter mode of for kth-level print, , are calculated as , (30) Since , calculated from the Eqs.30 and 31 could be calculated as (FIG.5E): . (32) Table 1 [00106] Feed rates and transition lengths used for each continuous diameter increase/decrease segment in the printing of structures resembling vascular networks in FIGS. 5A-5E, where the ink flow rate is 1 ml min-1. Diameter Transition time Feed rate Transition length chan e (s) (mm min-1) (mm) Table 2 [00107] Wait times to fill up the nozzle used for each discrete diameter change in the printing of structures resembling vascular networks in FIGS.5A-5E, where the ink flow rate is 1 ml min-1. Diameter change Wait time (mm to mm) (s) ACS-3DP [00108] Soft robots have garnered significant attention over the past decade for their ability to enable safe and adaptive interactions with the environment. Notable examples include soft robotic grippers capable of handling delicate objects such as fruits and glassware, bio-inspired soft robotic limbs designed for locomotion in unstructured terrains, and soft wearable devices for assistive rehabilitation. Central to these systems is the soft actuator, which enables complex object manipulation with simple control schemes. Among the various actuator types, inflatable actuators are often favored due to their capacity to generate large forces, achieve rapid actuation, and provide high compliance, all while comprising relatively simple, often single-material structures. These actuators operate by expanding internal voids or air channels with pressurized fluid or reducing volumes via vacuum. [00109] Various mechanisms have been developed to control the deformation of inflatable actuators, such as via designing complex air channel structures, by integrating them with 3D knitted or kirigami structures, or combining them with rigid components. However, extremely soft materials pose challenges to conventional subtractive manufacturing methods and many of these approaches still require manual assembly or multi-step molding, hindering complexity in shape and materials combinations, and scalability. As a result, researchers have fabricated hollow inflatable tubes with eccentric cross-sections through equally simple and elegant dip-coating and molding techniques, enhancing both manufacturability and scalability. [00110] To address molding-specific limitations, such as the need for a mold and limited local control, recent studies have explored 3D printing as an alternative. This approach enables fabrication without the need for manual assembly, but leads to prolonged production time and usually requires multiple voxel layers to create complex fluid channels, necessitating precise process controls to prevent defects such as air leaks. Additionally, traditional 3D printing methods such as fused filament fabrication or stereolithography often restrict material choices to less stretchable materials. [00111] In order to solve these deficiencies in the existing technology, in an embodiment of the present invention, a core can be added to the adaptive nozzle to facilitate an Adaptive Core-Shell 3D Printing (ACS-3DP) method, which builds upon AN3DP. ACS- 3DP adds a core to the actively controllable nozzle of AN3DP. The added core allows for the 3D printing of hollow core tubing and actuators. The present invention can be used for a direct ink writing process, known for its extensive material compatibility, including target materials for soft actuators, such as silicone rubbers. ACS-3DP enables the monolithic fabrication of hollow fiber actuators with precise control over wall thickness. It combines the dynamic functionality of an adaptive nozzle, which adjusts its cross-sectional shape during printing, with coaxial multi-material or multi-phase extrusion, previously used for creating composite core-shell materials or hollow filaments with uniform shell thickness for lightweighting. [00112] Unlike extruders with variable outlet shapes used in traditional formative manufacturing systems, the printhead of the present invention is lightweight, cost-effective, and compatible even with low-budget desktop 3D printers. It can be easily mounted on a gantry stage and connected to motor controllers via the operating software, making the system accessible to both hobbyists and professionals. Additionally, the ACS-3DP printhead enables rapid real-time adjustments, eliminating the need for manual setup changes. A key feature is its ability to simultaneously modify both the outlet shape and internal taper angle, optimizing extrusion for non-Newtonian shear-thinning inks like silicones. [00113] To achieve precise shell thickness control, undesired printhead deformation is minimized through mechanical reinforcements, while a tapered solid core with a wide, robust attachment at the ink inlet, gradually narrowing toward the tip, enhances core stability, as illustrated in FIGS.12A-12G. ACS-3DP precisely tunes wall thickness along the azimuthal angle within the cross-section, enabling accurate control of actuator deformation angles, actuation forces, and bending modes under pneumatic pressure, including targeted directional bending or largely undeformed states. Additionally, the precise local control provided by ACS-3DP allows for the integration of multiple unique deformation sections, within a single fiber, enabling complex deformation sequences under increasing pressure. By further modulating pressure profiles and utilizing viscoelasticity, differences in the actuator tip’s path during inflation and deflation can be introduced, facilitating cyclic and non-reciprocal motions using only a single pressure source. This makes ACS-3DP particularly relevant for mobile robotic applications, such as locomotion robots. [00114] FIGS.12A-12G illustrate perspective and sectional views of a nozzle and core design for minimizing Outlet Shape Errors in an Adaptive Core-Shell Nozzle. FIG.12A illustrates a perspective view of a solid core 42 attached to the ink inlet and the nozzle base 32. The solid core 42 is inserted into the nozzle base 32 after the adaptive nozzle 12 is integrated with the nozzle base 32. The pins 22 are actuated with cables, as shown in FIG. 12B the initial state to FIG.12C. FIG.12D illustrates a sectional view of an actuated state. The nozzle outlet shape may be distorted due to structural deformation caused by insufficient stiffness of the nozzle base. This distortion results in the nozzle outlet shape deviating from the ideal shape. To address this, as illustrated in FIG.12E a structural stiffener with wide anchoring points, as illustrated in FIGS.12F and 12G are added to the base plate, ensuring maximized moment arms, is introduced. [00115] The ACS-3DP printhead, as illustrated in FIG.13A, is based on an adaptive 3D printing nozzle and introduces an adaptive shell structure surrounding a circular solid core with a radius of rh, which creates hollow fiber cores, as illustrated in FIGS.13A and 13B. Fibers are typically printed on a substrate, resembling conventional material extrusion 3D printing, which works particularly well for long fibers with fiber length L fiber diameter 2Rf, as illustrated in FIG.13C. To avoid bending during extrusion and substrate-related imperfections, such as local flattening, short fibers, such as L > 2Rf , can also be extruded in air, which is advantageous for fibers with extremely thin wall thicknesses, as illustrated in FIG.13D. The precisely controlled variable thickness between the core and shell, as illustrated in FIG.13E, enables the generation of hollow fibers with azimuthally varying wall thickness, which can be adjusted in real-time along the fiber’s length. The printhead is mounted