CN105241411A - Stewart platform supporting leg length-measuring apparatus, and Stewart platform pose-testing system and method - Google Patents

Abstract

The invention discloses a Stewart platform supporting leg length-measuring apparatus, and a Stewart platform pose-testing system and method. The Stewart platform supporting leg length-measuring apparatus comprises a fixing clamp and a displacement sensor for measuring the telescoping amount of a supporting leg. The fixing clamp comprises a first clamping portion fixed on a supporting leg piston and a second clamping portion fixed on a supporting leg sleeve; and the displacement sensor is fixed on the second clamping portion. The Stewart platform supporting leg length-measuring apparatus can measure real-time lengths of supporting legs in the movement process of a Stewart platform, and has the advantages of simple structure and high cost performance, thereby being applied to measurement of the telescoping amount of the supporting legs of the Stewart platform at a certain time point. The Stewart platform pose-testing method can solve a real-time pose of the Stewart platform in the movement process according to measured lengths of the supporting legs by use of a value calculation method, thereby being suitable for measurement of the real-time pose of the Stewart platform in the movement process.

Description

Stewart platform legs length-measuring appliance and Stewart platform's position and pose test macro, method

Technical field

The invention belongs to imitation technology field, relate to a kind of Stewart six degree of freedom platform, particularly relate to a kind of Stewart platform legs length-measuring appliance, and Stewart platform's position and pose test macro, method.

Background technology

Stewart platform mechanism was proposed by Stewart in nineteen sixty-five, was the significant parallel manipulator device of automatic field most, belonged to space many rings parallel institution.Stewart platform is primarily of upper mounting plate, lower platform and six telescopic supporting leg compositions, and each ingredient can regard rigid body as, and its motion also can regard rigid motion as.The two ends of every bar supporting leg are connected with upper mounting plate, lower platform respectively by two ball pivots or ball pivot one end, one end universal joint.Stewart platform legs adopts sleeve-piston cylinder operator usually, and piston is flexible under hydraulic action, and the following hinge of sleeve is center of circle motion.

During work, lower platform is fixed, by adjusting the length of six supporting legs, the upper fulcrum of supporting leg drives upper mounting plate motion, to make upper mounting plate be in different attitude, such upper mounting plate just in the movement of three-dimensional space intercropping any direction and the rotation around any direction, can have six-freedom degree relative to lower platform.When propping up leg length consecutive variations, platform stance is just in dynamically, can use as analog simulation platform.

It is flexible that current supporting leg adopts hydraulic way to drive mostly, its principal feature be compact conformation, motion flexibly, good rigidity, load-bearing capacity are strong, precision is high.In use Stewart platform process, user must understand platform stance at any time, to grasp simulation accuracy.

From control angle, Stewart platform relates to two most basic problems: normal solution and instead to separate.Wherein,

Normal solution: the length of known six supporting legs, asks the spatial pose (i.e. three linear coordinate parameters of the upper mounting plate of Stewart platform and three rotational coordinates parameters) of platform.

Anti-solution: the spatial pose of known upper mounting plate, asks the length of six supporting legs.

The Kinematics analysis of Stewart platform solves easily, and Kinematics analysis will calculate the displacement of six supporting legs according to platform's position and pose, thus realizes the real-time control to target.The Kinematics analysis of Stewart platform has well-determined analytic solution, controls easily to realize time in fact.

The position forecast analytic solution of Stewart platform are global difficult problems, and its equation of constraint is the nonlinear multivariable system of equations of its output variable, mathematically there is no complete method and solves its analytic solution.

The pose of current measurement Stewart platform upper mounting plate does not mostly adopt the method measuring a leg length to calculate, the main athletic posture adopting obliquity sensor and gyroscope directly to measure upper mounting plate.Ultimate principle is: obliquity sensor and gyroscope are arranged on the upper mounting plate table top of Stewart platform, the output of obliquity sensor is directly angular displacement, gyro sensor exports as angular velocity amount, can obtain angular displacement, and then can calculate Stewart platform's position and pose attitude after integration.

But the angular displacement that obliquity sensor exports, generally can only use in static or quasi-static environments, utilize obliquity sensor cannot measure Stewart platform stance in a dynamic state.

