CN103714215A - Multi-strand spiral spring virtual model supporting force tactile feedback - Google Patents

Abstract

The invention provides a multi-strand spiral spring model supporting force tactile feedback. The multi-strand spiral spring model is formed by sequentially and rotationally connecting a plurality of multi-strand spiral springs in series. In the interactive process, output feedback is calculated through the multi-strand spiral spring model and reflected in real-time deformation simulation force tactile information signals of flexible bodies under the effect of given virtual external force, the sum of stretching or compression deformation generated on all layers in the multi-strand spiral spring model is externally equivalent to deformation of the surfaces of the flexible bodies. The stretching or compression deformation of all the layers of the multi-strand spiral spring model is calculated through the same method, calculation is simple, and deformation calculation speed is increased. The flexible bodies of different types can be simulated by adjusting the diameter, the medium diameter and the number of strands of the multi-strand spiral springs, and the application range is wide. The multi-strand spiral spring model can be applied to the fields of virtual surgical operation simulation, remote operation robot control and telemedicine.

Description

A kind of stranded wire helical spring dummy model of holding power tactile feedback

Technical field

The invention belongs to computer simulation technique field, relate in particular to a kind of stranded wire helical spring dummy model of holding power tactile feedback.

Background technology

In virtual operation artificial system, flexible body deformation model is mainly used in describing the reciprocal process between human organ flexible body and operating theater instruments, and it has directly determined precision, speed and the simulated effect of power sense of touch in operation simulation system.At present, solving the power sense of touch fidelity of flexible body deformation model and the contradiction between calculating real-time is the current important research topic of virtual operation artificial system.

The conventional flexible body deformation simulation haptic modeling method based on physical significance mainly contains several as follows: 1. free style deformation model core concept is that deformation operation does not directly act on object, but act on the embedded deformation space of object, embedded object along with deformation space be extruded, crooked or be twisted into arbitrary shape and corresponding distortion occurs, this model is comparatively simple, computing velocity is fast, but computational accuracy is low, poor robustness.2. 3DChainMail model: each volume element is connected with six unit of its arest neighbors, certain node in structure is during by push-and-pull, link meeting between unit absorbs this motion by the space between interstitital texture, by the constraint of the length that changes link, just can carry out modeling to different rigid bodies and flexible body.This model computing velocity is very fast, and real-time is better, but computational accuracy is low, poor robustness.3. finite element model basic thought is the discrete junior unit one by one that turns to of the continuous space at whole object place, each junior unit has some nodes, then kinetics equation is discrete to each junior unit, obtain the displacement of these nodes, then use previously selected interpolating function to carry out the displacement of every bit in computing unit; This model computational accuracy is high, and robustness is good, but comparatively complicated, computing velocity is slow.

In view of the above problems, in order to make Virtual Reality Human machine power haptic interaction process more meet people's self custom, improve mutual feeling of immersion and the sense of reality, need to set up a kind of dummy model of holding power tactile feedback.

Summary of the invention

Technical matters to be solved by this invention is to overcome the deficiencies in the prior art, a kind of stranded wire helical spring dummy model of holding power tactile feedback.

In order to solve the problems of the technologies described above, the technical solution adopted in the present invention is: a kind of stranded wire helical spring dummy model of holding power tactile feedback, comprises the steps:

Step 1, arranges stranded wire helical spring dummy model by layer;

Under given virtual external force F effect, at O place, arbitrfary point, flexible body surface, layering is horizontally disposed with identical stranded wire helical spring; Point O is on stranded wire helical spring center line, and stranded wire helical spring center line is vertical with horizontal direction;

Wherein, the diameter of i layer stranded wire helical spring is that d, central diameter are that D, number of share of stock are g; This i layer stranded wire helical spring is divided into two sections, and epimere is horizontally disposed with, and hypomere and epimere angle are α; I=1,2,3,4 ..., S, S is natural number;

Step 2, stranded wire helical spring property settings;

