CN110276158A - A kind of method that spiral type actuator rebuilds expansion shape - Google Patents
A kind of method that spiral type actuator rebuilds expansion shape Download PDFInfo
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Abstract
The present invention provides a kind of method that spiral type actuator rebuilds expansion shape, it is characterised in that includes the following steps: S1, obtains the relationship of input air pressure P Yu actuator expanded angle θ；S2, helical angle φ is obtained based on expanded angle θ；S3: configuration space parameter R is obtained0And C0；S4: according to obtained helical angle and configuration space parameter R0And C0Rebuild actuator expansion shape.The experimental results showed that the configuration space parameter of the available actuator complete length of designed configuration space parametric technique, rebuilds effect ideal, the theoretical expansion shape of segment reconstruction and practical expansion shape error are smaller.
Description
Technical field
The present invention relates to soft robot technical field more particularly to the weights of gas-powered software actuator expansion shape
It builds.
Background technique
Pneumatic software actuator is a kind of dynamic actuator of novel gas drive, with light, flexibility is good, response is rapid, anti-
The advantages that pressure energy power is strong, highly-safe.Thus in continuous type mechanical arm, software gripper, recovering aid gloves and Biomimetic Fish etc.
Research direction is widely used.Pneumatic software actuator becomes one of the important research object in soft robot field.Several allusion quotations
The pneumatic software actuator of type is: the fifties in last century, McKibben pneumatic muscles, the Jamming- of J.L.Mckibben invention
The combination of based actuator, Pneumatic-nets aerodynamic grid, pure torsion actuator and different types of actuator.It is existing
Stage, pneumatic software actuator have the following structure feature: 1) matrix of actuator is made of elastic material, and internal there are air cavitys
Or aerodynamic grid.Using the high pressure gas of input as driving, may be implemented to shrink, extend, be bent, reverse it is contour submissive, high
The compound movement of redundancy；2) initial configuration of actuator is mostly linear stretch type, and section is round, semicircle or rectangle；3) existing
Actuator be mostly by keeping input air pressure is constant to keep shape invariance.
The pneumatic software actuator of spiral type is a kind of novel gas-powered dynamic device, with light, flexibility is good, response is fast
The advantages that strong, highly-safe, the bionical performance of speed, anti-pressure ability is prominent.Under lesser input air pressure, spiral type actuator can be with
It realizes large range of expansion movement, has broad application prospects simultaneously.
The reconstruction of gas-powered software actuator expansion shape has the research and control of software actuator very heavy
The meaning wanted.However, not being provided with the expansion shape for rebuilding spiral type pneumatic software actuator in the prior art has efficacious prescriptions
Method.
Summary of the invention
The purpose of the present invention is to solve the problems of the prior art, propose that a kind of spiral type actuator rebuilds expansion shape
The method of shape.
In order to solve the above technical problems, the present invention proposes a kind of method that spiral type actuator rebuilds expansion shape, including
Following steps: S1, the relationship for obtaining input air pressure P Yu actuator expanded angle θ；S2, helical angle is obtained based on expanded angle θ
φ；S3: configuration space parameter R is obtained0And C0；S4: according to obtained helical angle and configuration space parameter R0And C0It rebuilds and causes
Dynamic device expansion shape.
In some embodiments of the invention, further include following technical characteristic:
In step S1, the method for obtaining the relationship of input air pressure P and actuator expanded angle θ include the following steps: S11,
According to the performance characteristics of elastic material, material model is established；S12, actuator statical model is established, wherein input air pressure P
With the relationship of actuator expanded angle θ are as follows:
In formula: Va is volume shared by gas intracavity gas, and Vs is volume Vs shared by silicon rubber；W is strain energy density；Input gas
Press P using standard atmospheric pressure as relative barometric pressure zero point, Pa=101.325KPa.
Helical angle φ is obtained according to the following formula:
Wherein k is helical curvature, and with the variation of actuator expansion shape, k is from just becoming negative.
According to upright projection of the shape graduation mark on strain limiting layer on graph paper, each unfolded state is successively acquired
Coordinate data, i.e. the coordinate value of spiral type actuator working space is converted into spiral type actuator by data processing
Configuration space parameter R0And C0。
In step S3, configuration space parameter R is obtained0And C0The step of specifically include: S31, calculate and transported under different deployed configurations
The origin of moving coordinate system { O }；S32, according to the coordinate of kinetic coordinate system { O } origin, the corresponding data of each unfolded state are adopted
Collect the coordinate translation of point into kinetic coordinate system { O }；S33, further according to fitting process, utilize intermediate calibration points corresponding r and φ
Obtain the corresponding configuration space parameter R of the unfolded state0And C0。
Using segment reconstruction method, actuator end portions, mid portion and root portion are fitted configuration space respectively
Parameter.