on a Cartesian gantry system that manages both printhead motion and the actuation of the printhead using microchips. The extrusion process utilizes a volumetric extruder for precise flow rate control. [00116] FIGS.13A-13F illustrate image and diagrammatic views of adaptive core- shell nozzle extrusion of hollow inflatable fibers. FIG.13A illustrates a photograph of the adaptive core-shell nozzle printhead. FIG.13B illustrates photos of the bottom view of the adaptive nozzle (left) and schematics of the corresponding target outlet modes (right) for extruding the ’fixed’ section (i) and deforming sections with four different directions (ii-v), where the arrows indicate the directions of the thinnest shell. FIGS.13C and 13D illustrate perspective views of inflatable fibers that are printed on a substrate or extruded in the air. FIG.13E illustrates a cross-sectional view of FIG.13C in the X-Z plane, showing how the solid core and adaptive shell create the thickness-varying inflatable fiber. FIG.13F illustrates photos of an inflatable fiber with two ’fixed’ sections (i) and a deforming section (ii) that bends upward under applied pressure, along with their respective cross-sections. For clarity, the outlets in FIG.13B are false-colored in black at 35% transparency to enhance contrast. Scale bar=5 mm. [00117] The outlet of the adaptive shell is octagonal, consisting of eight metal pin tips connected by a flexible silicone membrane forming the edges, as illustrated in FIG.13B. The membrane is designed to deform under actuated pin motion while resisting ink pressure. The distance (r) from the center to each octagonal vertex is controlled by actuators linked to the pins via cables. Actuator rotation pulls the cables, moving the pins outward, while compression springs restore them to their original positions. Four actuators are used, each controlling two neighboring pins, with control initially limited to two radii, r1 and r2, or a constant rf, as illustrated in FIG.13B. This simplification reduces control parameters for analysis while maintaining the ability to produce a practical variety of fibers. Using this configuration, ACS-3DP can fabricate hollow fibers consisting of ’fixed’ sections (i) and deformable sections oriented in four directions (ii-v). The ’fixed’ sections have a hollow radius of Rh and an outer radius of Rf , while the deformable sections have an outer radius varying between R1 and R2, as illustrated in FIG.13E. In the deformable sections, the region between the two pins closest to the fixed core achieves the smallest radius R1, while the opposite direction reaches the largest radius R2, as indicated by the arrow as illustrated in FIG.13E. The air channel in the core structure prevents negative air pressure and suction within the hollow filament as it is extruded, mitigating the risk of cross-sectional deformations or hole formation in thin wall sections. [00118] Polydimethylsiloxane (PDMS) rubber modified with fumed silica is used as the printing material due to its ability to maintain a hollow cross-section after extrusion, attributed to its substantial yield stress (τy = 500Pa) in the uncured state. Each fiber is printed at room temperature within seconds to minutes, while the pot life of PDMS lasts over three hours before significant thickening occurs, ensuring that curing time does not interfere with the printing process. The volumetric extruder automatically compensates for minor viscosity changes by adjusting pressure accordingly. After curing in an oven at 80°C, PDMS achieves a high elongation-at-break of approximately 500%, making it well-suited for inflatable fibers. Under pneumatic actuation (p > 0), the hollow fibers exhibit bending deflection towards the direction of R2 in the deforming section (R1 < R2) (ii), while remaining straight in the ‘fixed’ sections with an outer radius of Rf (i) as illustrated in FIG.13F. Even though only printing results with PDMS are shown herein, materials with higher stretchability, such as Ecoflex and Dragonskin, could also be used if greater deformation capability is needed. However, a rheology modifier, such as fumed silica, would be needed to ensure printability. [00119] The non-axisymmetric outlet shape of the ACS-3DP nozzle results in non- uniform fluid flow velocity at the outlet, with the flow being faster in the wider gap, as illustrated in FIG.14A. To quantify this effect, parameter sweep simulations were conducted by varying the shorter center-to-vertex distance r2 from 2.0 mm to 3.0 mm while maintaining the longer center-to-vertex distance r1 at 3.0 mm and the core radius rh at 1.5 mm. The results show that the fluid velocity ratio at the nozzle exit (V2/V1), where V2 and V1 are the minimum and maximum velocities, respectively, decreases as the nozzle asymmetry ratio (r1/r2) increases as illustrated in FIG.14B. This behavior arises due to the no-slip boundary condition of the fluid on the nozzle wall, which causes the fluid in the narrower gap to experience greater resistance from the walls than in the wider gap. This non-uniform extrusion velocity is likely to alter the cross-section of the printed filament from that of the nozzle outlet shape, particularly affecting the ratio of the thickest to the thinnest wall thickness (τ). [00120] FIGS.14A-14G illustrate graphical and image views of characterization of Adaptive Core-Shell Extrusion Process. FIG.14A illustrates a geometrical model of the adaptive core-shell nozzle for finite element simulation with a cross-sectional view (i). FIG. 14A illustrates fluid flow speed ratio (V2/ V1) as a function of the degree of nozzle asymmetry (r1/r2), where the color indicates the fluid flow speed at the nozzle exit. FIG.14C illustrates nozzle exit shapes with flow speed illustrated by color (top) and cross-sections of the printed hollow filaments fabricated by nozzle replicas, as illustrated in FIG.15B. FIG.14D illustrates thickness variation of the fibers in FIG.14C as a function of the azimuthal angle depending on the nozzle shapes (r2); analysis for r2 = 2.0mm is excluded due to an open cross-section. FIG.14E illustrates a photo of the printing process of a hollow fiber using a nozzle replica, as illustrated in FIG.14B, the nozzle exit shape (ii), and cross-sections of the printed filaments (iii) depending on the orientations of the thinnest filament thickness relative to the substrate (↑, →, ↓,←). FIG.14F illustrates thickness ratios (τ) of the printed filaments (T1/T2) to that of the nozzle outlet (t1/t2) depending on the nozzle shape (r1/ r2). FIG.14G illustrates photos of top views of filaments showing their surface qualities (false- colored in yellow). Scale bars=5 mm. [00121] To further analyze this hypothesis and isolate the effects of fluid velocity on the printed fil ament cross-sections from potential ACS-3DP nozzle and control errors, nozzle replicas were fabricated with fixed cross-sections, as illustrated in FIG.15C, replicating both internal and exit geometries of the ACS-3DP nozzle. Scanned images of the filament cross- sections, as illustrated in FIG.14C, and an analysis of wall thickness across azimuthal angles, as illustrated in FIG.14D, reveal significant differences between the nozzle outlet and the resulting printed filament shapes. [00122] FIGS.15A-15C illustrate perspective and schematic views of design of nozzle replicas for characterizing the adaptive core-shell nozzle extrusion process in FIGS.14A- 14G. FIG.15A illustrates an iso-view and FIG.15B illustrates a cross-sectional view of the nozzle design. FIG.15C illustrates bottom views of different nozzles (r2 = 3mm to 2 mm), illustrating outlet shapes colored in black. The air