CN210063339U - Rigid-flexible coupling variable-rigidity flexible robotic fish - Google Patents

Rigid-flexible coupling variable-rigidity flexible robotic fish Download PDF

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CN210063339U
CN210063339U CN201822116543.6U CN201822116543U CN210063339U CN 210063339 U CN210063339 U CN 210063339U CN 201822116543 U CN201822116543 U CN 201822116543U CN 210063339 U CN210063339 U CN 210063339U
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fish
flexible
rigidity
spine
rigid
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崔祚
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Guizhou Institute of Technology
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Abstract

The utility model discloses a rigidity and flexibility coupling becomes flexible machine fish of rigidity, the utility model discloses a fluid drive's multichannel structure simulates fish body muscle to utilize flexible beam structure to simulate fish body vertebra, with the variable rigidity characteristic that realizes flexible machine fish. The utility model discloses the experimental principle of the flexible bionic fish of just gentle coupling has been deduced respectively. The design method can lead the designed bionic fish to realize the change in a larger rigidity range through the optimization of the multi-channel structure parameters and the flexible beam parameters so as to obtain better swimming performance. The utility model discloses a flexible machine fish is made with multichannel muscular system superimposed mode in succession spine roof beam, has fully considered the influence that fish become rigidity characteristic to its propulsion performance on the whole, has important meaning to improving bionic machine fish propulsion performance.

Description

Rigid-flexible coupling variable-rigidity flexible robotic fish
Technical Field
The utility model discloses mainly use bionical underwater robot field, specifically be a design method of rigidity and flexibility coupling variable rigidity bionic fish and the bionic robot fish that this method designed.
Background
Traditionally, a ship or an autonomous unmanned submersible vehicle (AVU) is driven by a propeller, and has the obvious defects of low propelling speed, low efficiency, poor maneuverability, large disturbance on fluid environment and the like. In nature, the fishes obtain fast and efficient swimming performance and extremely high mobility through the swinging of the bodies and/or tail fins, and the unique swimming performance attracts more and more scientific researchers. In recent years, researchers have revealed the mechanism of highly efficient swimming of fish from the aspect of hydrodynamics and the like, but a biomimetic robotic fish based on a biological prototype has been far behind fish in nature in terms of swimming speed, propulsion efficiency and turning maneuverability. Although experimental research on the bionic robot fish has been practiced for many years, the corresponding design method is less and is not mature. So far, the design of the bionic robot fish swing propulsion model mainly comprises a rigid serial mechanism and a flexible structure.
Traditionally, the bionic robotic fish is a tail body swinging structure realized by a multi-joint rigid body series connection structure. The design utilizes a single degree of freedom of rotation for each joint to reproduce oscillatory motion, representative robotic fish including MIT developed tuna Robotuna, Draper laboratory robotic fish VCUUV, G series and MT series of robotic fish at the university of exercs, uk, PF series and UPF series of robotic fish developed by NMRI, and two joint robotic fish SPC-II and SPC-III developed by north navigation, and so on. Generally, the robot fish based on the series structure is simple in structure, each joint needs to be driven independently, the control is complex, and the swimming efficiency is low.
In recent years, in order to improve the swimming performance of the bionic robot fish, a bionic worker proposes a flexible fish body structure, and the structure considers the influence of the spine of the fish body and the muscles of the fish body distributed around the spine on the swimming performance. Representative robotic fish include flexible robotic fish made from silicone based materials by Alvarado and Marchese et al. The robot fish is of a flexible structure, and the steering engine is arranged in the fish body to drive the connecting rod mechanism to generate reciprocating motion so as to realize swinging propulsion of the fish body. The robot fish is simple and reliable in structure and can simulate the viscoelastic dynamic characteristics of the fish. However, due to the physical properties of viscoelastic materials (such as silica gel), the bending stiffness of the body of the manufactured flexible robotic fish cannot be changed, and the adaptability to different external fluid environments is poor.
Although the flexible robot fish has certain flexibility, the experimental scheme has certain defects, and the swimming speed, the propelling efficiency and the maneuverability of the flexible robot fish are far inferior to those of fishes in nature. Therefore, there is still a need for further research in designing and manufacturing machine fish. In fact, biological research shows that the body rigidity of the fish can be changed through muscles, so that the swinging frequency of the tail fin is matched with the natural frequency of the body of the fish, and the fast and efficient swimming performance is achieved. The bionic robot fish is designed without considering the influence of the rigidity of the fish body on the swimming performance.