Gyro sensor can use in dynamic environment, but it exists following shortcoming:

1. the vibration frequency of rigid body (or upper mounting plate of Stewart platform) and the change of amplitude by various degree affect measuring accuracy;

There is larger integral error in the attitude that 2. angular velocity integration obtains, and can build up along with the increase integral error of time, affects measuring accuracy;

3. high accuracy gyroscope price is very expensive, and cost performance is low.

Summary of the invention

For solving the above deficiency existed in prior art, the invention provides a kind of Stewart platform legs length-measuring appliance, the collapsing length of a certain moment supporting leg can be measured, having the advantages that structure is simple, cost performance is high;

Another object of the present invention, is to provide a kind of Stewart platform's position and pose test macro;

3rd object of the present invention, is to provide a kind of Stewart platform's position and pose method of testing, according to measuring the leg length obtained, utilizes numerical computation method to solve, in the hope of the real-time pose of Stewart platform in motion process.

For achieving the above object, the technical solution adopted in the present invention is as follows:

One, a Stewart platform legs length-measuring appliance, it comprises stationary fixture, and for measuring the displacement transducer of landing leg stretching amount; Described stationary fixture comprises for being fixed on the first clamping section on supporting leg piston, for being fixed on the second clamping section on supporting leg sleeve; Institute's displacement sensors is fixed on the second clamping section.

As limitation of the invention, described first clamping section comprises the first support, the first clamping plate; Described first support and the first Boards wall rear center position are with the first through hole for making piston pass through;

Described second clamping section comprises the second support, the second clamping plate; Described second support and the second Boards wall rear center position are with the second through hole for making sleeve pass through.

Restriction as to aforesaid way:

Institute's displacement sensors is stay-supported type displacement sensor; Described first support, the second support are respectively equipped with the first bracing wire fixed orifice, the second bracing wire fixed orifice; The stay cord of displacement transducer successively through the second bracing wire fixed orifice, the first bracing wire fixed orifice, and is fixed on the first bracing wire fixed orifice.

Described Stewart platform legs length-measuring appliance also comprises the calibration rod for ensureing the first clamping section, the second clamping section and piston coaxial line;

Described first support, the second support are respectively equipped with the first calibration hole, the second calibration hole; Described first clamping section, the second clamping section respectively with piston, sleeve connection after, calibration rod can be inserted in transition fit in the first calibration hole, the second calibration hole.

Two, the present invention discloses a kind of Stewart platform's position and pose test macro, it comprises the above-mentioned Stewart platform legs length-measuring appliance of six covers, also comprises data collecting instrument, total processor system;

Six supporting legs of described Stewart platform are fixed with Stewart platform legs length-measuring appliance respectively;

Described Stewart platform legs length-measuring appliance, data collecting instrument, total processor system are electrically connected successively.

Three, the invention also discloses a kind of Stewart platform's position and pose method of testing, it realizes based on above-mentioned Stewart platform's position and pose test macro, and it carries out according to following steps order:

A. install

Six supporting legs of Stewart platform install above-mentioned Stewart platform legs length-measuring appliance respectively; Installation process is as follows:

1. to be in floor level position locked for Stewart platform, and ensure that six leg lengths are in most short status, now Stewart platform legs length is it is known and equal that every bar props up leg length, i.e. l ₁=l ₂=l ₃=l ₄=l ₅=l ₆=L ₀;

2. the first clamping section, the second clamping section are fixed on respectively in advance on the piston of supporting leg, sleeve, and ensure the first clamping section, the second clamping section and piston coaxial line;

4. the first clamping section and piston are fixedly secured, the second clamping section and sleeve fixedly secure;

5. displacement transducer is fixed on the second clamping section;

B supporting leg calibrating length

1. six displacement transducers are received on Measurement channel corresponding to data collecting instrument successively;

2. total processor system control data Acquisition Instrument gathers the current output voltage values of six displacement transducers and by magnitude of voltage current for each displacement transducer as initial value;

C. supporting leg linear measure longimetry

1. control Stewart platform makes it move;

2. in Stewart Platform movement process, displacement transducer on each bar supporting leg can measure the length variations amount of supporting leg in Stewart Platform movement process respectively, the length variations amount of supporting leg can be changed into corresponding analog voltage signal by each displacement transducer, and the analog voltage signal of output is passed to data collecting instrument, the analog voltage signal that each displacement transducer exports by data collecting instrument carries out analog to digital conversion, be converted into digital signal, be passed to total processor system; Total processor system obtains the time series of displacement transducer output voltage wherein k=1,2,3 ... n, n are sampling number;