The active line of given virtual external force F is consistent with stranded wire helical spring center line, and under virtual external force F effect, if the stranded wire helical spring of M layer produces distortion before total in flexible body, M layer is called distortion cutoff layer; Wherein, M≤S, namely the number of plies of stranded wire helical spring at least equals M;

According to multiply spinning behaviour, set:

Under given virtual external force F effect, the deflection producing when ground floor stranded wire helical spring is stretched or compressed is X ₁if, X ₁reach the deflection value X that ground floor stranded wire helical spring is given _c1, in this case, suppose the deflection of front M-1 layer stranded wire helical spring, all the deflection value given with ground floor stranded wire helical spring is identical, is out of shape the deflection of cutoff layer M layer stranded wire helical spring, is not more than the deflection value that ground floor stranded wire helical spring is given;

Step 3, calculates the spring rate P of any one deck stranded wire helical spring, and its computing formula is;

$P=\frac{\mathrm{kG}{d}^{4}g}{8D^3}$

Wherein, k, G are respectively: the sth. made by twisting rope coefficient of stranded wire helical spring, shear elasticity; The spring rate of one deck stranded wire helical spring is all identical arbitrarily;

Twisting with the fingers rope coefficient k is:

$k=\frac{(1+\mathrm{\μ})\cos \mathrm{\α}}{1+\mathrm{\μ}{\cos }^2\mathrm{\α}}$

Wherein, μ is Poisson ratio;

Step 4, determines the external force that arbitrary layer of stranded wire helical spring consumes;

The external force F that ground floor stranded wire helical spring consumes ₁for:

Except ground floor and distortion cutoff layer M layer, the external force F that all the other each layer of stranded wire helical springs consume _jfor:

F _j=X _C1·P

The span of j is 2～M-1;

Step 5, distortion cutoff layer M layer produces the deflection X that stretches or compress _mfor:

$X_M=\frac{F-\underset{i=1}{\overset{M-1}{\mathrm{\Σ}}}{F}_i}{P}$

Step 6, in described stranded wire helical spring dummy model, is added each layer of stranded wire helical spring deflection, is equivalent to the distortion on virtual flexible body surface:

Wherein, X is that front M layer stranded wire helical spring produces stretching or compress variation sum, X _istretching or compress variation for i layer stranded wire helical spring generation in front M-1 layer.

The stranded wire helical spring dummy model of described a kind of holding power tactile feedback, the time delay time that front M layer stranded wire helical spring generation stretches or compression deformation total needs is not more than 1ms, also meets the requirement that refreshing frequency is not less than 1000Hz.

The stranded wire helical spring dummy model of described a kind of holding power tactile feedback, in all stranded wire helical spring numbers of plies, every layer produce to stretch or time delay time that compression deformation needs forms Geometric Sequence, meets:

t _i=q ^i-1t ₁

Wherein, t _irepresent that i layer stranded wire helical spring produces the time delay time of stretching or compression deformation needs, the common ratio that q is Geometric Sequence, t ₁be the time delay time that the 1st layer of stranded wire helical spring generation stretches or compression deformation needs, 1≤i≤M.

The stranded wire helical spring dummy model of described a kind of holding power tactile feedback, described stranded wire helical spring, at stranded wire helical spring, taking up an official post, one deck produces stretching or compression deformation reaches given deflection value X _c1after, its lower one deck starts to produce stretching or compression deformation.

The invention has the beneficial effects as follows: the stranded wire helical spring model that the present invention proposes a kind of holding power tactile feedback, described stranded wire helical spring model is rotated and composes in series successively by a plurality of stranded wire helical springs, in reciprocal process, output feedback is for adopting stranded wire helical spring model to calculate, reaction is under given virtual external force F effect, the signal of the power tactile data of flexible body real-time deformation emulation, in this stranded wire helical spring model, upper generation of all layers stretches or compress variation sum, is externally equivalent to the distortion on flexible body surface.Every layer of stretching of stranded wire helical spring model of the present invention or compress variation computing method are identical, calculate simply, have accelerated the speed that distortion is calculated; By regulating the diameter, central diameter, number of share of stock etc. of stranded wire helical spring, just can simulate dissimilar flexible body, applicability is wide; Can be applicable to the fields such as virtual surgery emulation, teleoperated vehicle's control, tele-medicine.