SUMMERY OF THE UTILITY MODEL
The utility model aims to provide a design method of the flexible bionic machine fish of rigid-flexible coupling variable rigidity and the bionic machine fish designed by the method, fully consider the influence of the variable rigidity characteristic of fish on the mobility performance to overcome the defects of the prior art.
The utility model discloses a following technical scheme realizes:
the utility model consists of a fish body part and a fish tail part which are fixedly connected by a connecting clapboard; the fish head part is provided with a lithium battery, a driving system and a control system; the fishtail part is provided with a flexible spine structure and a multi-channel muscle system; the flexible spine structure comprises a bottom plate and an elastic beam, spine hard blocks are arranged on the elastic beam, the spine hard blocks are fixed on different positions of the elastic beam, and the bending deformation is realized by driving the tail end spine block through a rope; the bottom plate is provided with a rope fixing end; the multichannel muscle system consists of a hard boundary layer and a deformation area, and a fluid channel is arranged in the multichannel muscle system; the deformation region is comprised of a viscoelastic material.
The utility model discloses a control the fluidic direction of flow, flow velocity and the pressure in multichannel muscular system and change bionic robot fish's bending stiffness. The fish muscle is simulated through a fluid-driven multi-channel structure, and the fish spine is simulated through a flexible beam structure, so that the variable stiffness characteristic of the flexible robot fish is realized. The utility model discloses the experimental principle of the flexible bionic fish of just gentle coupling has been deduced respectively. The design method can lead the designed bionic fish to realize the change in a larger rigidity range through the optimization of the multi-channel structure parameters and the flexible beam parameters so as to obtain better swimming performance.
The design idea of the rigid-flexible coupling variable-rigidity flexible bionic fish is derived from an important biological discovery that the rigidity of the body of the flexible fish can be changed by adjusting muscles so as to obtain the quick and efficient swimming performance. The utility model discloses a rigidity backbone roof beam carries out the atress analysis with multichannel muscular system superimposed mode mutually to the motion condition of this machine fish in the fluid, combines the biological parameter of the fish body, optimizes the selection through carrying out rigidity backbone roof beam parameter and multichannel fish body parameter, realizes the variable rigidity characteristic of flexible bionic fish to obtain high efficiency's characteristic of moving about.
The utility model relates to a concrete step does:
step 1: selecting fish bionic object and measuring related parameters
According to the research purpose, certain type of swing-propelled fish is selected as bionic object, such as fishes of Anguillar Japonicae, fishes of carangid and fishes of tuna, etc. Preliminarily measuring the bending rigidity of the fish body, dissecting the fish body at certain intervals, measuring the length, width, area and the like of the cross section of each section to obtain the appearance parameters of the fish body, and manufacturing the appearance mould of the bionic robot fish according to the appearance size of the fish body.
Step 2: design and manufacture flexible spine structure of fish body
The designed fish body rigid body spine structure mainly comprises an elastic beam, a spine hard block, a bottom plate and a rope fixing end. In the vertebral structure, the vertebral hard blocks are fixed on different positions of the elastic beam, and the bending deformation is realized by driving the tail vertebral blocks through the ropes. In this design, different bending stiffnesses can be achieved by selecting different numbers of vertebral hardblocks and multiple drive cables. Wherein, the elastic beam of the flexible spine can be made of different materials, and the different materials have different elastic moduli.
And step 3: design and manufacture of multi-channel fish muscle system
And designing multi-channel fish body muscle systems in different forms by combining the measured external parameters of the fish body so as to realize the variable stiffness characteristic of the fish body. For a multichannel muscle system, different channel widths, channel patterns, and widths between channels may be designed. In addition, the deformation of multichannel systems is also influenced by material properties. The robot fish can be optimized according to the design of channel parameters so as to obtain wide variation of the bending rigidity of the robot fish.
And 4, step 4: design of drive system and control system
The designed driving system and the control system are fixed at the head position of the bionic robot fish and are used for controlling the driving amplitude and the driving frequency of the robot fish so as to realize different propelling performances of the robot fish. The fish body can be driven by a direct current motor or a steering engine, and the reciprocating swinging motion of the fish body is realized by controllers such as a single chip microcomputer. The moment generated by the driver is transmitted to the spine of the fish body through the rope, and the part is simple in design requirement, small in size and high in control precision.
