CN102636139A - 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 the kinetic measurement of space six-freedom motion.The 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) are convertible into movement velocity, acceleration of motion, motion angular velocity, motion angular acceleration behind moving displacement and the angle differential.

Background technology

Existing industry, military measurement requirement to the object space motion are increasingly high, and environment becomes increasingly complex, and utilize original metering system, can not satisfy requirements such as measuring accuracy, environment, frequency, coupling.When carrying out the rocket projectile flight test; A series of reasons such as the high thrust that emission produces, thump, HTHP, blast are in the rugged environment emitter; Emitter influences its flight path, accuracy at target and closeness to the initial disturbance of rocket projectile (guided missile) emission, even causes the fighting capacity of whole army to descend.This just needs a kind of measuring mechanism that can adapt under the particular surroundings; Can accurately measure the six-freedom degree amount of movement of measurement point; Need carry out dynamic test and research to each principal element of the initial disturbance in the emission process, especially need to adapt to measuring method and device that omnidistance under the particular surroundings accurately measured emitter space six-freedom motion (move axially, translation, heave, pitching, driftage, lift-over).

Precision is one of main standard of weighing measurement mechanism or method, but is directly installed on the emitter like vibration acceleration sensor or vibrating speed sensors at present, through being integrated into speed or displacement, because range, frequency response and integral error etc. cause error bigger; Measurement based on machine vision receives the air refraction fluctuation and the smog dust of high temperature blast to make this method measuring error big, flue dust, hot environment in the time of can not adapting to emission, even can not use fully; Adopt three-axis gyroscope measurement space three axis angular rates, be integrated into angular displacement, this method is the energy measurement three-shaft displacement not, and error is bigger etc. to cause error bigger because range, frequency response and integral error etc. cause.

In other practical applications of industry, military affairs and space flight and aviation; The method of Measuring Object motion both at home and abroad can not be measured the six-freedom motion rule of moving object simultaneously at present; Integral error is big, and the measuring complex precision is 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 simultaneously to moving object.The 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) are convertible into movement velocity, acceleration of motion, motion angular velocity, motion angular acceleration behind moving displacement and the angle differential.

Technical scheme of the present invention is following: six displacement transducer dynamic measuring methods of a kind of space six-freedom motion is characterized in that may further comprise the steps:

Six displacement transducer dynamic measuring methods of a kind of space six-freedom motion is characterized in that may further comprise the steps:

1) build six displacement transducers parallel connection measuring mechanism:

The six displacement transducers parallel connection measuring mechanism of building comprises upper mounting plate, lower platform and six stay-supported displacement transducers; Respectively there are six mounting points to be used to install the stay-supported displacement transducer on upper mounting plate and the lower platform; Six mounting points on the identical platform are on a circle or place, hexagonal six angles, and 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 connection stay-supported displacement transducer; Six stay-supported displacement transducer touchless; Said lower platform is fixed on the pedestal, fixing testee on the upper mounting plate, and move with testee;

2) set up coordinate system:

On upper mounting plate, set up moving coordinate system o '-x ' y ' z ', set up quiet coordinate system o-xyz on the lower platform, A _i, B _iBe respectively the contact point of six stay-supported displacement transducers 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 _iExpression A _iB _iBetween displacement, in the 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 is separated:

When upper mounting plate changes, obtain the coordinate figure A of this stylish point based on the relation of putting on plane and the plane,

A＝T*A _i′+P

T is the direction cosine matrix of upper mounting plate attitude, A _i' be A _iPoint is in the position vector of moving coordinate system, and P is that moving coordinate system on the 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 two platforms is l up and down _I0, i=1,26; Line between each corresponding mounting points of two platforms is as six branches up and down, 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 the formula, A _Ix, A _Iy, A _IzBe the position of termination contact on the stay-supported displacement transducer in position fixing system, B _Ix, B _Iy, B _IzBe the position of termination contact under the stay-supported displacement transducer in position fixing system, because tested moving object is the length variations amount that the stay-supported displacement transducer records contrary the separating of the pose of upper mounting plate:

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

With six pose parameter substitution formulas (1.3) of tested moving object, can obtain the length variations amount that the stay-supported displacement transducer records when measuring testee, then according to formula l _I0=l _i-Δ l _iThe distance between the lower platform is gone up in adjustment again;

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 _iBe the coordinate of stay-supported displacement transducer lower extreme point in the quiet coordinate system of lower platform, l _iThe length that records for the stay-supported displacement transducer

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

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

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

Formula (1.4) can be regarded as with A _iBe the system of linear equations of unknown number, its Jacobi's system matrix number is:

$J=\left[\begin{array}{cc}\frac{\&PartialD;f_1}{\&PartialD;x_1}\frac{\&PartialD;f_1}{\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="x"\; filenames="HDA0000152515900000011.png"\; state="\{\{state\}\}">x</figure-callout>}}_2}\&CenterDot;& \frac{\&PartialD;f_1}{\&PartialD;x_6}\\ \frac{\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA0000152515900000011.png"\; state="\{\{state\}\}">f</figure-callout>}}_2}{\&PartialD;x_1}\frac{\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA0000152515900000011.png"\; state="\{\{state\}\}">f</figure-callout>}}_2}{\&PartialD;x_2}\&CenterDot;& \frac{\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA0000152515900000011.png"\; state="\{\{state\}\}">f</figure-callout>}}_2}{\&PartialD;x_6}\\ \&CenterDot;& \\ \frac{\&PartialD;f_6}{\&PartialD;x_1}\frac{\&PartialD;f_6}{\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="x"\; filenames="HDA0000152515900000011.png"\; state="\{\{state\}\}">x</figure-callout>}}_2}\&CenterDot;& \frac{\&PartialD;f_6}{\&PartialD;x_6}\end{array}\right]$

Ask the inverse matrix of Jacobi matrix through the elementary row conversion, be converted into plus-minus and the multiplying of asking matrix so fully; (x wherein 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, said 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 simultaneously, measuring accuracy is high.