In step S11, using the non-linear relation between Yeoh model foundation material stress and strain, strain energy density letter
Exponential model are as follows:
Wherein dkBe material parameter, J be after material deformation with the volume ratio before deformation, for incompressible material, J=1；
N is the order of strain energy density function；CiFor material parameter；I1For the 1st invariant of strain tensor, it may be assumed that
Wherein: λ1、λ2And λ3Respectively actuator shaft is to, radially and circumferentially principal extension ratio.
When making the elastic matrix of spiral type actuator using silica gel material, its material can be described using second order Yeoh model
Expect attribute, then has
W=C1(I1-3)+C2(I1-3)2,
The wherein classical value of silastic material parameter are as follows: C1=0.11MPa, C2=0.02MPa.
The helical is round, Archimedes spiral or logatithmic spiral, polar equation formula and cartesian coordinate equation
The relationship of formula is shown below:
Wherein the angle φ is helical angle；R is helical radius, and different helical types, the functional relation between r and φ is different；x
It is respectively coordinate value under corresponding cartesian coordinate system with y.
The polar equation formula of Archimedes spiral are as follows:
R=R0+C0φ
Wherein, R0It is helical starting point at a distance from polar origin；C0It is helical radius r with the rate of helical angle change；
For determining helical configuration, the polar equation expression formula of helical is unique, at this time R0And C0It is constant coefficient；
Circle is one kind of Archimedes spiral, polar equation formula are as follows:
R=R0+C0φ, C0=0
The polar equation formula of logatithmic spiral are as follows:
Compared with prior art, the beneficial effects of the present invention are as follows: the present invention devises a kind of pneumatic software actuating of spiral type
Device (spiral type actuator) configuration space parameter acquiring method, and shape is turned on to actuator and is rebuild.Experimental result table
Bright, the configuration space parameter of the available actuator complete length of designed configuration space parametric technique rebuilds effect ideal,
The theoretical expansion shape of segment reconstruction and practical expansion shape error are smaller.
Detailed description of the invention
Fig. 1 a, 1b, 1c are the pneumatic software actuator model figure of three kinds of spiral types respectively.
Fig. 2,3 are cast in the manufacturing process of spiral type actuator elastic matrix and stickup strain limiting layer signal respectively
Figure.
Fig. 4 is round helical configuration actuator configuration space parameter acquisition experimental data schematic diagram.
Fig. 5 is Archimedes spiral configuration actuator configuration space parameter schematic diagram.
Fig. 6 is logatithmic spiral configuration actuator configuration space parameter schematic diagram.
Fig. 7 a is round helical configuration expansion shape reconstructed results and model machine expansion shape contrast schematic diagram.
Fig. 7 b is Archimedes spiral configuration expansion shape reconstructed results and model machine expansion shape contrast schematic diagram.
Fig. 7 c is logatithmic spiral configuration expansion shape reconstructed results and model machine expansion shape contrast schematic diagram.
Fig. 8 is logatithmic spiral type actuator theory expansion shape segment reconstruction result schematic diagram.
Fig. 9 a, 9b, 9c are the configuration space parameter end segment of logatithmic spiral type actuator segment reconstruction, middle part respectively
Section and root segment are schemed between showing.
Specific embodiment
In order to which technical problem to be solved of the embodiment of the present invention, technical solution and beneficial effect is more clearly understood,
The present invention is further described in detail below with reference to the accompanying drawings and embodiments.It should be appreciated that specific implementation described herein
Example is not intended to limit the present invention only to explain the present invention.
It should be noted that it can be directly another when element is referred to as " being fixed on " or " being set to " another element
On one element or indirectly on another element.When an element is known as " being connected to " another element, it can
To be directly to another element or be indirectly connected on another element.In addition, connection can be for fixing
Effect is also possible to act on for circuit communication.
It is to be appreciated that term " length ", " width ", "upper", "lower", "front", "rear", "left", "right", "vertical",
The orientation or positional relationship of the instructions such as "horizontal", "top", "bottom" "inner", "outside" is that orientation based on the figure or position are closed
System is merely for convenience of the description embodiment of the present invention and simplifies description, rather than the device or element of indication or suggestion meaning must
There must be specific orientation, be constructed and operated in a specific orientation, therefore be not considered as limiting the invention.
In addition, term " first ", " second " are used for descriptive purposes only and cannot be understood as indicating or suggesting relative importance
Or implicitly indicate the quantity of indicated technical characteristic.Define " first " as a result, the feature of " second " can be expressed or
Implicitly include one or more this feature.In the description of the embodiment of the present invention, the meaning of " plurality " is two or two
More than, unless otherwise specifically defined.
Method proposed by the invention is specially adapted for the pneumatic software actuator of spiral type, below for the present invention
A kind of pneumatic software actuator of spiral type designed by people is described in detail.For this purpose, first being caused to the pneumatic software of the spiral type
Dynamic device is illustrated.