And 5: flexible variable-rigidity bionic robot fish integral forming method
The utility model discloses in, the rigidity and flexibility coupling variable rigidity machine fish that designs mainly comprises fish head part and fish tail part, and these two parts are connected admittedly by connecting the baffle. The fish head part accounts for about one third of the total length of the robot fish, and is mainly used for placing a lithium battery, a driving system (such as a steering engine and the like) and a control system inside the robot fish. The designed flexible spinal structure and multi-channel muscular system are arranged on the fishtail part, the structures are placed at a certain position of a fishbody mould, and a viscoelastic flexible tail part is formed by pouring viscoelastic material (such as silica gel and the like) and solidifying. The bending rigidity of the fish body is changed by controlling the flow direction, the flow speed and the pressure of the fluid in the multiple channels. In addition, the robot fish can optimize parameters of a vertebral structure and a multichannel system so as to further improve the propelling performance of the robot fish.
The utility model has the advantages that:
compare with the design method of current bionical machine fish, the utility model discloses a flexible machine fish is made with multichannel muscular system superimposed mode in succession spine roof beam, has fully considered the influence that fish become rigidity characteristic to its propulsion performance on the whole, has important meaning to improving bionical machine fish propulsion performance. The advantages are that:
(1) on the continuous flexible spine beam, different basic rigidity of the robot fish can be realized by changing the spine hard blocks and the rope driving number.
(2) For a multichannel muscle system, the channel type, the channel width and the distance between the channels can be optimally designed, and the larger-range variable rigidity of the robotic fish can be realized.
(3) The single drive unit (motor or steering engine and the like) of accessible drives, simple structure, and appearance matching degree is high, and whole compliance is good.
(4) The bending rigidity of the fish body can be matched by adjusting the driving amplitude and the driving frequency, so that the fast and efficient swimming performance of the flexible bionic fish can be obtained.
Drawings
FIG. 1 is a flexible spinal structure a of a biomimetic robotic fish;
FIG. 2 is a flexible spinal structure b of the biomimetic robotic fish;
FIG. 3 is a flexible spine structure c of the biomimetic robotic fish;
FIG. 4 is a schematic view of the bending deformation of the spine of the biomimetic robotic fish;
FIG. 5 is a force analysis diagram of a spine beam structure of a biomimetic robotic fish;
FIG. 6 is a schematic view of a multi-channel undeformed state of the biomimetic fish;
FIG. 7 is a schematic view of a multi-channel deformation state of a bionic fish;
FIG. 8 is a schematic diagram of the overall structure of the biomimetic robotic fish;
figure 9 is a cross-sectional view a-a of figure 8.
Description of reference numerals: the method comprises the following steps of 1-bottom plate, 2-elastic beam, 3-rope fixing end, 4-spine hard block, 5-fluid channel, 6-hard boundary layer, 7-deformation area, 8-direct current servo motor, 9-connecting partition plate, 10-multichannel muscle system and 11-tail fin.
Detailed Description
The present invention will be further explained with reference to the accompanying drawings:
the mathematical principle of the present invention will be described first.
(1) Rigidity analysis of flexible spine of bionic robot fish
The spine structure of the flexible robot fish mainly comprises a bottom plate 1, an elastic beam 2 and a spine hard block 4, and is driven by a rope to realize reciprocating swing motion, which is shown in attached figures 1-3. For a certain segment of the vertebral hardblock 4, the corresponding stiffness k is:
k(x)=E1I1(x)+E2I2(x) (1)
wherein E is1And E2The elastic modulus, I, of the materials corresponding to the elastic beam 2 and the vertebral block 4 respectively1(x) And I2(x) The sectional moments of inertia of the elastic beam 2 and the annular vertebral hard block 4 are related to the shape and the size. The utility model discloses in, change cross-sectional dimension and elastic modulus through adding vertebra hardblock 4 to the rigidity distribution condition of flexible machine fish is matchd in the initial step.