channel, centered within the solid core structure, is highlighted in white. [00123] To exclude errors caused by substrate-induced deformation of different shell sections, the experiments were repeated using various printing directions, as illustrated in FIG.14E and FIG.16A. Printing directions were defined based on the orientation of the thinnest thickness of the filament relative to the substrate: facing downward (Z–), rightward (Y+), leftward (Y–), or upward (Z+), as illustrated in FIG.14E. Filament thickness was analyzed in each orientation, as illustrated in FIG.16B, and averaged the thickness ratios (T1/T2). As expected, the results, as illustrated in FIG.14F, show that the average thickness ratio (T1/ T2) consistently exceeds the nozzle outlet ratio (t1/t2) across all orientations. Moreover, the discrepancy in τ becomes more pronounced as nozzle asymmetry increases, i.e., as (r1/r2) increases, as illustrated in FIG.14F, because the velocity ratio (V2/V1) decreases with greater nozzle asymmetry, as illustrated in FIGS.14B and 14F. [00124] FIGS.16A and 16B illustrate image and graphical views of a full set of cross- section images and thickness analysis results of hollow fibers printed with nozzle replicas. FIG.16A illustrates scanned images of printed fibers (”printed”) and the outlet shapes of the nozzles used to print them (”nozzle”), depending on the nozzle shape (r2 = 2.0mm to 3.0 mm, with r1 kept constant at 3.0mm for all nozzles) and print direction (↑, →, ↓, ←), which denotes the orientation of the thinnest shell relative to the substrate. The coordinate systems are consistent with FIG.14E; scale bar, 5 mm. FIG.16B illustrates thickness variations of the fibers in FIG.16A as a function of the azimuthal angle, depending on the nozzle shapes (r2) and print directions. [00125] The top views of the printed fibers demonstrate their continuity and surface quality, as illustrated in FIG.14G. With a relatively lower degree of asymmetry (r2 = 2.3 mm), the printed fibers exhibit smooth surfaces. However, as the asymmetry increases, the surface becomes progressively nonuniform 153 (r2 = 2.2 mm), leading to the gradual emergence of voids (r2 = 2.1 mm) and eventually resulting in a fully open fiber (r2 = 2.0 mm). Even small voids can cause air leakage, rendering the printed actuator nonfunctional. Consequently, excessively asymmetric nozzle configurations were avoided in the demonstrations and applications of the present invention, though further optimization of materials and process parameters may improve the quality of printed structures and enable fibers with higher stable asymmetry ratios. [00126] Given the material’s relatively high yield stress (τy ≈ 500 Pa) and storage modulus (G′ ≈ 104 − 105 Pa), surface tension is likely negligible. Similarly, while capillary forces may influence shape at smaller scales, the material’s resistance to deformation minimizes any significant effects. However, further analysis could potentially reduce the achievable r2 and optimize the wall thickness ratio. [00127] Finally, to evaluate the repeatability of the ACS-3DP process, seven repeated tests were conducted for each of two different outlet configurations using the actual adaptive core shell nozzle rather than fixed-outlet replicas, as illustrated in FIGS.17A and 17B. The standard deviation of the normalized root mean square (RMS) value relative to the mean curve was 0.0047 for the outlet shape with r1 = 5.3 mm and r2 = 5.9 mm, as illustrated in FIG. 17A, and 0.0326 for the outlet shape with r1 = 4.8 mm and r2 = 5.9 mm, as illustrated in FIG. 17B. Both cases demonstrated high repeatability, confirming the reliable production of inflatable fibers using the ACS-3DP method. However, the more asymmetric configuration, as illustrated in FIG.17B, exhibited a larger standard deviation, indicating increased extrusion instability, as observed in FIG.14A-14G. [00128] FIGS.17A and 17B illustrate schematic views of repeatability of actuator cross-section production. FIG.17A illustrates a schematic view of the target design and scanned cross-sections (1–7) of fibers extruded from an adaptive core-shell nozzle with an outlet shape of r1 = 5.3, mm and r2 = 5.9, mm, and a hole radius of 2.5 mm (top), along with thickness variations as a function of azimuthal angles (bottom). FIG.17B illustrate schematic views of the target design and scanned cross-sections (i–vii) of fibers extruded from an adaptive core-shell nozzle with an outlet shape of r1 = 4.8,mm and r2 = 5.9, mm, with a hole radius of 2.5 mm (top), along with thickness variations as a function of azimuthal angles (bottom). Scale bars, 10 mm. [00129] To investigate the parameter space more broadly, parameter sweeps were conduct using finite element analysis, focusing on how fiber geometries influence the bending angle α and actuation force, Fact, as illustrated in FIGS.18A-18K. For the analysis, the cross-section of the deformable section (II) of the printed filament is assumed to be an octagon with four shorter and four longer center-to-vertex distances, enclosing a circular hole. The ’fixed’ section (I) is modeled as a regular octagon with a circular hole, as illustrated in FIG.18A. A single-joint structure comprising a deformable section (II) sandwiched between two ’fixed’ sections (I), is assumed three parameters are selected for the sweeps, as illustrated in FIG.18A: the actuating joint length La, the degree of asymmetry τ , and the cross-sectional area Aratio, defined as the ratio of the area of the hole to the area of the skin. [00130] The degree of asymmetry τ and the cross-sectional area Aratio are defined as follows: Where R1 and R2 are the distance from the center of the hole to the nearest vertex and the distance to the farthest vertex of the deformable section (II), respectively. The value Rh denotes the radius of the hollow hole. The outer radius of the fixed section (I), Rf, is set to Rf=2Rh to ensure that section (I) undergoes minimal deformation compared to the deformable section (II), and the lengths of section (I) are set to La/2. [00131] The inflatable fiber is fixed at its base, with the other side remaining unconstrained, as illustrated in FIGS.18B and 18C. Input pressure p is applied along the side wall of the inner hole, causing the non-symmetric fibers to deflect with a bending angle α that increases as τ , La, or Aratio increases. These results align with previous studies on soft bending actuators, which demonstrated that the bending angle increases as the material’s shear modulus decreases or as the relative thickness of the skin decreases—corresponding to the parameters τ and Aratio, respectively. The input pressures for the simulations (p = 70 kPa, as illustrated in FIG.14B, and 30 kPa, as illustrated in FIG.18C, are selected as values that clearly highlight the differences in the deformed shapes caused by the parameters. The effect of input pressure p on the bending angle α for a fiber with parameters La = 30 mm, Rh = 1.5 mm, R1 = 1.9 mm, and R2 = 2.6 mm, as illustrated in FIG.18D, is further examined. The results show a clear increase in the deflection angle as the actuation pressure rises, with deflection reaching nearly 180◦ at p = 96 kPa. [00132] Next, the effects of inflatable fiber geometry on actuation force Fact are assessed. An inflatable actuator with a fixed base , as illustrated in FIG.18E, is analyzed. The tip of the inflatable actuator presses against a solid wall, generating a contact force (Fact). Simulation results show that Fact increases as τ or Aratio increases, as illustrated in FIGS.18E and 18F, which again aligns with previous studies. Additionally, to investigate the effect of input pressure p