3. total processor system calculates the physical length of the every bar supporting leg of Stewart platform concrete computation process is as follows:

Wherein K=[k ₁, k ₂, k ₃, k ₄, k ₅, k ₆], k _irepresent the sensitivity of i-th displacement transducer, k=1,2,3 ... n, n are sampling number; I=1,2,3,4,5,6;

The length pot life sequence of its six supporting legs in Stewart Platform movement process represent, wherein k=1,2,3 ... n, n are sampling number.

D.Stewart platform's position and pose resolves

1. with the central point of the lower platform of Stewart platform for reference point o, build fixing three-dimensional system of coordinate oxyz, with the central point of the upper mounting plate of certain moment Stewart platform for reference point o', build dynamic three-dimensional system of coordinate o'x'y'z'; Wherein z-axis and z' axle are respectively perpendicular to upper mounting plate, lower platform;

2. to set z' axle be ψ, y' be θ, x' around the angle of pitch of y-axis around the deflection angle of z-axis around the roll angle of x-axis is the transformation matrix of coordinates that then upper mounting plate rotates around each axle relative to lower platform is:

Upper mounting plate around the complete Rotation matrix of lower platform is:

3. set vector T as lower platform central point is to the vector of upper mounting plate central point, P _ifor the upper fulcrum of platform i-th supporting leg is in the position of coordinate system o'x'y'z', B _ifor the lower fulcrum of platform i-th supporting leg is in the position of coordinate system oxyz;

In coordinate system o'x'y'z', P _ithe coordinate of point is transformed in coordinate system oxyz by formula (4) coordinate transform mode; In coordinate system oxyz, vectorial oP _iuse q _irepresent, in coordinate system o'x'y'z', vectorial o ' P _ip can be used _irepresent, then:

In coordinate system oxyz, i-th supporting leg can be expressed as with vector correlation

Vector l _imould be namely the physical length l of platform legs _i, this vector correlation can be expressed as further:

4. 6 supporting legs of platform can obtain the identical nonlinear equation of 6 structures, namely

Solve the pose parameter that this system of equations just can obtain upper mounting plate, the coordinate of central point o' at coordinate system oxyz of coordinate system o'x'y'z' can be obtained, i.e. coordinate (the x of vector T _t, y _t, z _t), and the Eulerian angle that upper mounting plate rotates around each axle relative to lower platform

5. be the solution procedure of formula (7) below.

To formula (7) differential, change differentiating operator d into limited a small amount of, have

Matrix form is write as to six equations of formula (8), is arranged

Δ x=J ^-1in Δ l (9) formula

Δl＝[Δl ₁,Δl ₂,Δl ₃,Δl ₄,Δl ₅,Δl ₆] ^T

Write formula (9) as Iteration

x _k+1＝x _k+Δx＝x _k+J ^-1Δl＝x _k+J ^-1(l _k ^*-l _k)(10)

K=0 in formula, 1,2,3....n, n are iteration ends number of times.

for upper mounting plate is relative to the pose parameter of lower platform;

for at known x _kthe theory obtained by system of equations (7) in situation props up leg length;

for each the leg length of reality recorded by experiment;

Occur that unusual causing solves instability for avoiding solving J, formula (10) be rewritten into following form:

x _k+1＝x _k+J ⁺(l _k ^*-l _k)(11)

Wherein: J ⁺=J ^t(JJ ^t) ^-1, iterative initial value

x ₀＝[0,0,…,0] ^T

Stopping criterion for iteration

|l _k ^*-l _k|≤ε(12)

Wherein ε is any given iteration precision;

Formula (12) is converted to non-linear least square problem:

The minimum value result of formula (13) had both been optimum matching point, and the minimum value of formula (13) is corresponding the approximate current pose thinking upper mounting plate;

Input one group of l that a certain moment actual measurement must be fallen _k ^*with one group of iterative initial value of specifying, the pose of current upper mounting plate relative to lower platform just can be calculated; Each group l that reality is tested _k ^*upper mounting plate just can be calculated in whole motion process relative to the pose of lower platform with the iterative initial value of specifying.