Accompanying drawing explanation

Fig. 1 is stranded wire helical spring dummy model modeling method schematic diagram.

Fig. 2 is flexible body deformation simulation process flow diagram.

Fig. 3 is the modeling method process flow diagram of holding power tactile feedback in virtual protocol and flexible body reciprocal process.

Fig. 4 is in the modeling method of holding power tactile feedback, external force, the distortion number of plies and time delay time relationship schematic diagram.

Embodiment

The modeling method of the stranded wire helical spring dummy model of a kind of holding power tactile feedback the present invention being proposed below in conjunction with flow process shown in accompanying drawing is elaborated:

Stranded wire helical spring dummy model schematic diagram as shown in Figure 1.A stranded wire helical spring dummy model for holding power tactile feedback, its concrete steps are as follows:

Step 1, arranges stranded wire helical spring dummy model by layer;

Under given virtual external force F effect, at O place, arbitrfary point, flexible body surface, layering is horizontally disposed with identical stranded wire helical spring; Point O is on stranded wire helical spring center line, and stranded wire helical spring center line is vertical with horizontal direction;

Wherein, the diameter of i layer stranded wire helical spring is that d, central diameter are that D, number of share of stock are g; This i layer stranded wire helical spring is divided into two sections, and epimere is horizontally disposed with, and hypomere and epimere angle are α; I=1,2,3,4 ..., S, S is natural number; As shown in Figure 3, be the modeling method process flow diagram of holding power tactile feedback in virtual protocol and flexible body reciprocal process;

Step 2, stranded wire helical spring property settings;

The active line of given virtual external force F is consistent with stranded wire helical spring center line, and under virtual external force F effect, if the stranded wire helical spring of M layer produces distortion before total in flexible body, M layer is called distortion cutoff layer; Wherein, M≤S, namely the number of plies of stranded wire helical spring at least equals M;

According to multiply spinning behaviour, set:

Under given virtual external force F effect, the deflection producing when ground floor stranded wire helical spring is stretched or compressed is X ₁if, X ₁reach the deflection value X that ground floor stranded wire helical spring is given _c1, in this case, suppose the deflection of front M-1 layer stranded wire helical spring, all the deflection value given with ground floor stranded wire helical spring is identical, is out of shape the deflection of cutoff layer M layer stranded wire helical spring, is not more than the deflection value that ground floor stranded wire helical spring is given;

Step 3, calculates the spring rate P of any one deck stranded wire helical spring, and its computing formula is;

$P=\frac{k{\mathrm{Gd}}^{4}g}{8D^3}$

Wherein, k, G are respectively: the sth. made by twisting rope coefficient of stranded wire helical spring, shear elasticity; The spring rate of one deck stranded wire helical spring is all identical arbitrarily;

Twisting with the fingers rope coefficient k is:

$k=\frac{(1+\mathrm{\μ})\cos \mathrm{\α}}{1+\mathrm{\μ}{\cos }^2\mathrm{\α}}$

Wherein, μ is Poisson ratio;

Step 4, determines the external force that arbitrary layer of stranded wire helical spring consumes;

The external force F that ground floor stranded wire helical spring consumes ₁for:

Except ground floor and distortion cutoff layer M layer, the external force F that all the other each layer of stranded wire helical springs consume _jfor:

F _j=X _C1·P

The span of j is 2～M-1;

Step 5, distortion cutoff layer M layer produces the deflection X that stretches or compress _mfor:

$X_M=\frac{F-\underset{i=1}{\overset{M-1}{\mathrm{\Σ}}}{F}_i}{P}$

Step 6, in described stranded wire helical spring dummy model, is added each layer of stranded wire helical spring deflection, is equivalent to the distortion on virtual flexible body surface:

Wherein, X is that front M layer stranded wire helical spring produces stretching or compress variation sum, X _istretching or compress variation for i layer stranded wire helical spring generation in front M-1 layer.

