CN102636139B - Six-displacement-sensor dynamic measuring method of space six-degree-of-freedom movement - Google Patents

Abstract

The invention discloses a six-displacement-sensor dynamic measuring method of a space six-degree-of-freedom movement. According to the method, six displacement sensors are connected in parallel to carry out dynamic measurement on the six-degree-of-freedom movement of a moving object. The method mainly comprises a series of steps of: overlapping a parallel measurement mechanism of the six displacement sensors, establishing a coordinate system, converting coordinates, inversely solving positions, positively solving the positions and the like. The measurement mechanism comprises an upper platform, stay wire type displacement sensors and a lower platform. After the measurement mechanism is established, a position-posture relation between a stay wire length and the upper platform can be found by establishing the suitable coordinate system through converting the coordinates; the initial stay wire length can be calculated by inversely solving and a variation principle of the space six-degree-of-freedom movement of an object to be detected is calculated by changing and positively solving the stay wire length. The six-displacement-sensor dynamic measuring method can simultaneously measure a movement principle of a moving object to be measured in six degrees of freedom, the measurement precision is high, the algorithm is easy to realize and the reliability is strong; and the application range is wide and the six-displacement-sensor dynamic measuring method can be applied to important national defense fields of parallel machine tools, flight simulators, wind tunnel test model devices, space butt joint equipment and the like.

Description

Six displacement transducer dynamic measuring methods of space six-freedom motion

Technical field

The present invention relates to six displacement transducer dynamic measuring methods of a kind of space six-freedom motion, utilize six displacement transducer parallel connections moving object to be carried out to the kinetic measurement of space six-freedom motion.Space six-freedom motion comprises: three-degree-of-freedom motion displacement x (t), y (t), z (t) and three-degree-of-freedom motion angle θ x (t), θ y (t), θ z (t), be convertible into movement velocity, acceleration of motion, motion angular velocity, motion angular acceleration after moving displacement and angle differential.

Background technology

Existing industry, the military measurement to object space motion require more and more higher, and environment becomes increasingly complex, and utilize original metering system, can not meet the requirements such as measuring accuracy, environment, frequency, coupling.When carrying out rocket projectile flight test, a series of reasons such as the high thrust, thump, High Temperature High Pressure, blast that transmitting produces make emitter in rugged environment, emitter affects its flight path, accuracy at target and closeness to the initial disturbance of rocket projectile (guided missile) transmitting, even causes the fighting capacity of whole army to decline.This just need to have a kind of measuring mechanism that can adapt under particular surroundings, can accurately measure the six-freedom degree amount of movement of measurement point, need to each principal element carry out dynamic test and research to the initial disturbance in emission process, especially need to adapt to measuring method and the device of omnidistance Measurement accuracy emitter space six-freedom motion under particular surroundings (move axially, translation, heave, pitching, driftage, rolling).

Precision is one of main standard of weighing measurement mechanism or method, but at present as vibration acceleration sensor or vibrating speed sensors are directly installed on emitter, through being integrated into speed or displacement, because range, frequency response and integral error etc. cause error larger; Measurement based on machine vision is subject to air refraction fluctuation and the smog dust of high temperature blast to make the method measuring error large, and the flue dust can not adapt to launch time, hot environment, can not be used even completely; Adopt three-axis gyroscope measurement space three axis angular rates, be integrated into angular displacement, the method can not be measured three-shaft displacement, and because range, frequency response and integral error etc. cause, error is larger etc. causes error larger.

In other engineering application of industry, military affairs and space flight and aviation, the method of measuring object of which movement both at home and abroad at present can not be measured the six-freedom motion rule of moving object simultaneously, integral error is large, measures complicated precision low, can not accurately obtain the six-freedom motion of moving object simultaneously.

Summary of the invention

Technical matters to be solved by this invention is to provide six displacement transducer dynamic measuring methods of a kind of space six-freedom motion, can carry out space six-freedom motion high-acruracy survey to moving object simultaneously.Space six-freedom motion comprises: three-degree-of-freedom motion displacement x (t), y (t), z (t) and three-degree-of-freedom motion angle θ x (t), θ y (t), θ z (t), be convertible into movement velocity, acceleration of motion, motion angular velocity, motion angular acceleration after moving displacement and angle differential.