on the contact actuation force Fact, simulations are conducted on an inflatable fiber with parameters La = 25 mm, Rh = 1.5 mm, R1 = 2 mm, and R2 = 3 mm by varying p, as illustrated in FIG.18G. The results show that Fact increases exponentially as the input pressure p rises. Finally, to demonstrate the substantial actuation force achievable with single fibers produced via ACS-3DP, the effect of hole size on Fact is investigated using a fiber with a larger hole radius (Rh = 3 mm) , as illustrated in FIG.18H. The results show that a contact force of approximately 0.2 N can be obtained under a reasonable input pressure of 100 kPa. Based on these observations, fibers with hole radii of Rh = 2.5 mm and Rh = 3 mm are selected for subsequent applications. [00133] FIGS.18A-18K illustrate graphical and image views of characterization of inflatable fiber deformation. FIG.18A illustrates a schematic of an inflatable hollow fiber consisting of a deformable section (II) surrounded by ’fixed’ sections (I). Bending angles (α) of the inflatable fibers obtained by finite element analysis: FIG.18B illustrates a function of the degree of asymmetry (τ) and joint length (La) under an actuation pressure (p) of 70 kPa. FIG.18C illustrates as a function of area ratio (Aratio) and joint length (La) under an actuation pressure (p) of 30 kPa. FIG.18D illustrates a variation of α for an inflatable fiber (La = 30 mm, Rh = 1.5 mm, R1 = 1.9 mm, and R2 = 2.6mm) with p. FIG.18E illustrates a definition of actuation force (Fact) (top) and how it varies with τ and La (bottom), or f) with Aratio and La under p of 50 kPa. FIGS. 18G and 18H illustrate a variation of Fact with p for two different hole sizes (Rh): FIG.18G illustrates Rh = 1.5mm and FIG.18H illustrates Rh = 3 mm. FIGS. 18I-18K illustrate a demonstration of an inflatable fiber deforming into a complex 3D shape: FIG.18I illustrates a design of the fiber with seven sections (1-7), FIG.18J illustrates a cross- sectional view in the X-Y plane (top), in the X-Z plane for each section where arrows indicate the orientation of the thinnest shell (center), and exterior view of the fabricated actuator from the X-Y direction (bottom), and FIG.18K illustrates a fabricated fiber before actuation (left) and after actuation (right). To validate the experiments and demonstrate sequential actuation, a fiber following a complex 3D path is designed and fabricated, as illustrated in FIGS.18I-18K, where each section is designed to rotate by approximately 90 degrees from sections i to vii. Upon applying input pressure, the fiber, initially straight, deforms into a 3D shape as each section bends in the direction of its thickest wall, as illustrated in FIG.18K. The resulting shape aligns closely with the target design, as illustrated in FIG.18I, confirming the functionality of the fibers produced through the ACS- 3DP process. Finally, a low-cycle fatigue test was conducted on the inflatable fibers, as illustrated in FIGS.19A-19C. Under large-deformation actuation as illustrated in FIG.19A, the fibers exhibited a gradually increasing bending angle with repeated cycles at constant pressure and eventually ruptured after approximately100 cycles. For smaller deformation, as illustrated in FIG.19C, the fiber maintained a consistent bending angle for thousands of actuations, comparable to the cycle life of traditional inflatable actuators. While the cycle life is lower than that of rigid actuators, this trade-off is inherent to soft actuators and partially offset by the fast, low-cost customized ACS-3DP fabrication approach. [00134] FIGS.19A-19C illustrate image and graphical views of low-cycle fatigue tests of single-joint fibers. FIG.19A illustrates a single-joint fiber used in the fatigue test, consisting of a deformable section (ii) between two fixed sections (i and iii) (top), with scanned cross-sections of each section (i, ii, iii) (bottom). FIG.19B illustrates a bending angle (α) over test time (s) for large-deformation actuation under an input air pressure of 24 psi (165.47 kPa). Maximum and minimum bending angles at each cycle are marked by blue and red circles, respectively. The actuator ruptured after 124 cycles, following the last cycle shown in the graph. FIG.19C illustrates a smaller deformation actuation test under an input air pressure of 17 psi (117.21 kPa). Maximum and minimum bending angles at each cycle are marked by blue and red circles, respectively. The total cycle count is approximately 2000; scale bars, 10 mm. [00135] FIGS.20A-20F illustrate image and graphical views of a customized hand- assistive device fabricated using ACS-3DP. FIG.20A illustrates the design of five inflatable fibers for the assistive device and a photo of the wearer’s hand. FIG.20B illustrates that each fiber is controlled by an individual pressure (p1 to p5), assisting each phalanx. FIG.20C illustrates the device, whose cross-sectional views of the non-deform ’fixed’ section (I) and the deformable section (II) are shown on the right, enables various assistive modes, including FIG.20D, which illustrates a pincer grasp (p4, p5 > 0), FIG.20E illustrates a tripod grasp (p3, p4, p5 > 0), and f) hook grasp (p1 to p5 > 0), showing before actuation (i) and after actuation (ii). Scale bars, FIG.20A: 100 mm and FIG.20C: 10 mm [00136] To demonstrate the suitability of ACS-3DP for functional robotic structures that adaptively and seamlessly interact with their environments, a customized hand-assistive device was fabricated, as illustrated in FIGS.20A-20F. Hand-assistive devices augment the grasping force of patients with impaired hand function or support rehabilitation to restore hand-manipulating abilities. To maximize efficiency and ensure safety while transmitting the required force, actuators were customized to align with the wearer’s hand anatomy. The device consists of five fibers, each featuring multiple segments corresponding to the fingers, as illustrated in FIG.20A. For the actuators for the index and middle fingers, ’fixed’ segments align with the rigid phalanx sections of the fingers, while deformable segments are positioned over the finger joints. The thumb and ring finger actuators comprise a single deformable section, while the ring finger actuator contains one deformable section and one ’fixed’ segment. The detailed design is shown in FIG.21. [00137] FIG.21 illustrates an image view of a hand-assistive device design overlay of deformable and non-deformable (’fixed’) sections, with dimensions in mm, for the target design of the hand-assistive device. The dimensions are aligned with the locations of the hand’s joints and phalanges. Notably, the second and third fingers are replicated with added complexity to facilitate complex tasks. [00138] All deformable sections are designed so that the thickest sides make contact with the hand, ensuring the inner, expandable side bends naturally along the fingers’ movement direction. By attaching and controlling five independent compressed air sources (p1 p5), as illustrated in FIG.20B, the fabricated hand-assistive device, as illustrated in FIG.20C, performs various grasping modes required for daily tasks. For example, the device enables pincer grasping, as illustrated in FIG.20D, for manipulating small objects by actuating the thumb (p5 > 0) and index finger (p4 > 0), tripod grasping, as illustrated in FIG. 20E, for tasks like writing by actuating thumb (p5 > 0), index finger (p4 > 0), and middle finger (p3 > 0), and hook grasping, as illustrated in FIG.20F, for holding large objects, such as a cup, by actuating all fingers (p1 p5 > 0). The assistive force at each joint of the device is approximately 1 N under an input air pressure of