The flexible spine is regarded as a continuous multi-section variable-section Euler-Bernoulli beam, and the deformation deflection can be solved by an integral method. Firstly, the distribution of the vertebral hard blocks 4 is utilized to divide the vertebral structure into N sections, and the section sizes of all the sections are consistent. And solving the expression of the flexible spine deflection according to the relation among the bending moment, the shearing force and the load.
Figure DEST_PATH_GDA0002337504640000051
In the formula, Mi(x)、hiAnd thetaiBending moment, deflection and corner suffered by the ith section of vertebral unit. The deformation coordination conditions between the sections are utilized, namely:
hi(x)e=hi+1(x(bi(x)e=θi+1(x)b(3)
in the formula, hi(x)eAnd thetai(x)eRespectively showing the deflection and the corner h at the end position of the ith segment of the vertebra uniti+1(x)bAnd thetai+1(x)bRespectively representing the deflection and the rotation angle at the initial position of the spinal unit of the (i +1) th segment. According to solving each segmentFinally, the deformation curve of the flexible spine is obtained by fitting.
(2) Variable stiffness analysis of multi-channel systems
When the flexible spine bends, the channel is crushed and deformed. Fluid is applied to a multi-channel system, and the pressure generated by the fluid deforms the channels and changes the bending stiffness by changing the flow direction and the fluid pressure. Let δ and p be the loads applied by the fluid to the channel in the axial and lateral directions, respectively, and the corresponding resultant forces are F (x) and S (x), respectively, as shown in FIGS. 4-5.
During the deformation process, the channel is subjected to a spinal bending moment, denoted as m (x), and the lateral force is directed perpendicular to the channel surface. The utility model discloses in, the passageway is formed by the preparation of viscoelastic material, can receive the effect of elastic force and viscous force at the deformation in-process. Assuming the rotation angle of the channel micro-segment dx is theta, the external forces applied in the transverse direction are elastic forces Q (x) and-Q (x + dx), the projections of the external forces-F (x) and F (x + dx) on the axis, and the algebraic sum of the projections of the lateral forces S (x) generated by the air pressure on the axis is 0, which is not considered in the analysis.
From newton's second law, the lateral motion of the micro-segment channel satisfies the equation:
Figure DEST_PATH_GDA0002337504640000061
where ρ is the density of the channel unit;
a-area of the channel cross section;
h-deformation displacement of the channel.
According to material mechanics, the rotation angle θ and the elastic force q (x) can be expressed as:
Figure DEST_PATH_GDA0002337504640000062
wherein E-modulus of elasticity of the channel material;
i-section moment of inertia of the channel cross section;
mu-viscosity coefficient of fish tail model.
By substituting θ and q (x) for formula (2), the bending vibration differential equation of the channel unit can be obtained as follows:
Figure DEST_PATH_GDA0002337504640000071
to illustrate the variable stiffness property of the multichannel muscle system, let e (x), μ (x), i (x), and f (x) be constants, i.e. the channel unit is equivalent to a uniform beam with uniform cross section acted by external force, and the solution of the above formula can be written as:
h(x,t)=H(x)sin(wt+θ) (7)
substituting the general form of the solution into equation (4) yields:
EIH(4)(x)-FH″(x)-ρAw2H(x)=0 (8)
according to the equation, solving the natural frequency equation of the deformation channel is as follows:
Figure DEST_PATH_GDA0002337504640000072
from the above formula, F has an influence on the natural frequency of the bending vibration of the flexible channel, while the lateral force S of the air pressure load has no influence on the natural frequency, and after the tail of the fish body is subjected to the axial force F, the bending rigidity is increased, and the natural frequency is also increased. Equation (9) theoretically illustrates the feasibility of air pressure to change bending stiffness. The natural frequency w is set without considering the influence of the deformation of the fishtail caused by the air pressure on the natural frequency of the bending vibrationnIn direct proportion to the gas pressure P.
Secondly, the specific implementation process of the utility model is introduced. The method comprises the steps of taking swing propulsion fish as a bionic object, establishing a three-dimensional model of the robot fish through measuring the appearance of the bionic object, and designing and manufacturing an appearance mold corresponding to the robot fish. According to design requirements, a flexible spine and a fluid multi-channel system are respectively designed and placed in a fish body mold for molding, and the change condition of the bending rigidity of the robot fish is tested under the anhydrous condition. Then, the drive system and the control system are installed on the head of the fish body, and the head of the fish body is fixedly connected with the variable-rigidity tail body part. And finally, testing the variable stiffness characteristic of the flexible robot fish under water under different driving conditions, and further optimizing the swimming performance of the robot fish.