There are the biological configurations of a variety of helical forms in nature, such as nautilus, nummulite, plant tendril, hippocampus tail
[17] etc., wherein the tail of hippocampus is generally maintained at logatithmic spiral configuration, when hippocampus attempt to catch the objects such as seaweed, coral with
When resisting sea washes, tail can first carry out expansion campaign, carry out bending motion again then to encircle object；Disk-recording in life
The objects such as slot, mosquito-repellent incense, cam are also helical configuration.The big multiple coincidence Archimedes spiral of configuration or logarithm of these biologies or article
The helicals configuration such as helical.
It is enlightened by this, the application is ground for the design scheme and working method of the pneumatic software actuator of helical configuration
To study carefully, mode is implemented as follows in proposition, it is described below:
Spiral type actuator structure:
According to analytic geometry rudimentary knowledge, the mathematic(al) representation of helical has polar equation formula and cartesian coordinate equation
Formula, shown in the relationship of the two such as formula (1):
Wherein the angle φ is helical angle；R is helical radius, and different helical types, the functional relation between r and φ is different；x
It is respectively coordinate value under corresponding cartesian coordinate system with y.
Particularly, for round, Archimedes spiral and three kinds of logatithmic spiral it is common there is the helical for representing meaning, it is public
In formula (1), the polar equation formula of Archimedes spiral are as follows:
R=R0+C0φ (2)
Wherein, R0It is helical starting point at a distance from polar origin；C0It is helical radius r with the rate of helical angle change.
For determining helical configuration, the polar equation expression formula of helical is unique, at this time R0And C0It is constant coefficient.
Circle is considered as special Archimedes spiral, polar equation formula are as follows:
R=R0+C0φ, C0=0 (3)
The polar equation formula of logatithmic spiral are as follows:
According to formula (1)-(4) it is found that the structure parameters of helical have helical angle φ, helical starting point and polar origin
Distance R0；Helical radius r with helical angle change rate C0.It can be used for the helical mathematical expression of design spiral type actuator
Formula includes but is not limited to round, Archimedes spiral and logatithmic spiral and the combination of different helicals etc..
The pneumatic software actuator of spiral type has the following characteristics that
1) matrix of actuator is made by elastic material and is shaped, and intrinsic silicon has an inflation air cavity.Matrix cross sections
It include but is not limited to circular cross-section, semi-circular cross-section, square-section, rectangular section etc. with air cavity cross section；
2) actuator realizes expansion movement using the air pressure of input as driving.Its bigger curvature of air pressure is smaller, and curvature subtracts
It is small that a degree of negative cruvature expansion movement may be implemented after 0, (positive camber direction refers to actuator in two three quadrants
Expansion movement, negative cruvature refer to expansion campaign of the actuator in 41 quadrants).
3) it is pasted with strain limiting layer on the outside of matrix, for limiting axial stretching routine and enhancing expansion movement.
4) base end sealing obstruction head prevents gas leakage for blocking air cavity.
Three kinds of common spiral type actuatings with the circle for representing meaning, Archimedes spiral and logatithmic spiral configuration
Device, as shown in Fig. 1 a, 1b, 1c.
Spiral type actuator material:
The matrix of spiral type actuator is made by elastic material, can be used for manufacturing actuator matrix material include but
It is not limited to resin material, rubber material, silica gel material etc. (hardness is less than or equal to 50A).
The outer side strain limiting layer of spiral type actuator is made by elastic material, can be used for manufacturing the material of strain limiting layer
Material includes but is not limited to plain paper, fibrous braid (hardness is greater than common A4 paper) etc..Elastic material and elastic material
Difference be: the usually linear state of the stress-strain diagram of elastic material, commonly using Young's modulus and Poisson's ratio indicates；Superlastic
Property refer to that the stress and strain of material is no longer linear corresponding relationship, but indicated with strain energy density function.
Spiral type actuator manufacturing method:
The manufacturing process of spiral type actuator is divided into three steps:
1) matrix of actuator is manufactured.The mold using 3D printing technique manufacture, including kerve, bent intermediate are assembled first
Bar and end caps；It is then injected into elastic material；Finally preferably can cover steel plate in upper surface makes matrix uniform wall thickness flat
It is whole, and its solidification is waited at room temperature；
2) it selects suitable material, cuts the strain limiting layer for being suitble to size (width is equal to A, and length is equal to L)；For the ease of
Shape after label expansion portrays several shape graduation marks on strain limiting layer at equal intervals；
3) strain limiting layer is equably pasted onto actuator outer surface (with special silica gel treatment glue), will sealed
Obstruction head is pasted onto actuator distal end.
In order to protrude influence of the different helical configurations to actuator performance, in this example, three kinds of spiral type actuators it is outer
Side arc length length is uniformly selected as 150mm.According to complexity prepared by formula (2)-(4) and mold, other being calculated are tied
Structure parameter is as shown in table 1.Each component prepares material, as shown in table 2.