Technical scheme of the present invention is as follows: six displacement transducer dynamic measuring methods of a kind of space six-freedom motion, is characterized in that comprising the following steps:

Six displacement transducer dynamic measuring methods of space six-freedom motion, is characterized in that comprising the following steps:

1) build six displacement transducers measuring mechanism in parallel:

The six displacement transducers measuring mechanism in parallel of building comprises upper mounting plate, lower platform and six stay-supported type displacement sensors, on upper mounting plate and lower platform, respectively there are six mounting points for stay-supported type displacement sensor is installed, six mounting points in identical platform are on a circle or the place of hexagonal six angles, six mounting points of upper mounting plate are corresponding one by one with six mounting points of lower platform, between the mounting points of the mounting points of upper mounting plate and corresponding lower platform according to shortest distance principle connecting stay wire formula displacement transducer, six stay-supported type displacement sensor touchless, described lower platform is fixed on pedestal, on upper mounting plate, fix testee, and move with testee,

2) set up coordinate system:

On upper mounting plate, set up moving coordinate system o'-x'y'z', on lower platform, set up quiet coordinate system o-xyz, A _i, B _ibe respectively the contact point of six stay-supported type displacement sensors in upper mounting plate and lower platform, A _i, B _ivector representation in rectangular coordinate system o-xyz is respectively A (A _ix, A _iy, A _iz), B (B _ix, B _iy, B _iz), l _irepresent A _ib _ibetween displacement, in solution procedure, the six degree of freedom x (t) of moving object, y (t), z (t), θ x (t), θ y (t), θ z (t) are expressed as x, y, z, θ _x, θ _y, θ _z, be convenient to calculate;

3) inverse position solution:

In the time that upper mounting plate changes, obtain the coordinate figure A of this stylish point according to the relation of plane and Plane-point,

A＝T*A′ _i+P

$T=\left[\begin{array}{ccc}\cos {\mathrm{\θ}}_y\cos {\mathrm{\θ}}_x& -\sin {\mathrm{\θ}}_x\cos {\mathrm{\θ}}_z+\cos {\mathrm{\θ}}_x\sin {\mathrm{\θ}}_y\sin {\mathrm{\θ}}_z& \sin {\mathrm{\θ}}_x\sin {\mathrm{\θ}}_z+\cos {\mathrm{\θ}}_x\sin {\mathrm{\θ}}_y\cos {\mathrm{\θ}}_z\\ \sin {\mathrm{\θ}}_x\sin {\mathrm{\θ}}_y& \sin {\mathrm{\θ}}_x\sin {\mathrm{\θ}}_y\sin {\mathrm{\θ}}_z+\cos {\mathrm{\θ}}_x\cos {\mathrm{\θ}}_z& \sin {\mathrm{\θ}}_{\text{x}}\sin {\mathrm{\θ}}_y\text{cos}{\mathrm{\θ}}_z-\cos {\mathrm{\θ}}_x\sin {\mathrm{\θ}}_z\\ -\sin {\mathrm{\θ}}_y& \cos {\mathrm{\θ}}_y\sin {\mathrm{\θ}}_z& \cos {\mathrm{\θ}}_y\cos {\mathrm{\θ}}_z\end{array}\right]---\left(1.1\right)$

T is the direction cosine matrix of upper mounting plate attitude, A ' _ifor A _ipoint is in the position vector of moving coordinate system, and P is that moving coordinate system on upper mounting plate is with respect to the displacement vector in the quiet coordinate system of lower platform;

If the initial length between the corresponding mounting points of upper and lower two platforms is l _i0, i=1,2 ... 6; Line between the each corresponding mounting points of upper and lower two platform is as six branches, and the real-time measurement length of each branch can be expressed as the function of tested moving object location parameter:

$l_i=|A_i-B_i|=\sqrt{{(A_{\mathrm{ix}}-B_{\mathrm{ix}})}^2+{(A_{\mathrm{iy}}-B_{\mathrm{iy}})}^2+{(A_{\mathrm{iz}}-B_{\mathrm{iz}})}^2}=g_i(x,y,z,{\mathrm{\θ}}_x,{\mathrm{\θ}}_y,{\mathrm{\θ}}_z)---\left(1.2\right)$

In formula, A _ix, A _iy, A _izfor the position of termination contact on stay-supported type displacement sensor in position fixing system, B _ix, B _iy, B _izfor the position of termination contact under stay-supported type displacement sensor in position fixing system, because tested moving object is the length variations amount that stay-supported type displacement sensor records at the pose of upper mounting plate against solution:

Δl _i＝l _i-l _i0＝g _i(x,y,z,θ _x,θ _y,θ _z)-l _i0???(1.3)

By six pose parameter substitution formulas (1.3) of tested moving object, can obtain the length variations amount that while measuring testee, stay-supported type displacement sensor records, then according to formula l _i0=l _i-Δ l _iadjust again the distance between upper lower platform;

4) position normal solution

Just solving an equation by the contrary variation of solving an equation

l ²＝(A-B _i)(A-B _i) ^T

B _ifor the coordinate of stay-supported type displacement sensor lower extreme point in the quiet coordinate system of lower platform, l _ithe length recording for stay-supported type displacement sensor

Order $\underset{i=1}{\overset{6}{\mathrm{\Σ}}}{f}_i(x,y,z,{\mathrm{\θ}}_x,{\mathrm{\θ}}_y,{\mathrm{\θ}}_z)=(T_i*A_i^{\′}+P_i-B_i){(T_i*A_i^{\′}+P_i-B_i)}^T-l_i^2=0---\left(1.4\right)$

First make initial point x, y, z, θ _x, θ _y, θ _z=(0,0,0,0,0,0); By f _i(A _i) (i=1,2 ... 6) at A _inear carry out Taylor expansion, and get its linear segment:

$f_i\left(A_i\right)+\underset{k=1}{\overset{6}{\mathrm{\Σ}}}(x_k-x_k)\frac{\∂f_1\left(A_i\right)}{\∂x_k}=0$

Formula (1.4) can be regarded as with A _ifor the system of linear equations of unknown number, its Jacobin coefficient matrix is:

$J=\left[\begin{array}{c}\frac{{\∂f}_1}{{\∂x}_1}\frac{\∂f_1}{\∂x_2}\·\·\·\frac{{\∂f}_1}{{\∂x}_6}\\ \frac{\∂f_2}{{\∂x}_1}\frac{\∂f_2}{\∂x_2}\·\·\·\frac{\∂f_2}{{\∂x}_6}\\ \·\\ \·\\ \·\\ \frac{\∂f_6}{\∂x_1}\frac{\∂f_6}{{\∂x}_2}\·\·\·\frac{\∂f_6}{{\∂x}_6}\end{array}\right]$

Ask the inverse matrix of Jacobi matrix by Applying Elementary Row Operations, be converted into plus-minus and the multiplying of asking matrix so completely; Wherein (x ₁, x ₂, x ₃, x ₄, x ₅, x ₆)=(x, y, z, θ _x, θ _y, θ _z); Separate the athletic posture x that Nonlinear System of Equations (1.4) just can obtain testee, y, z, θ _x, θ _y, θ _z.

For simplified structure and algorithm, described upper mounting plate and lower platform are regular hexagon or circle, upper mounting plate be positioned at lower platform directly over.

The invention has the beneficial effects as follows:

1) can directly measure the characteristics of motion of tested moving object six-freedom degree, measuring accuracy is high simultaneously.

2) algorithm is easy to realize, and reliability is strong.

3) applied range, may be used in the national defence major fields such as parallel machine, flight simulator, model in wind tunnel device, space articulation equipment.

Brief description of the drawings

Fig. 1 is the structural representation of six displacement parallel institutions in the present invention.

The schematic diagram of the coordinate system that Fig. 2 sets up for the present invention.