The following experiment steps are described by taking carangidae fishes as bionic objects, and specifically comprise the following steps:
step 1: data measurement of biological prototypes
The carangid fish is selected as a bionic object, and the carangid fish has the characteristics of high tour speed and high tour efficiency. The length and the density of a living fish are measured, then the fish body is subjected to equidistant dissection, and the shape and the size of each part section are measured, wherein the shape and the size comprise a transverse size, a radial size, a dorsal fin length, a ventral fin length, a caudal fin length and the like. And finally, establishing a three-dimensional model of the fish body, measuring the mass of each part, calculating the mass distribution condition of each part along the length direction, and further calculating the distribution condition of the rigidity of the fish body.
Step 2: design and manufacture of spine structure of robotic fish
According to the measured fish body rigidity, the elastic beam 2 and the vertebra hard blocks 4 with proper sizes are selected, and the vertebra hard blocks 4 are arranged on the elastic beam 2 at equal intervals. One end of the rope is fixed on a rope fixing end 3 on the end piece, and the other end of the rope passes through the fine hole of the vertebra hard block 4 and is connected with the driving mechanism, so that the bending of the fish vertebra and the reciprocating swing of the flexible tail body are realized. As shown in fig. 1-3, different bending forms of the fish body can be simulated by optimizing the design of the number of the vertebral hard blocks 4 and the number of the rope drives.
And step 3: design and manufacture of multi-channel muscle system of robotic fish
And selecting a proper multichannel type and corresponding parameters to meet the variable stiffness design requirement of the bionic robot fish by combining the appearance parameters of the robot fish and the size of the flexible spine. As shown in fig. 6-7, the material of the multichannel system will directly affect the deformation of the fish body, and the array pattern of the channels and the channel parameters will directly affect the variable stiffness properties of the fish body. The multichannel muscle system 10 is thus composed of a hard boundary layer 6 and a deformation zone 7, in which the fluid channels 5 are arranged; the deformation zone 7 is composed of a viscoelastic material such as silicone. In addition, a plurality of channel loops can be selected to realize independent control at different positions of the flexible fish body so as to realize pitching, yawing, twisting and other movements of the fish body. Four multi-channel fluid circuits are selected for this example, as shown in fig. 9, and fig. 9 is a cross-sectional view of the structure of fig. 8. Wherein the fluid in the circuit is driven by a micro-pump and each multi-channel circuit is controllable by a micro-valve.
And 4, step 4: design and manufacture of bionic robot fish driving and control system
The motion control system of the flexible robot fish can be composed of a single chip microcomputer, a 7.4V lithium battery, a 5V voltage stabilizer and the like, and the selection of the control system mainly depends on the selection of a driver (a direct current motor, a stepping motor or a steering engine). In the embodiment, the steering engine HS-7940TH is selected as a driving unit, and the wireless remote control module adopts a chip PT2262/PT2272, so that the wireless remote control module has the characteristics of low power consumption and interference resistance. All parts, control system and wireless system are integrated into one robotic fish.
And 5: whole assembly and propulsion performance test of bionic robot fish
In the example, the total length of the designed imitation carangid robot fish is 360mm, and the length of the head of the carangid robot fish is 140 mm. The fish head shell is obtained by 3D printing and processing, and the fish tail is made of a viscoelastic material by using a die forming technology. The viscoelastic material selected in the embodiment is zero-degree silica gel, and has the advantages of good fluidity, high tear strength, good elasticity and the like. In the robotic fish, the drive element, the cable transmission mechanism and the control system are all placed at the head position of the fish body, and the surface of the fish body is covered by an elastic skin to ensure integral sealing.
The flexible robotic fish body adopts a fluid multi-channel structure to change the bending rigidity. In the embodiment, the length of the multi-channel structure of the designed robotic fish is 120mm, so that the flexibility of the robotic fish structure can be effectively improved. The position of the steering engine is fixed by a connecting partition plate and a steering engine fixing frame. The steering engine generates torque at the head of the fish body, the torque is transmitted to the tail of the fish body through the transmission rope and the movable plate, and the movable plate and the tail silica gel are solidified into a whole. In order to avoid the winding between the wires of the control module and the wireless module and the rotary rudder disk, the upper part and the lower part of the head of the fish body are isolated by a baffle plate in front of the steering engine. In addition, a special hole is arranged in the machine fishtail body to place a transmission rope so as to reduce friction.