Owing to have employed technique scheme, compared with prior art, acquired technical progress is in the present invention:

1. Stewart platform legs length-measuring appliance of the present invention, the collapsing length of a certain certain supporting leg of moment can be measured, during the landing leg stretching of Stewart platform, first clamping section, the second clamping section can along with sleeve-piston structure motions, there is relative displacement first clamping section, the second clamping section, landing leg stretching amount can be recorded by displacement transducer, then can to calculate on supporting leg length between lower link point according to stroke, have the advantages that structure is simple, cost performance is high;

2. Stewart platform's position and pose method of testing of the present invention, according to length between lower link point on the supporting leg calculated, utilizes process of iteration to carry out numerical solution, can try to achieve the real-time pose of Stewart platform in motion process.

Stewart platform legs length-measuring appliance of the present invention is applicable to the stroke measuring certain moment Stewart platform legs, and Stewart platform's position and pose test macro of the present invention and method are applicable to measure the real-time pose of Stewart platform in motion process.

Accompanying drawing explanation

Below in conjunction with drawings and the specific embodiments, the present invention is further described in detail.

Fig. 1 is the structural representation of the embodiment of the present invention 1;

Fig. 2 is the coordinate schematic diagram of the embodiment of the present invention 3.

In figure: 1, the first clamping section; 11, the first support; 12, the first clamping plate; 13, the first bracing wire fixed orifice; 14, the first calibration hole; 2, the second clamping section; 21, the second support; 22, the second clamping plate; 23, the second bracing wire fixed orifice; 24, the second calibration hole; 3, calibration rod; 4, stay-supported type displacement sensor.

Embodiment

Embodiment 1Stewart platform legs length-measuring appliance

A kind of Stewart platform legs length-measuring appliance, structure as shown in Figure 1, for measuring the stroke of the supporting leg of Stewart platform, comprises stationary fixture, stay-supported type displacement sensor 4, calibration rod 3.

Stationary fixture comprises the first clamping section 1 be fixed on supporting leg piston, the second clamping section 2 be fixed on supporting leg sleeve.

First clamping section 1 comprises the first support 11, first clamping plate 12.First support 11 is provided with the first bracing wire fixed orifice 13, first calibration hole 14.After first support 11 and the first clamping plate 12 are fixed, centre is with the first through hole for making piston pass through.

Second clamping section 2 comprises the second support 21, second clamping plate 22.Second support 21 is provided with the second bracing wire fixed orifice 23, second calibration hole 24.After second support 21 and the second clamping plate 22 are fixed, centre is with the second through hole for making sleeve pass through.

Stay-supported type displacement sensor 4 is fixed on the second support 21, and its stay cord successively through the second bracing wire fixed orifice 23, first bracing wire fixed orifice 13, and is fixed on the first bracing wire fixed orifice 13.

Calibration rod 3 is for ensureing the first clamping section 1, second clamping section 2 and piston coaxial line.First clamping section 2, clamping section 1, second respectively with piston, sleeve connection after, calibration rod 3 inserts in the first calibration hole 14, second calibration holes 24, takes off calibration excellent 3 after calibrate again.

The process that installs and measures of the present embodiment is as follows:

First the first clamping section 2, clamping section 1, second is fixed on respectively in advance on the piston of supporting leg, sleeve; Rod 3 will be calibrated and insert the first calibration hole 14, second calibration hole 24, to ensure the first clamping section 1, second clamping section 2 and piston coaxial line; Then the first clamping section 1 and piston are fixedly secured, the second clamping section 2 fixedly secures with sleeve; Then displacement transducer 4 is fixed on the second clamping section 2, and makes the free end of stay cord successively through the second bracing wire fixed orifice 23, first bracing wire fixed orifice 13, and be fixed on the first bracing wire fixed orifice 13; Finally take off calibration rod 3, complete installation.First clamping section 2, clamping section 1, second can along with sleeve-piston structure motion, there is relative displacement first clamping section 2, clamping section 1, second, landing leg stretching amount can be recorded by stay-supported type displacement sensor 4, then can to calculate on supporting leg length between lower link point according to stroke.

Embodiment 2Stewart platform's position and pose test macro

A kind of Stewart platform's position and pose test macro, it comprises the Stewart platform legs length-measuring appliance that six cover embodiments 1 provide, and data collecting instrument and total processor system.