Embodiment

Below in conjunction with drawings and Examples, the invention will be further described:

Six displacement transducer dynamic measuring methods of space six-freedom motion, comprise the following steps:

1) build six displacement transducers measuring mechanism in parallel:

As shown in Figure 1, the six displacement transducers measuring mechanism in parallel of building is made up of upper mounting plate 1, lower platform 3 and six stay-supported type displacement sensors 2.The shape of upper and lower platform 1,3 can be set arbitrarily as required, is preferably circle or regular hexagon.On upper mounting plate 1 and lower platform 3, respectively have six mounting points for stay-supported type displacement sensor 2 is installed, six mounting points in identical platform are on a circle or the place of hexagonal six angles.Six mounting points of upper mounting plate 1 are corresponding one by one with six mounting points of lower platform 3, between the mounting points of the mounting points of upper mounting plate 1 and corresponding lower platform 3 according to shortest distance principle connecting stay wire formula displacement transducer 2, six stay-supported type displacement sensor 2 touchless, when measurement, lower platform 3 is fixed on pedestal, on upper mounting plate 1, fix testee, and move with testee.If on testee or fixed pedestal, can determine respectively that six points are for the installation of stay-supported type displacement sensor, can cancel upper mounting plate or lower platform directly by installation of sensors on pedestal and testee (or two platforms are integrated on pedestal and testee).

2) set up coordinate system:

On upper mounting plate, set up moving coordinate system o'-x'y'z', on lower platform, set up quiet coordinate system o-xyz, A _i, B _ibe respectively the contact point of six stay-supported type displacement sensors in upper mounting plate and lower platform, i=1,2 ... 6.A _i, B _ivector representation in rectangular coordinate system o-xyz is respectively A (A _ix, A _iy, A _iz), B (B _ix, B _iy, B _iz), l _irepresent A _ib _ibetween displacement.In solution procedure, the six degree of freedom x (t) of moving object, y (t), z (t), θ x (t), θ y (t), θ z (t) are expressed as x, y, z, θ _x, θ _y, θ _z, be convenient to calculate.

3) inverse position solution:

In the time that testee moves, the position of upper mounting plate and state can change.If given locus and the attitude of upper mounting plate, is respectively x, y, z, θ _x, θ _y, θ _z, the length variations of asking each stay-supported type displacement sensor to record, is inverse position solution.In the time that upper mounting plate changes, can obtain according to the relation of plane and Plane-point the coordinate figure A of this stylish point.

A＝T*A′ _i+P

$T=\left[\begin{array}{ccc}\cos {\mathrm{\θ}}_y\cos {\mathrm{\θ}}_x& -\sin {\mathrm{\θ}}_x\cos {\mathrm{\θ}}_z+\cos {\mathrm{\θ}}_x\sin {\mathrm{\θ}}_y\sin {\mathrm{\θ}}_z& \sin {\mathrm{\θ}}_x\sin {\mathrm{\θ}}_z+\cos {\mathrm{\θ}}_x\sin {\mathrm{\θ}}_y\cos {\mathrm{\θ}}_z\\ \sin {\mathrm{\θ}}_x\sin {\mathrm{\θ}}_y& \sin {\mathrm{\θ}}_x\sin {\mathrm{\θ}}_y\sin {\mathrm{\θ}}_z+\cos {\mathrm{\θ}}_x\cos {\mathrm{\θ}}_z& \sin {\mathrm{\θ}}_{\text{x}}\sin {\mathrm{\θ}}_y\text{cos}{\mathrm{\θ}}_z-\cos {\mathrm{\θ}}_x\sin {\mathrm{\θ}}_z\\ -\sin {\mathrm{\θ}}_y& \cos {\mathrm{\θ}}_y\sin {\mathrm{\θ}}_z& \cos {\mathrm{\θ}}_y\cos {\mathrm{\θ}}_z\end{array}\right]---\left(1.1\right)$

T is the direction cosine matrix of upper mounting plate attitude, A ' _ifor A _ipoint is in the position vector of moving coordinate system, and P is that moving coordinate system on upper mounting plate is with respect to the displacement vector in the quiet coordinate system of lower platform.