around 150 kPa, as illustrated in FIGS.22A- 22C, closely aligning with the simulation results, as illustrated in FIGS.18G and 18H, and comparable to other soft actuators for hand assistance, which generate approximately 2 N at the same pressure. [00139] FIGS.22A-22C illustrate schematic and graphical views of actuation force measurement of inflatable fiber. FIG.22A illustrates a schematic of single-joint fiber design with a deformable section (ii) between fixed sections (i and iii) (top), along with its cross- section (bottom). The right end of the fiber is clamped, while all other sides remain unconstrained. FIG.22B illustrates that the fiber inflates, its left end contacts the ground, generating an actuation force fact. FIG.22C illustrates a graphical view of actuation force (fact) as a function of input air pressure (p), with corresponding images of the fiber at each pressure level; scale bars, 10 mm. [00140] The ACS-3DP process is relatively faster than other manufacturing methods and can produce various customized fibers without requiring setup changes. This capability allows users to replace actuators more frequently at a low cost—an important advantage given the susceptibility of soft actuators to damage and the varying and changing assistance levels required by patients during rehabilitation as their symptoms improve. A drawback of inflatable actuators is their reliance on compressed air. While this can be partially addressed through solutions such as air supplies for at-home rehabilitation or portable, backpack like devices, in the future, this fabrication method can be integrated with more accessible technologies, such as battery-driven dielectric elastomer actuators. [00141] To further demonstrate the capabilities of ACS-3DP, a crawling turtle robot was fabricated to demonstrate the invention, as illustrated in FIGS.23A-23H. Studies have shown that the complex kinematic motions of a turtle’s fins enable adaptive maneuvering over challenging terrains, as illustrated in FIG.23A, serving as inspiration for mimicking such motions with advanced soft actuators. Here, complex kinematic motion can be achieved using only a single pressure source per fin by employing pre-programmed inflatable fibers, as illustrated in FIG.23B. Specifically, inflatable fibers consisting of five sections (i–v) are designed, as illustrated in FIG.23C. Sections i, iii, and v are structured to remain largely undeformed under actuation pressure, while sections ii and iv deform significantly. Section ii has a thin wall in the Y+ direction, causing it to bend in the Y– direction when pressurized, whereas section iv has a thin wall in the X+ direction, resulting in bending in the X– direction. Additionally, the wall thickness difference between the thinnest and thickest sides in section ii is more pronounced than in section iv, ensuring that section ii bends before section iv as the input pressure increases. [00142] FIGS.23A-23H illustrate graphical and image views of an ACS-3DP of inflatable fibers for a crawling turtle robot. FIG.23A illustrates a sea turtle in nature that crawls using its fins, and FIG.23B illustrates a turtle robot that mimics this locomotion mechanism using inflatable fibers. FIG.23C illustrates an exemplary actuator design for the right fin. FIG.23D illustrates a crawling mechanism of the turtle robot (top) with actuation schemes of the inflatable fibers (bottom) provided as the pressure (p) profile over a cycle. FIG.23E illustrates a sequence of the extrusion process. FIG.23F illustrates a surface view (left) and cross-sectional view of the inflatable fiber, where white arrows indicate the orientation of the thinnest shell. Scale bar=5 mm. FIG.23G illustrates a trajectory of a tracking point marked on the inflatable fiber for one cycle in the X-Y plane, showing sequential and hysteretic actuation even under a single pressure source. FIG.23H illustrates snapshots of the turtle robot moving in the X+ direction during a single actuation cycle. [00143] With the inflatable fiber design, the turtle robot progresses in the X+ direction under cyclic pneumatic actuation, as illustrated in FIG.23D. During the initial low-pressure phase—Inflation Phase I—the inflatable fins lift the robot’s body as segment ii actuates while the other segments remain inactive. As the actuation pressure (P) increases during Inflation Phase II, the fins propel the body forward in the X+ direction and lift it further, with segment iv being primarily actuated while segment ii remains largely constant. Finally, during the Deflation Phase, the fins return to their original shape as the pressure rapidly decreases. Importantly, due to the hysteresis of soft materials, the fins follow a different path during deflation compared to inflation, as shown in the side view (vi). This hysteresis motion is critical for forward crawling, as noted in previous studies, since without it, the robot would merely oscillate in place. [00144] The inflatable fibers are fabricated sequentially from section i to v, as illustrated in FIG.23E, using ACS-3DP. The top view of the fabricated fiber highlights clear transitions from section ii to iii (I) and from sections iii and iv to v (II), with corresponding cross-sections shown on the right, as illustrated in FIG.12F. The printed fiber exhibits hysteresis, as confirmed through video tracking analysis using a high-speed camera, as illustrated in FIG.23G, which enables sequential actuation: bending occurs in the Y– direction during Inflation Phase I, followed by bending in the X– direction during Inflation Phase II. Also, the sequence of actuation can vary depending on the design. When integrated with a pressure system, the turtle robot crawls forward in the X+ direction under gradual inflation and rapid deflation cycles, as illustrated in FIG.23H. Each actuation cycle takes approximately 2 s and produces a forward motion of 4.3 mm, corresponding to approximately 2.5% of the turtle’s body length. [00145] An Adaptive Core-Shell 3D printing process is presented herein for the direct and monolithic fabrication of anisotropic inflatable fiber actuators. The fabricated fibers consist of ‘fixed’ and deformable sections, with the deformable sections designed to bend in various spatial directions under applied pressure. The degree of bending and the sequence of actuation for each segment are controlled through thickness variations along the azimuthal direction within the cross-section and through actuation speed, respectively. The applicability of these anisotropic fibers is demonstrated in robotic applications, including a customized hand-assistive device and a crawling turtle robot that leverages viscoelasticity to achieve non- reciprocal fiber deformation using a single pressure input. [00146] In the next generation of the ACS-3DP method, the co-extrusion of sacrificial material can be incorporated into the inner hollow channel alongside the elastomeric shell material. This enhancement would improve the stability of the ACS-3DP process by minimizing distortion of the hollow section and expand its usability by enabling the stacking of multiple fibers in three-dimensional space. Finally, ACS-3DP may be integrated with different 3D printing methods, such as multi-material or subvoxel printing, enabling fibers to achieve higher actuation forces by incorporating strain-constraining rigid material strips or functionalities like sensing. Further, applying a multi-core system to ACS-3DP could enable the fabrication of multi-DOF actuation fibers, whereas the current design is limited to one DOF, significantly expanding its potential applications. [00147] Materials: The extrusion ink materials are