The pneumatic software actuator structure parameter of 1 spiral type of table
The pneumatic software actuator of 2 spiral type of table prepares material
For above-mentioned spiral type, pneumatically its embodiment for rebuilding expansion shape is given below in soft actuator, the present invention.
Embodiment 1
According to helical mathematic(al) representation (1)-(4) analysis, it is assumed that the pole of spiral type actuator unfolded state after inflation
Equation in coordinates form is still identical with initial configuration expression-form, then determines that the configuration space parameter of helical configuration has 3, respectively
It is helical angle φ, helical starting point and polar origin distance R0；Helical radius r with helical angle change rate C0.It can be with
Helical mathematic(al) representation for design spiral type actuator include but is not limited to round, Archimedes spiral and logatithmic spiral with
And the combination etc. of different helicals.
The method that the present embodiment obtains the relationship of input air pressure P and actuator expanded angle θ in step sl is to pass through gas
Dynamic software actuator models to realize.
Pneumatic software actuator modeling aspect, since there are material nonlinearities, several during pneumatic software actuator activation
What non-linear and constraint is non-linear, and the mathematical model of pneumatic software actuator is caused to be difficult to set up.Most models only predict it
Variation tendency and can not achieve and be accurately controlled.In document, common modeling method has: 1) driving generated using input air pressure
Equilibrium relation modeling between torque and silastic material generated reaction force square, although this method is it can be readily appreciated that model
Difficulty is solved, integral operation therein is unable to get analytic solutions, and model accuracy is not high；2) principle of virtual work and constant curvature are based on
Model modeling, the model accuracy that this method is established is higher, but requires actuator to meet constant curvature and assume and accurately several
What deformation parameter；3) in addition there are also researchers is modeled using the methods of Lagrange's equation, Cosserat theory, these methods are built
Vertical model accuracy is higher, but multiple operation is needed to seek energy, and formula is tediously long and derives complicated, it is difficult to actually be answered
With.
Therefore, software actuator pneumatic for spiral type, because of the Chang Qu that it does not meet the principle of virtual work and constant curvature model is built
Rate is assumed, also lacks effective modeling method at present.For this purpose, the present embodiment proposes following method:
The structure of spiral type actuator shows that its motion mode is different from the bending motion of existing software actuator, spiral shell
The expansion campaign of positive negative cruvature both direction may be implemented with the increase of input air pressure for linear actuator.Input air pressure is different,
The corresponding expanded angle of actuator is different.The present embodiment is based on elastic material model, geometrical relationship and the principle of virtual work to set
The pneumatic software actuator of the spiral type of meter proposes a kind of general method for establishing statical model, the statics mould established
Type based on the assumption that
1) matrix of actuator even variation during expansion, i.e. input air pressure are uniformly applied to air cavity surface；
2) strain limiting layer thickness is sufficiently small, and will not generate stretcher strain；
3) silastic material approximation is incompressible, i.e., the total volume of elastic matrix remains unchanged during expansion.
Material model
According to the performance characteristics of elastic material, strain energy density function is generallyd use to establish between stress and strain
Nonlinear model.Common function model has Neo-Hookean model, Yeoh model, Mooney-Rivlin model etc..Wherein,
Yeoh model is strong for large deformation behavior description ability, and its model parameter can be obtained with simple uniaxial tensile test.Cause
This uses the non-linear relation between Yeoh model foundation material stress and strain herein.Strain energy density function model are as follows:
Wherein J be material deformation after with the volume ratio before deformation, for incompressible material, J=1；N is strain energy density
The order of function；Ci is material parameter；I1 is the 1st invariant of strain tensor, it may be assumed that
Wherein: λ 1, λ 2 and λ 3 are respectively actuator shaft to, radially and circumferentially principal extension ratio.
This example is made the elastic matrix of spiral type actuator of ElastosilM4601 silica gel material, for the silica gel
The binomial parameter form of material use formula (7) the Yeoh model classics can accurately be fitted its stress-strain spy
Property, in which: C1=0.11MPa, C2=0.02MPa.
W=C1(I1-3)+C2(I1-3)2 (7)
Actuator statical model
As shown in Fig. 2, establishing actuator coordinate system.Spiral type actuator is strained into the start bit under limiting layer original state
The origin for being defined as world coordinate system { W } is set, the kinetic coordinate system under actuator unfolded state is defined as coordinate system { O }, is caused
Deformation relationship of the dynamic device after inflation on three directions can indicate are as follows:
Spiral type actuator (positive camber) after Fig. 2 expansion
Wherein: la0, Sa0 and t0 are respectively arc length length, air cavity section on the outside of spiral type actuator air cavity under original state
Long-pending and wall thickness；La, Sa and t are respectively arc length length, air cavity sectional area and wall on the outside of spiral type actuator air cavity under inflated condition
It is thick；T=t1 < t2；α is air cavity sectional area geometric corrections parameter.Since with the increase of input air pressure, the deformation of air cavity cross section
Can be increasingly severe, so that being not stringent rectangular section, therefore introduces geometric corrections parameter alpha and geometry deformation is repaired
Just.