The stranded wire helical spring model of described a kind of holding power tactile feedback, the time delay time that described front M layer stranded wire helical spring generation stretches or compression deformation total needs is not more than 1ms, also meets the requirement that refreshing frequency is not less than 1000Hz.

The stranded wire helical spring model of described a kind of holding power tactile feedback, in its all stranded wire helical spring numbers of plies, every layer produce to stretch or time delay time that compression deformation needs forms Geometric Sequence, meets:

t _i=q ^i-1t ₁

Wherein, t _irepresent that i layer stranded wire helical spring produces the time delay time of stretching or compression deformation needs, the common ratio that q is Geometric Sequence, t ₁be the time delay time that the 1st layer of stranded wire helical spring generation stretches or compression deformation needs, 1≤i≤M.

The stranded wire helical spring model of described a kind of holding power tactile feedback, at stranded wire helical spring, taking up an official post, one deck produces stretching or compression deformation reaches given deflection value X _c1after, its lower one deck starts to produce stretching or compression deformation.As shown in Figure 4, be in the modeling method of holding power tactile feedback, external force, the distortion number of plies and time delay time relationship schematic diagram.

Take virtual hand and virtual kidney model is below example, enumerates the embodiment of technical solution of the present invention.

In this example, all virtual hand and virtual kidney model all directly adopt the OBJ form of deriving from 3DS MAX2013 software, with 599 particles, 1181 virtual hand and 2260 particles that triangle gridding forms, the virtual kidney model of 4831 triangle gridding formations is that example is carried out deformation simulation, and in experimentation, model obtains and revise very convenient; Operating system is Windows2000, take 3DS MAX2013, OpenGL shape library as basis, carries out emulation on VC++2012 Software Development Platform.

When virtual hand being detected and collide on virtual kidney surface any point, under given virtual external force F effect, the inner multiply spiral bullet model of filling of regional area that virtual hand and virtual kidney are mutual, in reciprocal process, output is fed back to and adopts multiply spiral bullet model, the reaction of calculating is virtual kidney under given virtual External Force Acting, the signal of the power tactile data of real-time deformation emulation, as shown in Figure 2;

When in given virtual external force F=1.3 * 10 ^-3n acts on O place, arbitrfary point, flexible body surface, and layering is horizontally disposed with identical stranded wire helical spring; Point O is on stranded wire helical spring center line, and stranded wire helical spring center line is vertical with horizontal direction;

Wherein, the diameter of i layer stranded wire helical spring is d=1 * 10 ^-3m, central diameter are D=30 * 10 ^-3m, number of share of stock are g=3; This i layer stranded wire helical spring is divided into two sections, and epimere is horizontally disposed with, and hypomere and epimere angle are

i=1,2,3,4 ..., S, S is natural number;

If the active line of given virtual external force F is consistent with stranded wire helical spring center line, and under given virtual external force F effect, if the stranded wire helical spring of M layer produces distortion before total in flexible body, M layer is called distortion cutoff layer; M≤S, namely the number of plies number of stranded wire helical spring at least equals M;

In given virtual external force F=1.3 * 10 ^-3under N effect, the deflection producing when ground floor stranded wire helical spring is stretched or compressed is X ₁if, X ₁reach the deflection value X that ground floor stranded wire helical spring is given _c1=0.95 * 10 ^-3m, in this case, suppose the deflection of front M-1 layer stranded wire helical spring, all the deflection value given with ground floor stranded wire helical spring is identical, the deflection that is out of shape cutoff layer M layer stranded wire helical spring, is not more than the deflection value that ground floor stranded wire helical spring is given;

The material of arbitrary layer of stranded wire helical spring is all identical, and gets shear elasticity G=3.09 * 10 ⁷pa, Poisson ratio μ=0.26, the equal round off method of middle, the last data of computation process retains after radix point 3;