prepared using a PDMS material (DOWSIL SE 1700; Dow Corp.) by mixing the material with 10% w/w curing agent in a centrifugal mixer (2000 rpm for 2 minutes; Flak-Tek). The colors are adjusted by adding 0.24% w/w pigment (Silc-Pig; Smooth-On). Adaptive Core-Shell Printhead: The printhead is modified from a previous design proposed in reference, which outlines the details of the printhead. A solid core structure is added to the ink inlet component, as illustrated in FIG. 12A. Since even minor deflection in the nozzle base significantly affects the precision of the extruded filament, as illustrated in FIGS.12B-12D, the nozzle is reinforced with a stiffener, as illustrated in FIG.12E. Specifically, when the nozzle is actuated from its initial state, as illustrated in FIG.12B, to expand one side, increasing the outlet thickness in that direction to l1, as illustrated in FIG.12C, an insufficiently stiff nozzle base may deform under the actuation force applied at its top. This deformation distorts both the core structure and pin positions, resulting in a mismatch in the exit configuration, where l′1 ≠ l1 and l′2 ≠ l2, as illustrated in FIG.12D. The added stiffener, as illustrated in FIG.12E, maximizes the anchoring points’ width, increasing stiffness in the X-Z plane, as illustrated in FIG.12F. Additionally, the height of the anchoring points is maximized to enhance stiffness in the Y-Z plane, as illustrated in FIG.12G. [00148] To provide additional stability during extrusion, the core structure is designed to protrude from the adaptive nozzle shell, as proposed in reference. An air channel outlet is incorporated into the core’s center, preventing hollow core shrinkage caused by potential negative pressure. Both the nozzle base and the ink inlet module with the solid core are fabricated using a Digital Light Processing (DLP) 3D printer (Sonic Mini 8K, Phrozen) and washed with isopropyl alcohol to prevent clogging. [00149] Silicone rubber membranes and compression springs with different geometries are used depending on the diameter range of the inflatable fibers to be printed. These components define the diameter range achievable by the adaptive nozzle. For inflatable fibers with an outer diameter range of 3 mm–10 mm, as illustrated in FIGS.13, 14, 17-20, and 22, a longer compression spring (free length 20 mm, OD 6 mm; CREEYA compression springs assortment kit) and a membrane with an initial tip diameter of 2 mm are used. For fibers with an outer diameter greater than 10 mm, as required for the turtle robot application, as illustrated in FIGS.12A-12H, a shorter compression spring (free length 15 mm, OD 6 mm; CREEYA compression springs assortment kit) and a membrane with an initial tip diameter of 5 mm are used. The latter configuration allows the adaptive nozzle to expand to larger diameters. ACS-3DP and 3D Printing with Nozzle Replica: All inflatable fibers are printed or extruded using a gantry system (Engine SR, HYREL). The adaptive nozzle with a solid core structure is connected to a syringe filled with printing ink (Becton, Dickinson and Company), mounted on a syringe pump (FUSION 200-X, Chemyx). The syringe is linked to the nozzle inlet via a PVC tube (1/8 inch x 1/4 inch) and an adapter (25x Male luer lock 1/8 inch 3.2- mm PP Hose Barb Adapter, RSN Lab). [00150] The fiber designed to deform into a 3D shape for demonstration, as illustrated in FIGS.18J and 18K, is fabricated on a substrate with a core structure of rh = 1mm. The nozzle outlet geometry is set as r1 = 4mm and r2 = 2.66mm for every section (i-vii) with varying orientations, and the length of each section is 15 mm. The flow rate is set at 3.5 ml min−1, while the print height (a gap between the nozzle tip and the substrate) is maintained at 8 mm for all sections. [00151] The fibers for the repeatability test are fabricated in air with a core structure of rh = 2.5mm under a constant flow rate of 2 ml min−1, and are illustrated in FIGS.17A and 17B. [00152] The fibers for the low-cycle fatigue test, as illustrated in FIGS.17A and 17B, are fabricated in air with a core structure of rh = 2.5mm under a constant flow rate of 2 ml min−1. The length of the deformable section ii, la, is set as 19 mm. [00153] The fibers for the hand-assistive device, as illustrated in FIGS.20A-20F, are fabricated with a core structure of rh = 2.5mm. The single-joint version of a fiber in the hand assistive device for actuation force measurement is fabricated in air with a core structure of rh = 2.5mm, and the length of the deformable section ii, la, is set to 19 mm, as illustrated in FIGS.12A-12C. The nozzle outlet is adjusted to produce deformable section (ii) to be nearly identical to deformable section of the hand assistive device, as illustrated in FIGS.15D-15F and ’fixed’ sections (i and iii) to that of the device, as illustrated in FIGS.15D-15F. [00154] The fiber for the turtle robot, as illustrated in FIGS.13A-13G is fabricated with a core structure of rh = 3mm. The nozzle outlet geometry is set as r1 = r2 = 7mm for sections (i, iii, v), r1 = 7mm and r2 = 4.66mm for section (ii), and r1 = 7mm and r2 = 5mm for section (iv). Under a constant flow rate of 2 ml min−1, the extrusion times are set as follows: 25 s for section (i), 35 s for section (ii), 50 s for sections (iii) and (iv), and 100 s for section (v). [00155] The filaments fabricated on a substrate to characterize the extrusion process using the nozzle replicas, as illustrated in FIGS.13A-13G are printed at a constant flow rate of 2 ml min−1 and a constant feed rate of 60 mm min−1 with a print height of 10 mm. The fiber shown in FIGS.18A-18K is cured in an oven (Heratherm, Thermo Fisher Scientific) for 1 hour at 80°C, while the other fibers, as illustrated in FIGS.13, 17, 19, 20, 22, and 23 are cured for 30 minutes at the same temperature. [00156] Fluid Flow Simulation: A commercial multiphysics simulation software (COMSOL Multiphysics 6.1, COMSOL) is used to numerically analyze fluid flow inside the adaptive core shell nozzle, as illustrated in FIGS.14A-14G. Since the extrusion process can be characterized as low-Reynolds number fluid flow, the Laminar Flow module is utilized. The ink’s non-Newtonian shear thinning behavior is modeled using the Herschel-Bulkley- Papanastasiou model, with the following assumed parameters: a fluid consistency coefficient (m) of 900 Pa· s, a flow behavior index (n) of 0.23, and a yield stress (τy) of 500 N/m2. A ’no- slip’ boundary condition is applied to the walls, while a mass flow rate of 0.1608 × 10−4, kg/s (equivalent to 2, ml/min for the SE 1700 ink) is imposed at the inlet, effectively assuming a uniform positive pressure at the nozzle inlet. The pressure then gradually decreases to a static pressure of 0 Pa (ambient conditions) at the outlet. Due to nozzle asymmetry and the ink’s rheological properties, the rate and distribution of the pressure drop vary around the outlet, leading to local deviations in flow rates. The simulation employs the ’Physics-Controlled Mesh’ option with an element size set to ’Finer’ to ensure accurate resolution of flow characteristics. [00157] Finite Element Analysis of Inflatable Fibers: A commercial multiphysics simulation software (COMSOL Multiphysics 6.1, COMSOL) is used to numerically investigate the solid behavior of the inflatable fibers. A stationary analysis is conducted, taking into account geometrically nonlinear behavior. A Mooney-Rivlin hyperelastic model with nine parameters for rubber is used to model the cured SE 1700 material. Fixed constraints are imposed at the bottom of the fiber, while a pressure load is applied to the inner walls of the fiber to simulate air pressure. [00158] For the contact