If the initial length between the corresponding mounting points of upper and lower two platforms is l _i0, i=1,2 ... 6; Line between each corresponding mounting points is as six branches, and the real-time measurement length of each branch can be expressed as the function of tested moving object location parameter:

$l_i=|A_i-B_i|=\sqrt{{(A_{\mathrm{ix}}-B_{\mathrm{ix}})}^2+{(A_{\mathrm{iy}}-B_{\mathrm{iy}})}^2+{(A_{\mathrm{iz}}-B_{\mathrm{iz}})}^2}=g_i(x,y,z,{\mathrm{\θ}}_x,{\mathrm{\θ}}_y,{\mathrm{\θ}}_z)---\left(1.2\right)$

In formula, A _ix, A _iy, A _izfor the position of termination contact on stay-supported type displacement sensor in position fixing system, B _ix, B _iy, B _izfor the position of termination contact under stay-supported type displacement sensor in position fixing system.Because tested moving object is the length variations amount that stay-supported type displacement sensor records at the pose of upper mounting plate against solution:

Δl _i＝l _i-l _i0＝g _i(x,y,z,θ _x,θ _y,θ _z)-l _i0???(1.3)

By six pose parameter substitution formulas (1.3) of tested moving object, can obtain the length variations amount that while measuring testee, stay-supported type displacement sensor records, then according to formula l _i0=l _i-Δ l _iadjust again the distance between upper lower platform.

4) position normal solution

Position normal solution adopts Newton iteration method, and its basic thought is nonlinear equation F (x)=0 to be converted into certain linear equation solve.Of the present invention just solving an equation can be by the contrary variation of solving an equation.

l ²＝(A-B _i)(A-B _i) ^T

B _ifor the coordinate of stay-supported type displacement sensor lower extreme point in the quiet coordinate system of lower platform.L _ifor six mounting points of upper mounting plate are from the distance (being the length that stay-supported type displacement sensor records) of six mounting points of lower platform

Order $\underset{i=1}{\overset{6}{\mathrm{\Σ}}}{f}_i(x,y,z,{\mathrm{\θ}}_x,{\mathrm{\θ}}_y,{\mathrm{\θ}}_z)=(T_i*A_i^{\′}+P_i-B_i){(T_i*A_i^{\′}+P_i-B_i)}^T-l_i^2=0---\left(1.4\right)$

First make initial point x, y, z, θ _x, θ _y, θ _z=(0,0,0,0,0,0).By f _i(A _i) (i=1,2 ... 6) at A _inear carry out Taylor expansion.And get its linear segment, obtain:

$f_i\left(A_i\right)+\underset{k=1}{\overset{6}{\mathrm{\Σ}}}(x_k-x_k)\frac{\∂f_1\left(A_i\right)}{\∂x_k}=0$

Formula (1.4) can be regarded as with A _ifor the system of linear equations of unknown number, its Jacobin coefficient matrix is:

$J=\left[\begin{array}{c}\frac{{\∂f}_1}{{\∂x}_1}\frac{\∂f_1}{\∂x_2}\·\·\·\frac{{\∂f}_1}{{\∂x}_6}\\ \frac{\∂f_2}{{\∂x}_1}\frac{\∂f_2}{\∂x_2}\·\·\·\frac{\∂f_2}{{\∂x}_6}\\ \·\\ \·\\ \·\\ \frac{\∂f_6}{\∂x_1}\frac{\∂f_6}{{\∂x}_2}\·\·\·\frac{\∂f_6}{{\∂x}_6}\end{array}\right]$

Ask the inverse matrix of Jacobi matrix by Applying Elementary Row Operations, be converted into plus-minus and the multiplying of asking matrix so completely.Wherein (x ₁, x ₂, x ₃, x ₄, x ₅, x ₆)=(x, y, z, θ _x, θ _y, θ _z).Separate the athletic posture x that Nonlinear System of Equations (1.4) just can obtain testee, y, z, θ _x, θ _y, θ _z.