Six supporting legs of Stewart platform are fixed with Stewart platform legs length-measuring appliance respectively.The output terminal of Stewart platform legs length-measuring appliance is connected with the input end of data collecting instrument, data collecting instrument is for receiving the length variations signal of the supporting leg of each stay-supported type displacement sensor 4 collection, the output terminal of data collecting instrument is connected with the input end of total processor system, total processor system is for receiving the signal of data collecting instrument transmission, and signal is calculated, finally draw the pose of upper mounting plate relative to lower platform.

Embodiment 3Stewart platform's position and pose method of testing

A kind of Stewart platform's position and pose method of testing, it realizes based on the system of embodiment 2, carries out according to following steps order:

A., Stewart platform legs length-measuring appliance is installed

Six supporting legs of Stewart platform are installed Stewart platform legs length-measuring appliance described in embodiment 1 respectively; Installation steps are carried out in the following order:

1. to be in floor level position locked for Stewart platform, and ensure that six leg lengths are in most short status, now Stewart platform legs length is it is known and equal that every bar props up leg length, i.e. l ₁=l ₂=l ₃=l ₄=l ₅=l ₆=L ₀;

2. the first clamping section 2, clamping section 1, second is fixed on respectively in advance on the piston of supporting leg, sleeve;

3. will calibrate rod 3 and insert the first calibration hole 14, second calibration hole 24, to ensure the first clamping section 1, second clamping section 2 and piston coaxial line;

4. the first clamping section 1 and piston are fixedly secured, the second clamping section 2 fixedly secures with sleeve;

5. stay-supported type displacement sensor 4 is fixed on the second clamping section 2;

6. the free end of the stay cord of stay-supported type displacement sensor 4 is passed the second bracing wire fixed orifice 23, first bracing wire fixed orifice 13 successively, and be fixed on the first bracing wire fixed orifice 13.

7. calibration rod 3 is taken off;

B. supporting leg calibrating length

1. six stay-supported type displacement sensors 4 are received on Measurement channel corresponding to data collecting instrument successively;

2. total processor system control data Acquisition Instrument gathers the current output voltage values of six stay-supported type displacement sensors 4 and by magnitude of voltage current for each stay-supported type displacement sensor 4 as initial value;

C. supporting leg linear measure longimetry

1. control Stewart platform makes it move;

2. in Stewart Platform movement process, stay-supported type displacement sensor 4 on each bar supporting leg can measure the length variations amount of supporting leg in Stewart Platform movement process respectively, the length variations amount of supporting leg can be changed into corresponding analog voltage signal by each stay-supported type displacement sensor 4, and the analog voltage signal of output is passed to data collecting instrument, the analog voltage signal that each stay-supported type displacement sensor 4 exports is carried out analog to digital conversion by data collecting instrument, be converted into digital signal, be passed to total processor system; Total processor system obtains the time series of stay-supported type displacement sensor 4 output voltage wherein k=1,2,3 ... n, n are sampling number;

3. total processor system calculates the physical length of the every bar supporting leg of Stewart platform concrete computation process is as follows:

$l_k^{*}=K*\left(v_k-v_b\right)+l_c$

Wherein K=[k ₁, k ₂, k ₃, k ₄, k ₅, k ₆] _,k _irepresent the sensitivity of i-th stay-supported type displacement sensor, k=1,2,3 ... n, n are sampling number; I=1,2,3,4,5,6;

The length pot life sequence of its six supporting legs in Stewart Platform movement process represent, wherein k=1,2,3 ... n, n are sampling number.

D.Stewart platform's position and pose resolves

1. with the central point of the lower platform of Stewart platform for reference point o, build fixing three-dimensional system of coordinate oxyz, with the central point of the upper mounting plate of certain moment Stewart platform for reference point o', build dynamic three-dimensional system of coordinate o'x'y'z'; Wherein z-axis and z' axle are respectively perpendicular to upper mounting plate, lower platform;

2. to set z' axle be ψ, y' be θ, x' around the angle of pitch of y-axis around the deflection angle of z-axis around the roll angle of x-axis is the transformation matrix of coordinates that then upper mounting plate rotates around each axle relative to lower platform is:

Upper mounting plate around the complete Rotation matrix of lower platform is:

3. set vector T as lower platform central point is to the vector of upper mounting plate central point, P _ifor the upper fulcrum of platform i-th supporting leg is in the position of coordinate system o'x'y'z', B _ifor the lower fulcrum of platform i-th supporting leg is in the position of coordinate system oxyz;

In coordinate system o'x'y'z', P _ithe coordinate of point is transformed in coordinate system oxyz by formula (4) coordinate transform mode; In coordinate system oxyz, vectorial oP _iuse q _irepresent, in coordinate system o'x'y'z', vectorial o ' P _ip can be used _irepresent, as shown in Figure 2, then:

In coordinate system oxyz, i-th supporting leg can be expressed as with vector correlation

Vector l _imould be namely the physical length l of platform legs _i, this vector correlation can be expressed as further:

4. 6 supporting legs of platform can obtain the identical nonlinear equation of 6 structures, namely

Solve the pose parameter that this system of equations just can obtain upper mounting plate, the coordinate of central point o' at coordinate system oxyz of coordinate system o'x'y'z' can be obtained, i.e. coordinate (the x of vector T _t, y _t, z _t), and the Eulerian angle that upper mounting plate rotates around each axle relative to lower platform

5. be the solution procedure of formula (7) below.

To formula (7) differential, change differentiating operator d into limited a small amount of, have

Matrix form is write as to six equations of formula (8), is arranged

Δx＝J ^-1Δl(9)

In formula

Δl＝[Δl ₁,Δl ₂,Δl ₃,Δl ₄,Δl ₅,Δl ₆] ^T

Write formula (9) as Iteration

x _k+1＝x _k+Δx＝x _k+J ^-1Δl＝x _k+J ^-1(l _k ^*-l _k)(10)

K=0 in formula, 1,2,3....n, n are iteration ends number of times.

for upper mounting plate is relative to the pose parameter of lower platform;

for at known x _kthe theory obtained by system of equations (7) in situation props up leg length;

for each the leg length of reality recorded by experiment;

Occur that unusual causing solves instability for avoiding solving J, formula (10) be rewritten into following form:

x _k+1＝x _k+J ⁺(l _k ^*-l _k)(11)

Wherein: J ⁺=J ^t(JJ ^t) ^-1, iterative initial value

x ₀＝[0,0,…,0] ^T

Stopping criterion for iteration

|l _k ^*-l _k|≤ε(12)

Wherein ε is any given iteration precision;

Formula (12) is converted to non-linear least square problem:

The minimum value result of formula (13) had both been optimum matching point, and the minimum value of formula (13) is corresponding the approximate current pose thinking upper mounting plate;

Input one group of l that a certain moment actual measurement must be fallen _k ^*with one group of iterative initial value of specifying, the pose of current upper mounting plate relative to lower platform just can be calculated; Each group l that reality is tested _k ^*upper mounting plate just can be calculated in whole motion process relative to the pose of lower platform with the iterative initial value of specifying.

Claims (6)

1. a Stewart platform legs length-measuring appliance, is characterized in that: it comprises stationary fixture, and for measuring the displacement transducer of a leg length; Described stationary fixture comprises for being fixed on the first clamping section on supporting leg piston, for being fixed on the second clamping section on supporting leg sleeve; Institute's displacement sensors is fixed on the second clamping section.

2. Stewart platform legs length-measuring appliance according to claim 1, is characterized in that: described first clamping section comprises the first support, the first clamping plate; Described first support and the first Boards wall rear center position are with the first through hole for making piston pass through;

Described second clamping section comprises the second support, the second clamping plate; Described second support and the second Boards wall rear center position are with the second through hole for making sleeve pass through.

3. Stewart platform legs length-measuring appliance according to claim 2, is characterized in that: institute's displacement sensors is stay-supported type displacement sensor; Described first support, the second support are respectively equipped with the first bracing wire fixed orifice, the second bracing wire fixed orifice; The stay cord of displacement transducer successively through the second bracing wire fixed orifice, the first bracing wire fixed orifice, and is fixed on the first bracing wire fixed orifice.