Since air pressure uniformly acts on air cavity inner surface, geometrical relationship shown in available formula (9) and formula (10):
Wherein: n is the increment that air cavity sectional dimension is generated with air pressure increase；A0 and b0 is respectively helical under original state
Type actuator air cavity section is long and wide；A, b, A and B are respectively spiral type actuator air cavity section length, air cavity section under inflated condition
Face is wide, actuator section is long, actuator section is wide；
In addition, since spiral type actuator wall thickness change in gas replenishment process and the geometrical relationship of expanded angle are difficult to accurate table
It states, is calculated to simplify, it is assumed that wall thickness and expanded angle are at simple linear decrease relationship shown in formula (11).Wherein β is to draw
The wall thickness geometric corrections parameter entered；θ is spiral type actuator expanded angle under inflated condition.
T=t0-βθ (11)
The arc length length of spiral type actuator can be acquired by integral operation, as shown in Figure 1, when spiral type under inflated condition
When actuator is located at the second quadrant or third quadrant of world coordinate system { W }, L is indicated are as follows:
For round helical, g (φ) can be embodied as:
G (φ)=R0 (13)
For Archimedes spiral, g (φ) can be embodied as:
For logatithmic spiral, g (φ) can be embodied as:
As shown in figure 3, under the inflated condition spiral type actuator be located at world coordinate system { W } fourth quadrant or first as
In limited time, L should rewrite are as follows:
Volume Va shared by gas intracavity gas and volume Vs shared by silicon rubber can be respectively indicated are as follows:
Because the total volume of elastic matrix remains unchanged during expansion, have:
Vs=Vs0 (18)
Wherein Vs0 can be with approximate representation are as follows:
Vs0≈L0A0B0-la0a0b0 (19)
In this example, and because strain limiting layer will not generate elongation strain, spiral type actuator in actuation process
Outside arc length length remains unchanged, and calculates to simplify, it is assumed that arc length length la and strain limit on the outside of spiral type actuator air cavity
The length L of preparative layer is remained unchanged in actuation process, can be indicated are as follows:
Simultaneous formula (9)-(11) and (18)-(20) can acquire the expression formula of n under the state.Formula (19) is about n and θ
Implicit function, it is extremely difficult to be translated into explicit function form.Therefore, by slove () function in mathematical software MatLab
Carry out implicit function solution.
It, can be specific for designed spiral type actuator λ 1, λ 2 and λ 3 according to the analysis to actuator geometrical relationship
It indicates are as follows:
According to the principle of virtual work, system is when being not affected by any external force, it is believed that inflates what the air pressure P of generation was done
Function is completely converted into the expansion deformation of spiral type actuator, and the summation of air pressure P work done and elastic matrix work done
It is zero:
PdVa+VsDW=0 (22)
Formula (22) both sides simultaneously can obtain θ derivation:
According to formula (7), W derivation can be obtained:
According to formula (21), distinguishing derivation to λ 1, λ 2 and λ 3 can be obtained:
Finally, the relationship of available input air pressure P and actuator expanded angle θ are as follows:
In formula: dVa/d θ and dW/d θ can be rewritten as the expression formula for containing only variable θ.Input air pressure P is with standard atmospheric pressure
As relative barometric pressure zero point, Pa=101.325KPa.
The relationship of description input air pressure P and actuator expanded angle θ is available for according to above-mentioned modeling method.And because
It is that actuator expanded angle θ and the relationship of helical angle φ are as depicted in figs. 1 and 2.In Fig. 1 and Fig. 2, spiral type actuator is answered
The initial position become under limiting layer original state is defined as the origin of world coordinate system { W }, by the fortune under actuator unfolded state
Moving coordinate system is defined as coordinate system { O }.Therefore helical angle φ can be obtained according to modeling method and formula (5).
Wherein k is helical curvature, and with the variation of actuator expansion shape, k is from just becoming negative.
According to upright projection of the shape graduation mark on strain limiting layer on graph paper, each expansion shape can be successively acquired
The coordinate data of state, but shape graduation mark acquisition data be spiral type actuator working space coordinate value, need through
Cross the configuration space parameter R that data processing is converted into spiral type actuator0And C0。
Obtain configuration space parameter R0And C0The step of (S3) in be described as follows:
Firstly, calculating the origin of kinetic coordinate system { O } under different deployed configurations.Circle is general in world coordinate system { W }
Expression formula is:
x2+y2+ Dx+Ey+F=0 (6)
Wherein D, E and F are parameters to be asked.It can uniquely really according to three points being not arranged on the same straight line in theorem plane
A fixed circle, upper 3 points of circle is brought into the origin of formula (6) available kinetic coordinate system { O } are as follows:
Wherein ri, OXi and OYi are respectively the radius and fortune of the corresponding circle of actuator strain limiting layer under air pressure P=i state
Coordinate value of the origin of moving coordinate system { O } in world coordinate system { W }.