The present invention is according to the preliminary motion of moving object, utilize Inverse Kinematics Solution to obtain the length of displacement transducer, adjust upper mounting plate and the distance value of lower platform or the length of displacement transducer, build parallel institution formula six displacement transducers, utilize dynamic measuring method, according to the normal solution computing method of displacement transducer, obtain the six-freedom motion rule of moving object.

5) measuring mechanism precision analysis:

If the precision of measuring mechanism of the present invention is L=L ₁× L ₂, wherein, L ₁for the sensitivity (unit is mv/um) of stay-supported type displacement sensor, L ₂for the space geometry sensitivity (unit is um/um) of measuring mechanism, under normal circumstances, the sensitivity of six stay-supported type displacement sensors is identical, L now ₁also be the sensitivity of single displacement transducer.

Claims (2)

1. six displacement transducer dynamic measuring methods of space six-freedom motion, is characterized in that comprising the following steps:

1) build six displacement transducers measuring mechanism in parallel:

The six displacement transducers measuring mechanism in parallel of building comprises upper mounting plate, lower platform and six stay-supported type displacement sensors, on upper mounting plate and lower platform, respectively there are six mounting points for stay-supported type displacement sensor is installed, six mounting points in identical platform are on a circle or the place of hexagonal six angles, six mounting points of upper mounting plate are corresponding one by one with six mounting points of lower platform, between the mounting points of the mounting points of upper mounting plate and corresponding lower platform according to shortest distance principle connecting stay wire formula displacement transducer, six stay-supported type displacement sensor touchless, described lower platform is fixed on pedestal, on upper mounting plate, fix testee, and move with testee,

2) set up coordinate system:

On upper mounting plate, set up moving coordinate system o'-x'y'z', on lower platform, set up quiet coordinate system o-xyz, A _i, B _ibe respectively the contact point of six stay-supported type displacement sensors in upper mounting plate and lower platform, A _i, B _ivector representation in rectangular coordinate system o-xyz is respectively A (A _ix, A _iy, A _iz), B (B _ix, B _iy, B _iz), l _irepresent A _ib _ibetween displacement, in solution procedure, the six degree of freedom x (t) of moving object, y (t), z (t), θ x (t), θ y (t), θ z (t) are expressed as x, y, z, θ _x, θ _y, θ _z, be convenient to calculate;

3) inverse position solution:

In the time that upper mounting plate changes, obtain the coordinate figure A of this stylish point according to the relation of plane and Plane-point,

A＝T*A′ _i+P

$T=\left[\begin{array}{ccc}\cos {\mathrm{\θ}}_y\cos {\mathrm{\θ}}_x& -\sin {\mathrm{\θ}}_x\cos {\mathrm{\θ}}_z+\cos {\mathrm{\θ}}_x\sin {\mathrm{\θ}}_y\sin {\mathrm{\θ}}_z& \sin {\mathrm{\θ}}_x\sin {\mathrm{\θ}}_z+\cos {\mathrm{\θ}}_x\sin {\mathrm{\θ}}_y\cos {\mathrm{\θ}}_z\\ \sin {\mathrm{\θ}}_x\sin {\mathrm{\θ}}_y& \sin {\mathrm{\θ}}_x\sin {\mathrm{\θ}}_y\sin {\mathrm{\θ}}_z+\cos {\mathrm{\θ}}_x\cos {\mathrm{\θ}}_z& \sin {\mathrm{\θ}}_{\text{x}}\sin {\mathrm{\θ}}_y\text{cos}{\mathrm{\θ}}_z-\cos {\mathrm{\θ}}_x\sin {\mathrm{\θ}}_z\\ -\sin {\mathrm{\θ}}_y& \cos {\mathrm{\θ}}_y\sin {\mathrm{\θ}}_z& \cos {\mathrm{\θ}}_y\cos {\mathrm{\θ}}_z\end{array}\right]---\left(1.1\right)$

T is the direction cosine matrix of upper mounting plate attitude, A ' _ifor A _ipoint is in the position vector of moving coordinate system, and P is that moving coordinate system on upper mounting plate is with respect to the displacement vector in the quiet coordinate system of lower platform;