4. Stewart platform legs length-measuring appliance according to claim 2, is characterized in that: it also comprises the calibration rod for ensureing the first clamping section, the second clamping section and piston coaxial line;

Described first support, the second support are respectively equipped with the first calibration hole, the second calibration hole; Described first clamping section, the second clamping section respectively with piston, sleeve connection after, calibration rod can be inserted in transition fit in the first calibration hole, the second calibration hole.

5. a Stewart platform's position and pose test macro, is characterized in that: it comprises the Stewart platform legs length-measuring appliance according to any one of six cover claim 1-4, also comprises data collecting instrument, total processor system;

Six supporting legs of Stewart platform are fixed with described Stewart platform legs length-measuring appliance respectively;

Described Stewart platform legs length-measuring appliance, data collecting instrument, total processor system are electrically connected successively.

6. a Stewart platform's position and pose method of testing, it realizes based on the Stewart platform's position and pose test macro of claim 5, it is characterized in that it carries out according to following steps order:

A. install

Six supporting legs of Stewart platform are installed Stewart platform legs length-measuring appliance according to any one of claim 1-4 respectively; Installation process is as follows:

1. to be in floor level position locked for Stewart platform, and ensure that six leg lengths are in most short status, now Stewart platform legs length is it is known and equal that every bar props up leg length, i.e. l ₁=l ₂=l ₃=l ₄=l ₅=l ₆=L ₀;

2. the first clamping section, the second clamping section are fixed on respectively in advance on the piston of supporting leg, sleeve, and ensure the first clamping section, the second clamping section and piston coaxial line;

3. the first clamping section and piston are fixedly secured, the second clamping section and sleeve fixedly secure;

4. displacement transducer is fixed on the second clamping section;

B supporting leg calibrating length

1. six displacement transducers are received on Measurement channel corresponding to data collecting instrument successively;

2. total processor system control data Acquisition Instrument gathers the current output voltage values of six displacement transducers and by magnitude of voltage current for each displacement transducer as initial value;

C. supporting leg linear measure longimetry

1. control Stewart platform makes it move;

2. in Stewart Platform movement process, displacement transducer on each bar supporting leg can measure the length variations amount of supporting leg in Stewart Platform movement process respectively, the length variations amount of supporting leg can be changed into corresponding analog voltage signal by each displacement transducer, and the analog voltage signal of output is passed to data collecting instrument, the analog voltage signal that each displacement transducer exports by data collecting instrument carries out analog to digital conversion, be converted into digital signal, be passed to total processor system; Total processor system obtains the time series of displacement transducer output voltage wherein k=1,2,3 ... n, n are sampling number;

3. total processor system calculates the physical length of the every bar supporting leg of Stewart platform concrete computation process is as follows:

$1_k^{*}=K*(v_k-v_b)+l_c$

Wherein K=[k ₁, k ₂, k ₃, k ₄, k ₅, k ₆], k _irepresent the sensitivity of i-th displacement transducer, k=1,2,3 ... n, n are sampling number; I=1,2,3,4,5,6;

The length pot life sequence of its six supporting legs in Stewart Platform movement process represent, wherein k=1,2,3 ... n, n are sampling number.

D.Stewart platform's position and pose resolves

1. with the central point of the lower platform of Stewart platform for reference point o, build fixing three-dimensional system of coordinate oxyz, with the central point of the upper mounting plate of certain moment Stewart platform for reference point o', build dynamic three-dimensional system of coordinate o'x'y'z'; Wherein z-axis and z' axle are respectively perpendicular to upper mounting plate, lower platform;

2. to set z' axle be ψ, y' be θ, x' around the angle of pitch of y-axis around the deflection angle of z-axis around the roll angle of x-axis is the transformation matrix of coordinates that then upper mounting plate rotates around each axle relative to lower platform is:

$\left[\begin{array}{c}x\\ y\\ z\end{array}\right]=R_P^B\left[\begin{array}{c}{x}^{\′}\\ y^{\′}\\ z^{\′}\end{array}\right]---\left(1\right)$

Upper mounting plate around the complete Rotation matrix of lower platform is:

3. set vector T as lower platform central point is to the vector of upper mounting plate central point, P _ifor the upper fulcrum of platform i-th supporting leg is in the position of coordinate system o'x'y'z', B _ifor the lower fulcrum of platform i-th supporting leg is in the position of coordinate system oxyz;