Therefore, the sth. made by twisting rope coefficient k of one deck stranded wire helical spring is arbitrarily:

$k=\frac{(1+\mathrm{\μ})\cos \mathrm{\α}}{1+\mathrm{\μ}{\cos }^2\mathrm{\α}}=\frac{(1+0.26)\×\cos \frac{\mathrm{\π}}{6}}{1+0.26\×{\cos }^2\frac{\mathrm{\π}}{6}}=0.913$

The spring rate P of arbitrary layer of stranded wire helical spring is:

$P=\frac{\mathrm{kG}{d}^{4}g}{8D^3}=\frac{0.913\×3.09\×{10}^7\×{(1\×{10}^{-3})}^4\×3}{8\×{(30\×{10}^{-3})}^3}0.392N/m$

If the deflection value that the deflection producing when given virtual external force F can make the stranded wire helical spring of ground floor be stretched or compress is given with the stranded wire helical spring of ground floor is identical, the external force F that stranded wire helical spring of ground floor consumes ₁for:

F ₁=X _C1·P=0.95×10 ^-3×0.392=0.372×10 ^-3N,

F ₁=0.372×10 ^-3N<F=1.3×10 ^-3N，

Suppose the time delay time t that stranded wire helical spring generation stretches or compression deformation needs of ground floor ¹=10 ^-5s;

Suppose that haptic feedback refreshing frequency is 1200Hz, the inverse of haptic feedback refreshing frequency $T=\frac{1}{1200}s;$

The time delay time T that stranded wire helical spring generation stretches or compression deformation needs of ground floor ₁=t ₁=10 ^-5s<T;

Therefore the external force F that, the stranded wire helical spring of ground floor consumes ₁=0.372 * 10 ^-3n<F=1.3 * 10 ^-3n, and the generation of the stranded wire helical spring of ground floor stretches or the time delay time of compression deformation needs meets requirement more than haptic feedback refreshing frequency 1000Hz; Only have after the deflection value that stranded wire helical spring is stretched or compression deformation is given to ground floor stranded wire helical spring of ground floor, the stranded wire helical spring that the second layer is corresponding just starts be stretched or compress.

If given virtual external force F, the deflection producing in the time of making the stranded wire helical spring of the second layer be stretched or compress, arrives the deflection value that the stranded wire helical spring of ground floor is given identical, the external force F that stranded wire helical spring of the second layer consumes ₂for:

F ₂=X _C1·P=0.95×10 ^-3×0.392=0.372×10 ^-3N，

F ₁+F ₂=2×0.372×10 ^-3=0.744×10 ^-3N<F=1.3×10 ^-3N，

The time delay time of interlayer meets the time delay time t that produces stretching or compression deformation needs with the stranded wire helical spring of ground floor ₁for first term, the Geometric Sequence that the q of take is common ratio,

Before two-layer stranded wire helical spring produce to stretch and become or compressed shape amounts to the time delay time needing: T ₂=t ₁+ t ₂=(1+q) t ₁=2.2 * 10 ^-5s<T;

Therefore, the external force sum of front two-layer stranded wire helical spring consumption is less than given virtual external force, and the time delay time that front two-layer stranded wire helical spring generation distortion total needs meets requirement more than refreshing frequency 1000Hz; Only have stranded wire helical spring when the second layer to be stretched or compressed to be deformed to after the deflection value that the stranded wire helical spring of ground floor is given, the 3rd layer of corresponding stranded wire helical spring just starts be stretched or compress.