And finally, placing the developed rigid-flexible coupling variable-rigidity flexible robot fish in water, and adjusting the swinging frequency and the rotating amplitude of the steering engine through a wireless remote control system and a control system to ensure that the robot fish obtains different swimming performances under the conditions of different rigidities.
The above is only the specific application example of the present invention, and the present invention has other embodiments, and all technical solutions adopting equivalent replacement or equivalent transformation are all within the protection scope claimed by the present invention.

Claims (5)

1. The utility model provides a flexible machine fish of rigid-flexible coupling variable rigidity which characterized in that: the fish body part and the fish tail part are fixedly connected by a connecting clapboard (9); the fish head part is provided with a lithium battery, a driving system and a control system; the fishtail part is provided with a flexible spine structure and a multi-channel muscular system (10); the flexible spine structure comprises a bottom plate (1) and an elastic beam (2), spine hard blocks (4) are arranged on the elastic beam (2), the spine hard blocks (4) are fixed on different positions of the elastic beam (2), and the bending deformation is realized by driving the spine blocks at the tail end through a rope; a rope fixing end (3) is arranged on the bottom plate (1); the multichannel muscle system (10) is composed of a hard boundary layer (6) and a deformation area (7), and a fluid channel (5) is arranged in the multichannel muscle system; the deformation zone (7) is made of a viscoelastic material.
2. The rigid-flexible coupling variable stiffness flexible robotic fish of claim 1, wherein: the bending rigidity of the bionic robot fish is changed by controlling the flow direction, the flow speed and the pressure of the fluid in the multi-channel muscular system (10).
3. The rigid-flexible coupling variable stiffness flexible robotic fish of claim 2, wherein: the bionic robot fish is of a flexible structure and can be made of viscoelastic materials.
4. The rigid-flexible coupling variable stiffness flexible robotic fish of claim 1, wherein: the driving system is a single driving system, and the driving source comprises a direct current servo motor (8) or a steering engine.
5. The rigid-flexible coupling variable stiffness flexible robotic fish of claim 1, wherein: the fish tail part is also provided with a tail fin (11).
CN201822116543.6U 2018-12-17 2018-12-17 Rigid-flexible coupling variable-rigidity flexible robotic fish Expired - Fee Related CN210063339U (en)

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Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109515669A (en) * 2018-12-17 2019-03-26 贵州理工学院 A kind of design method and its bionic machine fish of Coupled Rigid-flexible variation rigidity flexible machine fish
CN111688887A (en) * 2020-05-27 2020-09-22 西安交通大学 Active variable-stiffness pectoral fin based on nylon artificial muscle and bionic underwater robot
CN111946766A (en) * 2020-08-06 2020-11-17 武汉理工大学 Rigid-flexible heterogeneous and microstructure coupling material, and preparation method and application thereof
CN112550653A (en) * 2020-12-04 2021-03-26 浙江大学 Soft fish robot driven by chemical energy release reaction
CN115071919A (en) * 2022-06-16 2022-09-20 华南理工大学 Flexible bionic robot fish based on beam theory and design method thereof

Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109515669A (en) * 2018-12-17 2019-03-26 贵州理工学院 A kind of design method and its bionic machine fish of Coupled Rigid-flexible variation rigidity flexible machine fish
CN111688887A (en) * 2020-05-27 2020-09-22 西安交通大学 Active variable-stiffness pectoral fin based on nylon artificial muscle and bionic underwater robot
CN111946766A (en) * 2020-08-06 2020-11-17 武汉理工大学 Rigid-flexible heterogeneous and microstructure coupling material, and preparation method and application thereof
CN112550653A (en) * 2020-12-04 2021-03-26 浙江大学 Soft fish robot driven by chemical energy release reaction
CN115071919A (en) * 2022-06-16 2022-09-20 华南理工大学 Flexible bionic robot fish based on beam theory and design method thereof
CN115071919B (en) * 2022-06-16 2023-09-26 华南理工大学 Flexible bionic robot fish based on beam theory and design method thereof

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