In coordinate system o'x'y'z', P _ithe coordinate of point is transformed in coordinate system oxyz by formula (4) coordinate transform mode; In coordinate system oxyz, vectorial oP _iuse q _irepresent, in coordinate system o'x'y'z', vectorial o ' P _ip can be used _irepresent, then:

$q_i=T+R_B^P\·p_i---\left(4\right)$

In coordinate system oxyz, i-th supporting leg can be expressed as with vector correlation

$l_i=q_i-b_i=T+R_B^P\·p_i-b_i---\left(5\right)$

Vector l _imould be namely the physical length l of platform legs _i, this vector correlation can be expressed as further:

$l_i=\sqrt{l_i^T\·l_i}=\sqrt{l_{ix}^2+l_{iy}^2+l_{iz}^2},(i=1,2...6)---\left(6\right)$

4. 6 supporting legs of platform can obtain the identical nonlinear equation of 6 structures, namely

Solve the pose parameter that this system of equations just can obtain upper mounting plate, the coordinate of central point o' at coordinate system oxyz of coordinate system o'x'y'z' can be obtained, i.e. coordinate (the x of vector T _t, y _t, z _t), and the Eulerian angle that upper mounting plate rotates around each axle relative to lower platform

5. be the solution procedure of formula (7) below.

To formula (7) differential, change differentiating operator d into limited a small amount of, have

Matrix form is write as to six equations of formula (8), is arranged

Δx＝J ^-1Δl(9)

In formula

Δl＝[Δl ₁,Δl ₂,Δl ₃,Δl ₄,Δl ₅,Δl ₆] ^T

$J=\left[\begin{array}{cccc}\frac{\∂f_1}{\∂\mathrm{\ψ}}/\frac{\∂f_1}{\∂l_1}& \frac{\∂f_1}{\∂\mathrm{\θ}}/\frac{\∂f_1}{\∂l_1}& ...& \frac{\∂f_1}{\∂z_c}/\frac{\∂f_1}{\∂l_1}\\ \frac{\∂f_2}{\∂\mathrm{\ψ}}/\frac{\∂f_2}{\∂l_2}& \frac{\∂f_2}{\∂\mathrm{\θ}}/\frac{\∂f_2}{\∂l_2}& ...& \frac{\∂f_2}{\∂z_c}/\frac{\∂f_2}{\∂l_2}\\ ...& ...& ...& ...\\ \frac{\∂f_6}{\∂\mathrm{\ψ}}/\frac{\∂f_6}{\∂l_6}& \frac{\∂f_6}{\∂\mathrm{\θ}}/\frac{\∂f_6}{\∂l_6}& ...& \frac{\∂f_6}{\∂z_c}/\frac{\∂f_6}{\∂l_6}\end{array}\right]$

Write formula (9) as Iteration

x _k+1＝x _k+Δx＝x _k+J ^-1Δl＝x _k+J ^-1(l _k ^*-l _k)(10)

K=0 in formula, 1,2,3....n, n are iteration ends number of times.

for upper mounting plate is relative to the pose parameter of lower platform;

for at known x _kthe theory obtained by system of equations (7) in situation props up leg length;

for each the leg length of reality recorded by experiment;

Occur that unusual causing solves instability for avoiding solving J, formula (10) be rewritten into following form:

x _k+1＝x _k+J ⁺(l _k ^*-l _k)

(11)

Wherein: J ⁺=J ^t(JJ ^t) ^-1, iterative initial value

x ₀＝[0,0,…,0] ^T

Stopping criterion for iteration

|l _k ^*-l _k|≤ε(12)

Wherein ε is any given iteration precision;

Formula (12) is converted to non-linear least square problem:

$\underset{x}{min}\underset{i=1}{\overset{6}{\Σ}}{g}_i{\left(x\right)}^2---\left(13\right)$

$s.t.g_i\left(x\right)=l_i^2-f_i\left(x\right)$

The minimum value result of formula (13) had both been optimum matching point, and the minimum value of formula (13) is corresponding the approximate current pose thinking upper mounting plate;

Input one group of l that a certain moment actual measurement must be fallen _k ^*with one group of iterative initial value of specifying, the pose of current upper mounting plate relative to lower platform just can be calculated; Each group l that reality is tested _k ^*upper mounting plate just can be calculated in whole motion process relative to the pose of lower platform with the iterative initial value of specifying.