force simulations, as illustrated in FIGS.18E-18H, an aluminum plate is virtually placed parallel to the actuator with a gap of 0.1 mm. A contact condition using the ‘Penalty’ method provided by the software is imposed between the fiber and the plate. The ‘Physics- Controlled Mesh’ option with a ’Normal’ element size is used. To solve the geometrically nonlinear problem, input pressure is employed as a continuation parameter. An interval of 10000 Pa is used for deformation investigations, as illustrated in FIGS.18B and 18C, and an interval of 1000 Pa is used for contact force investigations, as illustrated in FIGS.18E and 18F, starting from 0Pa. [00159] For exploring the effect of input pressure on the bending angle, as illustrated in FIG.18D, and the contact actuation force of an inflatable fiber with a hole radius rh = 1.5mm, as illustrated in FIG.18G, a continuation method with an interval of 100 Pa is used, and all intermediate results are utilized for the graphs. For the exploration of the effect of input pressure on contact force with a fiber with a hole radius rh = 3mm, as illustrated in FIG. 18H, an interval of 1000 Pa is used, and all intermediate results are included in the graph. [00160] To automatically conduct the parameter sweep while changing design parameters, an automated MATLAB code is used in conjunction with an interface program (COMSOL Multiphysics 6.1 with MATLAB interface, COMSOL). [00161] For the investigation of the effects of parameters τ and La, as illustrated in FIGS.18B and 7G, La is varied from 5 mm to 30 mm in increments of 5 mm, and R2 is varied from R1 to 2Rh in increments of 0.1 mm, where with Aratio = 1.5. [00162] For the investigation of the effects of parameters Aratio and La, as illustrated in FIGS.18C and 7F, La is varied from 5 mm to 30 mm in increments of 5 mm, and R2 is varied from Rh + 0.1mm to 2 Rh in increments of 0.2 mm, while ensuring that the hole radius Rh remains smaller than the closest point to the center on the outer cross-section. This condition is expressed as: where R1 = Rh + (R2 − Rh). [00163] The bending angles (α) are derived as the angle between the line connecting the centers of the top and bottom 8 vertices of the octagonal prism-shaped ’fixed’ section (I) and the original longitudinal direction of the undeformed fiber. The contact actuation forces (Fact) are obtained directly from the finite element analysis software. [00164] Calibration of Adaptive Nozzle: The adaptive nozzle is carefully calibrated before each extrusion, as the behavior of inflatable fibers is sensitive to thickness errors. A microscopic camera (AF4115ZTW 1.3-MP wide-angle FLC wireless-ready polarizer, SunriseDino) is used to observe the bottom of the nozzle during calibration. [00165] High-speed Video Analysis: The sequential actuation with hysteresis of the inflatable fiber for the turtle robot is recorded using a high-speed camera (FASTCAM SA5, Photron). Tracking points are marked on the inflatable fiber and analyzed using the ’vision.PointTracker’ function in MATLAB, which employs the Kanade-Lucas-Tomasi (KLT) algorithm. A single tracking point showing the clearest path is selected for the tracking analysis. [00166] Cross-Sectional Analysis of Printed Fibers: The cross-sections of the fibers printed with nozzle replicas are analyzed using MATLAB code. Regions of interest on the cross-section images are selected using the roipoly function. Small noise and bubbles are removed using the bwareaopen function with a threshold of 500. The inner and outer boundaries are extracted using the boundaries function. Finally, assuming the center of the inner hole as the mean coordinate of the inner boundary, the distance between the inner and outer boundaries from the center is calculated as a function of the azimuthal angle, ranging from 0◦ to 360◦. The cross-sectional analysis to investigate the repeatability of the ACS-3DP process is conducted in the same manner. After obtaining the thickness as a function of the azimuthal angle, the seven curves are averaged and the root mean square (RMS) value of each curve is calculated with respect to the mean curve. Then, the RMS values are normalized by dividing them by the mean distance of the mean curve. Finally, the standard deviation of the seven curves is computed based on the mean RMS values. These values are obtained for each of the seven repeated tests for the first outlet shape, as illustrated in FIG. 17A, and the second outlet shape, as illustrated in FIG.17B. [00167] Hand-assistive Device: A nitrile glove (heavy-duty nitrile gloves, large size, Medprayer) is used as the orange glove for the hand-assistive device, with the inflatable fibers adhered to it using instant adhesion (Super glue, Loctite). Each fiber is connected to a syringe (Becton, Dickinson and Company) through silicone tubing (1/8” inner diameter × 3/16” outer diameter, uxcell) via adapters (male luer lock, 1/8 inch, MEETOOT). The fibers are actuated with air. [00168] Turtle Robot : The turtle robot body is designed using SolidWorks, as illustrated in FIGS.14A and 14B, and fabricated with a DLP 3D printer (Sonic Mini 8K, Phrozen) using high-resolution resin (Aqua Gray 8K, Phrozen). For visual purposes, the body is coated with a liquid rubber material (Flex Seal, Flex Seal). The printed fibers and robot body are connected via adapters (male luer lock, 3/16 inch, MEETOOT) with additional sealing to prevent air leakage. A Kevlar cable (0.014 inch in diameter, McMaster) is routed for this purpose. The air inlet of the robot body is connected to a syringe (Becton, Dickinson and Company) via silicone tubing (1/8” inner diameter × 3/16” outer diameter, uxcell) and an adapter (male luer lock, 1/8 inch, MEETOOT). The fibers are actuated with air. [00169] FIGS.14A and 14B illustrate a turtle robot body design. FIG.14A illustrates an iso-view of the CAD design of the robot body. FIG.14B illustrates a transparent top view of the body showing air channels that connect pressure inlets to the connections for inflatable actuators. [00170] Low Cycle Fatigue Tests of an Inflatable Fiber: The fiber was connected to a syringe barrel (Nordson EFD) through an adapter (male luer lock, 1/8 inch, MEETOOT) and tightly sealed with a hose clamp (5/8”, Storehouse Automotive Hose Clamp Assortment, 40 Pc.). The actuation pressure was supplied using a pressure pump (Ultimus V, Nordson EFD) and regulated by a pneumatic solenoid valve (VQD1151-5MO, SMC), which was controlled through 0-24 V digital relays (WAGO). Air was used as the pressure source. The right end of the fiber was clamped onto the wall. For each cycle, the air pressure was applied for 1 second to reach the maximum pressure, and released rapidly with the solenoid valve. After recording the cyclic tests with a camera, the bending angles were extracted from the recorded videos— manually for cases of large deformation and automatically for small deformations using boundary detection with the MATLAB function bwboundaries. [00171] Investigation of the actuation force of an inflatable fiber : The fiber was connected to a syringe barrel (Nordson EFD) through an adapter (male luer lock, 1/8 inch, MEETOOT) and tightly sealed with a hose clamp (5/8”, Storehouse Automotive Hose Clamp Assortment, 40 Pc.). The actuation pressure (p) was supplied by a pressure pump (Digital Syringe Dispenser 98666, LOCTITE). Air was used as the pressure source. The right end of the fiber was clamped onto a positioning arm, while the left end was positioned above a scale (Precision Balance ME1002T/00, METTLER TOLEDO) with a 3 mm gap. The actuation forces were measured using the scale in grams and then converted to Newtons by assuming