If the initial length between the corresponding mounting points of upper and lower two platforms is l _i0, i=1,2 ... 6; Line between the each corresponding mounting points of upper and lower two platform is as six branches, and the real-time measurement length of each branch can be expressed as the function of tested moving object location parameter:

$l_i=|A_i-B_i|=\sqrt{{(A_{\mathrm{ix}}-B_{\mathrm{ix}})}^2+{(A_{\mathrm{iy}}-B_{\mathrm{iy}})}^2+{(A_{\mathrm{iz}}-B_{\mathrm{iz}})}^2}=g_i(x,y,z,{\mathrm{\θ}}_x,{\mathrm{\θ}}_y,{\mathrm{\θ}}_z)---\left(1.2\right)$

In formula, A _ix, A _iy, A _izfor the position of termination contact on stay-supported type displacement sensor in position fixing system, B _ix, B _iy, B _izfor the position of termination contact under stay-supported type displacement sensor in position fixing system, because tested moving object is the length variations amount that stay-supported type displacement sensor records at the pose of upper mounting plate against solution:

Δl _i＝l _i-l _i0＝g _i(x,y,z,θ _x,θ _y,θ _z)-l _i0???(1.3)

By six pose parameter substitution formulas (1.3) of tested moving object, can obtain the length variations amount that while measuring testee, stay-supported type displacement sensor records, then according to formula l _i0=l _i-Δ l _iadjust again the distance between upper lower platform;

4) position normal solution

Just solving an equation by the contrary variation of solving an equation

l ²＝(A-B _i)(A-B _i) ^T

B _ifor the coordinate of stay-supported type displacement sensor lower extreme point in the quiet coordinate system of lower platform, l _ithe length recording for stay-supported type displacement sensor

Order $\underset{i=1}{\overset{6}{\mathrm{\Σ}}}{f}_i(x,y,z,{\mathrm{\θ}}_x,{\mathrm{\θ}}_y,{\mathrm{\θ}}_z)=(T_i*A_i^{\′}+P_i-B_i){(T_i*A_i^{\′}+P_i-B_i)}^T-l_i^2=0---\left(1.4\right)$

First make initial point x, y, z, θ _x, θ _y, θ _z=(0,0,0,0,0,0); By f _i(A _i) (i=1,2 ... 6) at A _inear carry out Taylor expansion, and get its linear segment:

$f_i\left(A_i\right)+\underset{k=1}{\overset{6}{\mathrm{\Σ}}}(x_k-x_k)\frac{\∂f_1\left(A_i\right)}{\∂x_k}=0$

Formula (1.4) can be regarded as with A _ifor the system of linear equations of unknown number, its Jacobin coefficient matrix is:

$J=\left[\begin{array}{c}\frac{{\∂f}_1}{{\∂x}_1}\frac{\∂f_1}{\∂x_2}\·\·\·\frac{{\∂f}_1}{{\∂x}_6}\\ \frac{\∂f_2}{{\∂x}_1}\frac{\∂f_2}{\∂x_2}\·\·\·\frac{\∂f_2}{{\∂x}_6}\\ \·\\ \·\\ \·\\ \frac{\∂f_6}{\∂x_1}\frac{\∂f_6}{{\∂x}_2}\·\·\·\frac{\∂f_6}{{\∂x}_6}\end{array}\right]$

Ask the inverse matrix of Jacobi matrix by Applying Elementary Row Operations, be converted into plus-minus and the multiplying of asking matrix so completely; Wherein (x ₁, x ₂, x ₃, x ₄, x ₅, x ₆)=(x, y, z, θ _x, θ _y, θ _z); Separate the athletic posture x that Nonlinear System of Equations (1.4) just can obtain testee, y, z, θ _x, θ _y, θ _z.

2. six displacement transducer dynamic measuring methods of space according to claim 1 six-freedom motion, is characterized in that: described upper mounting plate and lower platform are regular hexagon or circle, upper mounting plate be positioned at lower platform directly over.