Then, according to the coordinate of kinetic coordinate system { O } origin, by the coordinate of the corresponding data collection point of each unfolded state
It is moved in kinetic coordinate system { O }.Then, the transformation according to helical mathematic(al) representation from cartesian coordinate system to polar coordinate system is closed
System, calculates the corresponding helical radius r of each graduation mark and helical angle φ.
Further according to fitting algorithms such as including but not limited to least square method, cubic spline interpolations, several intermediate are utilized
Calibration points corresponding r and φ obtains the corresponding configuration space parameter R of the unfolded state0And C0。
Experimental verification:
Experimental procedure is divided into four steps:
1) every kind of spiral type actuator manufactures 5 respectively, is manufactured with a batch actuator using identical injection mold,
Therefore model machine meets same standard and is comparable.
2) to each spiral type actuator, the expansion exercise testing in the case where different input air pressure P are acted on, input are successively carried out
Air pressure range is 0~39KPa, a length of 5KPa of incremental step；
3) upright projection according to the shape graduation mark on strain limiting layer on graph paper is tested every time, and successively acquisition is each
The coordinate data of a unfolded state；
4) the average expansion exercise data of every kind of actuator is then calculated.
The above method is utilized respectively to be tested.
For the spiral type actuator of circular in configuration, since the corresponding expansion of its shape graduation mark is bent under a certain unfolded state
Rate is identical, then 3 adjacent points (x1, y1) is successively chosen from graduation mark, (x2, y2), (x3, y3) bring formula (27) into and counted
It calculates, coordinate value and helical radius of the origin of kinetic coordinate system { O } in world coordinate system { W } can be acquired.
It is the kinetic coordinate system origin of input air pressure P and round spiral type actuator under circular in configuration, configuration sky shown in Fig. 4
Between parameter R0And C0Relational graph, the design parameter of three kinds of spiral types replenished in Tables 1 and 2.From figure as it can be seen that working as P ≈
When 25KPa, soft actuator expansion shape is approximately the straight line with the negative Y direction of world coordinate system, so this unfolded state lower half
Diameter tends to be infinite.Under other states, it is believed that | OX | ≈ r, OY ≈ 0.This explanation is unfolded about spiral type actuator after inflation
Still identical hypothesis is to set up to the equation in coordinates form of state with initial configuration expression-form.
For the spiral type actuator of Archimedes spiral configuration, due to straining on limiting layer under any unfolded state
The corresponding helical radius of shape graduation mark is gradually increased with acquisition order, namely is unfolded what curvature was not constant between, so not
Data processing method identical with circular in configuration can be directlyed adopt.Phase on the spiral type actuator of Archimedes's configuration is assumed herein
Three adjacent graduation marks, then can be approximately according to formula (27), only using above-mentioned 3 points of determinations approximatively on the same circle
The method of one circle calculates coordinate value of kinetic coordinate system { O } origin in world coordinate system { W }.Then, according to formula (29),
Configuration space parameter is fitted using least square method.It is input air pressure P and Archimedes under Archimedes spiral configuration shown in Fig. 5
Kinetic coordinate system origin, the configuration space parameter R of spiral type actuator0And C0Relational graph.
For the spiral type actuator of logatithmic spiral configuration, it is also assumed that three adjacent graduation marks are close on strain limiting layer
As on the same circle.Then, approximately according to formula (6), the method uniquely justified using above-mentioned 3 points of determinations calculates movement
Coordinate value of coordinate system { O } origin in world coordinate system { W }.In addition, using least square method fitting configuration space parameter it
Before, take logarithm to obtain deforming expression formula as follows on formula (4) both sides:
Ln r=ln R0+C0φ (9)
Then lnr and φ is recycled to be fitted to obtain lnR0And C0, finally to lnR0It carries out exponent arithmetic and obtains R0.Shown in Fig. 6
It is kinetic coordinate system origin, the configuration space parameter R of input air pressure P and logatithmic spiral type actuator under logatithmic spiral configuration0And C0
Relational graph.
In order to verify the feasibility of S3 section configuration space parameter acquiring method, according to the statical model of related patents 2 and
The configuration space parameter R that Data Processing in Experiment obtains in S3 section0And C0, three kinds of spiral type actuators are successively rebuild in input air pressure P
Theoretical expansion shape under=0KPa, 10KPa, 20KPa and 30KPa, as shown in Figure 7.