the gravitational acceleration in the lab to be 9.81 m/s2. [00172] It should be noted that the control of the print nozzles and 3D printing systems described herein can be executed with a program(s) fixed on one or more non-transitory computer readable medium. The non-transitory computer readable medium can be loaded onto a computing device, server, 3D printer device processor, smartphone, tablet, phablet, or any other suitable device known to or conceivable by one of skill in the art. [00173] It should also be noted that herein the steps of the method described can be carried out using a computer, non-transitory computer readable medium, or alternately a computing device, microprocessor, or other computer type device independent of or incorporated with an imaging or signal collection device. An independent computing device can be networked together with the 3D printing hardware either with wires or wirelessly. The computing device for executing the present invention can be a completely unique computer designed especially for the implementation of this method. Indeed, any suitable method of analysis known to or conceivable by one of skill in the art could be used. It should also be noted that while specific equations are detailed herein, variations on these equations can also be derived, and this application includes any such equation known to or conceivable by one of skill in the art. [00174] A non-transitory computer readable medium is understood to mean any article of manufacture that can be read by a computer. Such non-transitory computer readable media includes, but is not limited to, magnetic media, such as a floppy disk, flexible disk, hard disk, reel-to-reel tape, cartridge tape, cassette tape or cards, optical media such as CD-ROM, writable compact disc, magneto-optical media in disc, tape or card form, and paper media, such as punched cards and paper tape. [00175] It should be noted that the software associated with the present invention is programmed onto a non-transitory computer readable medium that can be read and executed by any of the computing devices mentioned in this application. The non-transitory computer readable medium can take any suitable form known to one of skill in the art. The non- transitory computer readable medium is understood to be any article of manufacture readable by a computer. Such non-transitory computer readable media includes, but is not limited to, magnetic media, such as floppy disk, flexible disk, hard disk, reel-to-reel tape, cartridge tape, cassette tapes or cards, optical media such as CD-ROM, DVD, Blu-ray, writable compact discs, magneto-optical media in disc, tape, or card form, and paper media such as punch cards or paper tape. Alternately, the program for executing the method and algorithms of the present invention can reside on a remote server or other networked device. Any databases associated with the present invention can be housed on a central computing device, server(s), in cloud storage, or any other suitable means known to or conceivable by one of skill in the art. All of the information associated with the application is transmitted either wired or wirelessly over a network, via the internet, cellular telephone network, RFID, or any other suitable data transmission means known to or conceivable by one of skill in the art. [00176] The many features and advantages of the invention are apparent from the detailed specification, and thus, it is intended by the appended claims to cover all such features and advantages of the invention which fall within the true spirit and scope of the invention. Further, since numerous modifications and variations will readily occur to those skilled in the art, it is not desired to limit the invention to the exact construction and operation illustrated and described, and accordingly, all suitable modifications and equivalents may be resorted to, falling within the scope of the invention.

Claims

What is claimed is: 1. A device for three-dimensional (3D) printing comprising: a base plate; a nozzle comprising a nozzle membrane and pins, wherein the nozzle is coupled to the base plate, wherein the nozzle comprises an exit, and wherein the nozzle is configured to allow precise control of a cross-sectional shape of the exit; stepper motors, wherein the pins are coupled to the stepper motors to actuate changes in the cross-sectional shape of the exit. 2. The device of claim 1 further comprising cables connecting the pins to the stepper motors. 3. The device of claim 1 wherein the stepper motors are further coupled to the pins by a pulley system. 4. The device of claim 2 wherein the cables further comprise high strength inextensible fibers. 5. The device of claim 1 further comprising springs for returning the pins to their original positions. 6. The device of claim 1, wherein the nozzle is further configured with a tapered internal channel shape suitable for shear-thinning ink. 7. The device of claim 1 further comprising an ink inlet module. 8. The device of claim 1 further comprising a solid core. 9. The device of claim 8, wherein the solid core is configured to allow for extrusion of a hollow filament. 10. A device for three-dimensional (3D) printing comprising: a base plate; a nozzle comprising a nozzle membrane and pins, wherein the nozzle is coupled to the base plate, wherein the nozzle comprises an exit, and wherein the nozzle is configured to allow precise control of a cross-sectional shape of the exit; a core configured to be disposed within the nozzle; stepper motors, wherein the pins are coupled to the stepper motors to actuate changes in the cross-sectional shape of the exit. 11. The device of claim 10 further comprising cables connecting the pins to the stepper motors. 12. The device of claim 11 wherein the cables further comprise high strength inextensible fibers. 13. The device of claim 10 further comprising springs for returning the pins to their original positions. 14. The device of claim 10, wherein the nozzle is further configured with a tapered internal channel shape suitable for shear-thinning ink. 15. The device of claim 10 further comprising an ink inlet module. 16. The device of claim 15 wherein the solid core comprises a wide attachment at the ink inlet module and wherein the solid core narrows from the wide attachment. 17. The device of claim 10 wherein wall thickness of a printed tube varies along the azimuthal angle within a cross-section. 18. The device of claim 10, wherein the solid core is configured to allow for extrusion of a hollow filament. 19. The device of claim 10 wherein the solid core defines an internal air channel. 20. The device of claim 10 wherein the stepper motors are further coupled to the pins by a pulley system.
PCT/US2025/029573 2024-05-15 2025-05-15 Adaptive 3d printing nozzle Pending WO2025240751A1 (en)

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US20230271379A1 (en) * 2020-08-06 2023-08-31 Signify Holding B.V. Continuous hollow tube printing using fdm
WO2024094869A1 (en) * 2022-11-04 2024-05-10 Centre National De La Recherche Scientifique A nozzle for 3d printing, a system to control said nozzle

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US20200061910A1 (en) * 2016-12-08 2020-02-27 President And Fellows Of Harvard College Core-shell nozzle for three-dimensional printing and method of use
US20200398472A1 (en) * 2017-06-28 2020-12-24 The Boeing Company Apparatuses and methods for shaping an extrudable material
US20190091926A1 (en) * 2017-09-26 2019-03-28 Technology Research Association For Future Additive Manufacturing Nozzle and additive manufacturing apparatus
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