If the deflection value that the deflection producing when given virtual external force F can make the stranded wire helical spring of the 3rd layer be stretched or compress is given with the stranded wire helical spring of ground floor is identical, the external force F that stranded wire helical spring of the 3rd layer consumes ₃for:

F ₃=X _C1·P=0.95×10 ^-3×0.392=0.372×10 ^-3N

F ₁+F ₂+F ₃=3×0.372×10 ^-3=1.116×10 ^-3N<F=1.3×10 ^-3N，

The stranded wire helical spring of three first layers produces the time delay time that stretching becomes or compressed shape total needs: T ₂=t ₁+ t ₂=(1+q+q ²) t ₁=3.64 * 10 ^-5s<T;

Therefore, the external force sum of the stranded wire helical spring consumption of three first layers is less than given virtual external force, and the time delay time that the stranded wire helical spring of three first layers generation distortion total needs meets requirement more than refreshing frequency 1000Hz; Only have when the stranded wire helical spring of the 3rd layer is stretched or compressed and be deformed to after the deflection value that the stranded wire helical spring of ground floor is given, the 4th layer of corresponding stranded wire helical spring just starts be stretched or compress.

If the deflection value that the deflection producing when given virtual external force F can make the stranded wire helical spring of the 4th layer be stretched or compress is given with the stranded wire helical spring of ground floor is identical, the external force F that stranded wire helical spring of the 4th layer consumes ₄for:

F ₄=X _C1·P=0.95×10 ^-3×0.392=0.372×10 ^-3N

F ₁+F ₂+F ₃+F ₄=4×0.372×10 ^-3=1.488×10 ^-3N>F=1.3×10 ^-3N，

Because the external force sum of the stranded wire helical spring consumption of first four layers is not less than given virtual external force, the 4th layer is distortion cutoff layer, do not need to judge whether again to meet the requirement of refreshing frequency, the deflection value that during the now stranded wire helical spring of three first layers distortion, the deflection of generation stretching or compression is given with the stranded wire helical spring of ground floor is identical, and the deflection that the stranded wire helical spring that distortion cutoff layer is the 4th layer produces while being stretched or compressed is:

$X_4=\frac{F-\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{F}_i}{P}=\frac{1.3\&times;{10}^{-3}-1.166\&times;{10}^{-3}}{0.392}=0.342\&times;{10}^{-3}m$

Therefore in given virtual external force F=1.3 * 10 ^-3under N effect, in the modeling method of stranded wire helical spring dummy model, the stack of the deflection sum that the stranded wire helical spring of first four layers produces while being stretched or compressed distortion is externally equivalent to the distortion on virtual flexible body surface, and deflection sum is:

$X=\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{X}_i+X_4=3\&times;0.95\&times;{10}^{-3}+0.342\&times;{10}^{-3}=3.192\&times;{10}^{-3}m.$

Attention: calculate at the multiply spin model that adopts flexible body deformation simulation in the process of flexible body real-time deformation emulation under given virtual external force is used, if it is excessive that d, D, these parameters of g, α are chosen, the distortion number of plies number of the multiply spin model of flexible body deformation simulation is just few, calculated amount is little, real-time is good, but deformation simulation poor effect; If it is too small that d, D, these parameters of g, α are chosen, the distortion number of plies of the stranded wire helical spring model of flexible body deformation simulation is just more, and calculated amount is large, and real-time is not good, but deformation simulation effect is better; In addition t is being set ₁and t _ibetween proportionate relationship time, consider the hardware configuration of program operation computer-chronograph itself, therefore in the process of the whole program of debugging, compromise and select these parameters, constantly repeatedly debug, thereby make deformation effect more true to nature.

For verifying implementation result of the present invention, operator is by the deformation simulation that the handle of PHANTOM OMNI hand controller end touches, perception and control virtual hand are reversed virtual kidney, and by the power tactile data Real-time Feedback producing in reciprocal process to operator.Experimental result shows, this model algorithm is simple, computing velocity is fast, haptic device is steady, deformation effect is true to nature, can meet the requirement of virtual operation simulation interactive system real time and stability, thereby makes operator to the perception of virtual environment and more accurately true alternately.