Compare and analyze three kinds of spiral type actuator reconstructed results, it is available such as to draw a conclusion: round spiral type actuator
Reconstructed results are the most accurate, Archimedes's line style actuator and logatithmic spiral type actuator exist in actuator starting point and end
Different degrees of error.As a result illustrate, according to the collected coordinate data of shape graduation mark, calculated using least square fitting
Method, configuration space parameter R of the available spiral type actuator under different unfolded states0And C0.In conjunction with statical model, into
And the theoretical expansion shape of actuator can be rebuild.But with the increase of input air pressure, the deformation extent of actuator is increasingly
Greatly, the error between the terminal position of actuator model machine and theoretical expansion shape is also increasing.Error Producing reason is main
Be: 1) inherent characteristic of actuator itself, actuator distal end are difficult to realize negative curvature inflection；2) frictional force and gravity affect cause
The expansion movenent performance of dynamic device；3) number of shape graduation mark is insufficient.
In order to further decrease the error of reconstruction, segment reconstruction method can be used, by actuator end portions, middle part portion
Divide the separation for being fitted configuration space parameter three segmentations respectively with root portion that can be adjusted according to actual reconstruction effect.
For logatithmic spiral type actuator, amount to 16 shape graduation marks in this example from actuator distal end to root, it will
The corresponding coordinate points of 1-3 shape graduation mark divide actuator distal end segmentation into, by the corresponding coordinate click and sweep of 4-8 shape graduation mark
Actuator root segment successively segment reconstruction is divided into for actuator middle section, by the corresponding coordinate points of 9-16 shape graduation mark
Theoretical expansion shape of three kinds of spiral type actuators at input air pressure P=0KPa, 10KPa, 20KPa and 30KPa, such as Fig. 8 institute
Show.The configuration space parameter of the reconstruction of three segmentations is as shown in Figure 9.Actuator theory expansion shape segment reconstruction result is obviously excellent
In whole body reconstruction result.
In conclusion the present embodiment preferred design a kind of pneumatic software actuator of spiral type (spiral type actuator) configuration
Spatial parameter acquisition methods, and shape is turned on to actuator and is rebuild.The experimental results showed that designed configuration space is joined
The configuration space parameter of the available actuator complete length of counting method rebuilds effect ideal, the theoretical expansion shape of segment reconstruction
Shape and practical expansion shape error are smaller.
The above content is a further detailed description of the present invention in conjunction with specific preferred embodiments, and it cannot be said that
Specific implementation of the invention is only limited to these instructions.For those skilled in the art to which the present invention belongs, it is not taking off
Under the premise of from present inventive concept, several equivalent substitute or obvious modifications can also be made, and performance or use is identical, all answered
When being considered as belonging to protection scope of the present invention.
Claims (10)
1. a kind of method that spiral type actuator rebuilds expansion shape, it is characterised in that include the following steps:
S1, the relationship for obtaining input air pressure P Yu actuator expanded angle θ；
S2, helical angle φ is obtained based on expanded angle θ；
S3: configuration space parameter R is obtained0And C0；
S4: according to obtained helical angle and configuration space parameter R0And C0Rebuild actuator expansion shape.
2. the method that spiral type actuator as described in claim 1 rebuilds expansion shape, it is characterised in that: in step S1, obtain
Include the following steps: to input air pressure P and the method for the relationship of actuator expanded angle θ
S11, the performance characteristics according to elastic material, establish material model；
S12, actuator statical model is established, wherein the relationship of input air pressure P and actuator expanded angle θ are as follows:
In formula: Va is volume shared by gas intracavity gas, and Vs is volume Vs shared by silicon rubber；W is strain energy density；Input air pressure P
Using standard atmospheric pressure as relative barometric pressure zero point, Pa=101.325KPa.
3. the method that spiral type actuator as claimed in claim 2 rebuilds expansion shape, it is characterised in that: obtain according to the following formula
Helical angle φ:
Wherein k is helical curvature, and with the variation of actuator expansion shape, k is from just becoming negative.
4. the method that spiral type actuator as described in claim 1 rebuilds expansion shape, it is characterised in that in step S3, according to
Upright projection of the shape graduation mark on limiting layer on graph paper is strained, the coordinate data of each unfolded state is successively acquired,
That is the coordinate value of spiral type actuator working space is joined by the configuration space that data processing is converted into spiral type actuator
Number R0And C0。
5. the method that spiral type actuator as claimed in claim 4 rebuilds expansion shape, which is characterized in that in step S3, obtain
Take configuration space parameter R0And C0The step of specifically include:
S31, the origin for calculating kinetic coordinate system { O } under different deployed configurations；
S32, according to the coordinate of kinetic coordinate system { O } origin, by the coordinate translation of the corresponding data collection point of each unfolded state
Into kinetic coordinate system { O }；
S33, further according to fitting process, obtain the corresponding configuration space of the unfolded state using intermediate calibration points corresponding r and φ
Parameter R0And C0。
6. the method that spiral type actuator as claimed in claim 4 rebuilds expansion shape, which is characterized in that use segment reconstruction
Actuator end portions, mid portion and root portion are fitted configuration space parameter by method respectively.
7. the method that spiral type actuator as claimed in claim 2 rebuilds expansion shape, which is characterized in that in step S11, adopt
With the non-linear relation between Yeoh model foundation material stress and strain, strain energy density function model are as follows:
Wherein dkBe material parameter, J be after material deformation with the volume ratio before deformation, for incompressible material, J=1；N is to answer
Become the order of energy density function；CiFor material parameter；I1For the 1st invariant of strain tensor, it may be assumed that
Wherein: λ1、λ2And λ3Respectively actuator shaft is to, radially and circumferentially principal extension ratio.
8. the method that spiral type actuator as claimed in claim 7 rebuilds expansion shape, it is characterised in that,
When making the elastic matrix of spiral type actuator using silica gel material, its material category can be described using second order Yeoh model
Property, then have
W=C1(I1-3)+C2(I1-3)2,
The wherein classical value of silastic material parameter are as follows: C1=0.11MPa, C2=0.02MPa.
9. the method that spiral type actuator as claimed in claim 5 rebuilds expansion shape, it is characterised in that, the helical is
Round, Archimedes spiral or logatithmic spiral, the relationship such as following formula of polar equation formula and cartesian coordinate equation
It is shown:
Wherein the angle φ is helical angle；R is helical radius, and different helical types, the functional relation between r and φ is different；X and y
Coordinate value under respectively corresponding cartesian coordinate system.
10. the method that spiral type actuator as claimed in claim 9 rebuilds expansion shape, it is characterised in that, Archimedes's spiral shell
The polar equation formula of line are as follows:
R=R0+C0φ
Wherein, R0It is helical starting point at a distance from polar origin；C0It is helical radius r with the rate of helical angle change；For
The polar equation expression formula of determining helical configuration, helical is unique, at this time R0And C0It is constant coefficient；
Circle is one kind of Archimedes spiral, polar equation formula are as follows:
R=R0+C0φ, C0=0
The polar equation formula of logatithmic spiral are as follows:
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Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20030197095A1 (en) * | 2001-12-07 | 2003-10-23 | Daniel Preston | Steerable parachute control system and method |
| JP2004058817A (en) * | 2002-07-29 | 2004-02-26 | Toyota Motor Corp | Steering device |
| CN108371609A (en) * | 2018-03-27 | 2018-08-07 | 华中科技大学 | A kind of software driver for assisting human hand thumb stretching, extension and abduction |
| CN108427322A (en) * | 2018-03-16 | 2018-08-21 | 南京航空航天大学 | A kind of modeling method of the big flexible flier based on on-line identification |
| CN109325315A (en) * | 2018-11-13 | 2019-02-12 | 清华大学深圳研究生院 | A kind of statics modeling method of continuous type mechanical arm |
-
2019
- 2019-06-28 CN CN201910580059.5A patent/CN110276158B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20030197095A1 (en) * | 2001-12-07 | 2003-10-23 | Daniel Preston | Steerable parachute control system and method |
| JP2004058817A (en) * | 2002-07-29 | 2004-02-26 | Toyota Motor Corp | Steering device |
| CN108427322A (en) * | 2018-03-16 | 2018-08-21 | 南京航空航天大学 | A kind of modeling method of the big flexible flier based on on-line identification |
| CN108371609A (en) * | 2018-03-27 | 2018-08-07 | 华中科技大学 | A kind of software driver for assisting human hand thumb stretching, extension and abduction |
| CN109325315A (en) * | 2018-11-13 | 2019-02-12 | 清华大学深圳研究生院 | A kind of statics modeling method of continuous type mechanical arm |
Non-Patent Citations (6)
| Title |
|---|
| DEEPAK TRIVEDI ET AL.: "Geometrically Exact Models for Soft Robotic Manipulators", 《IEEE TRANSACTIONS ON ROBOTICS》 * |
| JIANTAO SUN ET AL.: "26，A Novel Design of Serial Variable Stiffness Actuator Based on an Archimedean Spiral Relocation Mechanism", 《IEEE/ASME TRANSACTIONS ON MECHATRONICS》 * |
| SEID HOSSEIN SADAT ET AL.: "Large-Deflection Spiral-Shaped Micromirror Actuator", 《JOURNAL OF MICROELECTROMECHANICAL SYSTEMS》 * |
| ZHIYUAN ZHANG ET AL.: "Kinematic Analysis of Novel Soft Robotic Arm Based on Virtual Work Principle", 《PROCEEDINGS OF THE 2018 IEEE》 * |
| ZHIYUAN ZHANG ET AL.: "Shape Detection and Reconstruction of Soft Robotic Arm Based on Fiber Bragg Grating Sensor Array", 《2018 IEEE INTERNATIONAL CONFERENCE ON ROBOTICS AND BIOMIMETICS (ROBIO)》 * |
| 王华等: "软体弯曲驱动器设计与建模", 《北京航空航天大学学报》 * |
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