Claims (4)

1. a stranded wire helical spring dummy model for holding power tactile feedback, is characterized in that, comprises the steps:

Step 1, arranges stranded wire helical spring dummy model by layer;

Under given virtual external force F effect, at O place, arbitrfary point, flexible body surface, layering is horizontally disposed with identical stranded wire helical spring; Point O is on stranded wire helical spring center line, and stranded wire helical spring center line is vertical with horizontal direction;

Wherein, the diameter of i layer stranded wire helical spring is that d, central diameter are that D, number of share of stock are g; This i layer stranded wire helical spring is divided into two sections, and epimere is horizontally disposed with, and hypomere and epimere angle are α; I=1,2,3,4 ..., S, S is natural number;

Step 2, stranded wire helical spring property settings;

The active line of given virtual external force F is consistent with stranded wire helical spring center line, and under virtual external force F effect, if the stranded wire helical spring of M layer produces distortion before total in flexible body, M layer is called distortion cutoff layer; Wherein, M≤S, namely the number of plies of stranded wire helical spring at least equals M;

According to multiply spinning behaviour, set:

Under given virtual external force F effect, the deflection producing when ground floor stranded wire helical spring is stretched or compressed is X ₁if, X ₁reach the deflection value X that ground floor stranded wire helical spring is given _c1, in this case, suppose the deflection of front M-1 layer stranded wire helical spring, all the deflection value given with ground floor stranded wire helical spring is identical, is out of shape the deflection of cutoff layer M layer stranded wire helical spring, is not more than the deflection value that ground floor stranded wire helical spring is given;

Step 3, calculates the spring rate P of any one deck stranded wire helical spring, and its computing formula is;

$P=\frac{k{\mathrm{Gd}}^{4}g}{8D^3}$

Wherein, k, G are respectively: the sth. made by twisting rope coefficient of stranded wire helical spring, shear elasticity; The spring rate of one deck stranded wire helical spring is all identical arbitrarily;

Twisting with the fingers rope coefficient k is:

$k=\frac{(1+\mathrm{\&mu;})\cos \mathrm{\&alpha;}}{1+\mathrm{\&mu;}{\cos }^2\mathrm{\&alpha;}}$

Wherein, μ is Poisson ratio;

Step 4, determines the external force that arbitrary layer of stranded wire helical spring consumes;

The external force F that ground floor stranded wire helical spring consumes ₁for:

Except ground floor and distortion cutoff layer M layer, the external force F that all the other each layer of stranded wire helical springs consume _jfor:

F _j=X _C1·P

The span of j is 2～M-1;

Step 5, distortion cutoff layer M layer produces the deflection X that stretches or compress _mfor:

$X_M=\frac{F-\underset{i=1}{\overset{M-1}{\mathrm{\&Sigma;}}}{F}_i}{P}$

Step 6, in described stranded wire helical spring dummy model, is added each layer of stranded wire helical spring deflection, is equivalent to the distortion on virtual flexible body surface:

Wherein, X is that front M layer stranded wire helical spring produces stretching or compress variation sum, X _istretching or compress variation for i layer stranded wire helical spring generation in front M-1 layer.

2. the stranded wire helical spring dummy model of a kind of holding power tactile feedback according to claim 1, is characterized in that, the time delay time that described front M layer stranded wire helical spring generation stretches or compression deformation total needs is not more than 1ms.

3. the stranded wire helical spring dummy model of a kind of holding power tactile feedback according to claim 1, is characterized in that, in all stranded wire helical spring numbers of plies, every layer produce to stretch or time delay time that compression deformation needs forms Geometric Sequence, meets:

t _i=q ^i-1t ₁

Wherein, t _irepresent that i layer stranded wire helical spring produces the time delay time of stretching or compression deformation needs, the common ratio that q is Geometric Sequence, t ₁be the time delay time that the 1st layer of stranded wire helical spring generation stretches or compression deformation needs, 1≤i≤M.

4. according to the stranded wire helical spring dummy model of a kind of holding power tactile feedback described in claim 1 or 2 or 3, it is characterized in that described stranded wire helical spring reaches given deflection value X in take up an official post one deck distortion of stranded wire helical spring _c1after, its lower one deck starts to produce stretching or compression deformation.

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