2) algorithm is easy to realize good reliability.

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.

Description of drawings

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

Fig. 2 is the synoptic diagram of the coordinate system that the present invention set up.

Embodiment

Below in conjunction with accompanying drawing and embodiment the present invention is described further:

Six displacement transducer dynamic measuring methods of a kind of space six-freedom motion may further comprise the steps:

1) build six displacement transducers parallel connection measuring mechanism:

As shown in Figure 1, the six displacement transducers parallel connection measuring mechanism of building is made up of upper mounting plate 1, lower platform 3 and six stay-supported displacement transducers 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 to be used to install stay-supported displacement transducer 2, six mounting points on the identical platform are place, perhaps hexagonal six angles on a circle.Six mounting points of upper mounting plate 1 are corresponding one by one with six mounting points of lower platform 3; Connect stay-supported displacement transducer 2 according to shortest distance principle between the mounting points of the mounting points of upper mounting plate 1 and corresponding lower platform 3; Six stay-supported displacement transducer 2 touchless; Lower platform 3 is fixed on the pedestal during measurement, fixing testee on the upper mounting plate 1, and move with testee.If on testee or fixed pedestal; Can confirm respectively that six points are used for the installation of stay-supported displacement transducer, then can cancel upper mounting plate or lower platform and directly sensor is installed on pedestal and the testee (or be integrated into pedestal and testee on two platforms).

2) set up coordinate system:

On upper mounting plate, set up moving coordinate system o '-x ' y ' z ', set up quiet coordinate system o-xyz on the lower platform, A _i, B _iBe respectively the contact point of six stay-supported displacement transducers in upper mounting plate and lower platform, i=1,26.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 _iExpression A _iB _iBetween displacement.In the 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 is separated:

When testee moved, the position of upper mounting plate and state can change.If the 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 displacement transducer to record is inverse position and separates.When upper mounting plate changes, can obtain the coordinate figure A of this stylish point based on the relation of putting on plane and the plane.

A＝T*A _i′+P

T is the direction cosine matrix of upper mounting plate attitude, A _i' be A _iPoint is in the position vector of moving coordinate system, and P is that moving coordinate system on the 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 two platforms is l up and down _I0, i=1,26; 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:

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

In the formula, A _Ix, A _Iy, A _IzBe the position of termination contact on the stay-supported displacement transducer in position fixing system, B _Ix, B _Iy, B _IzBe the position of termination contact under the stay-supported displacement transducer in position fixing system.Because tested moving object is the length variations amount that the stay-supported displacement transducer records contrary the separating of the pose of upper mounting plate:

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

With six pose parameter substitution formulas (1.3) of tested moving object, can obtain the length variations amount that the stay-supported displacement transducer records when measuring testee, then according to formula l _I0=l _i-Δ l _iThe distance between the lower platform is gone up in adjustment again.

4) position normal solution

The position normal solution adopts Newton iteration method, and its basic thought is to be converted into certain linear equation to nonlinear equation F (x)=0 to find the solution.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 _iBe the coordinate of stay-supported displacement transducer lower extreme point in the quiet coordinate system of lower platform.l _iBe the distance (be length that stay-supported displacement transducer record) of six mounting points of upper mounting plate from six mounting points of lower platform

Order $\underset{i=1}{\overset{6}{\mathrm{\&Sigma;}}}{f}_i(x,y,z,{\mathrm{\&theta;}}_x,{\mathrm{\&theta;}}_y,{\mathrm{\&theta;}}_z)=(T_i*{A^{\&prime;}}_i+P_i-B_i){(T_i*{A^{\&prime;}}_i+P_i-B_i)}^T-l_i^2=0---\left(1.4\right)$

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

$f_i\left(A_i\right)+\underset{k=1}{\overset{6}{\mathrm{\&Sigma;}}}(x_k-x_k)\frac{\&PartialD;f_i\left(A_i\right)}{\&PartialD;x_k}=0$

Formula (1.4) can be regarded as with A _iBe the system of linear equations of unknown number, its Jacobi's system matrix number is:

$J=\left[\begin{array}{cc}\frac{\&PartialD;f_1}{\&PartialD;x_1}\frac{\&PartialD;f_1}{\&PartialD;x_2}\&CenterDot;& \frac{\&PartialD;f_1}{\&PartialD;x_6}\\ \frac{\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA0000152515900000011.png"\; state="\{\{state\}\}">f</figure-callout>}}_2}{\&PartialD;x_1}\frac{\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA0000152515900000011.png"\; state="\{\{state\}\}">f</figure-callout>}}_2}{\&PartialD;x_2}\&CenterDot;& \frac{\&PartialD;{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA0000152515900000011.png"\; state="\{\{state\}\}">f</figure-callout>}}_2}{\&PartialD;x_6}\\ \&CenterDot;& \\ \frac{\&PartialD;f_6}{\&PartialD;x_1}\frac{\&PartialD;f_6}{\&PartialD;x_2}\&CenterDot;& \frac{\&PartialD;f_6}{\&PartialD;x_6}\end{array}\right]$

Ask the inverse matrix of Jacobi matrix through the elementary row conversion, be converted into plus-minus and the multiplying of asking matrix so fully.(x wherein 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 the contrary length that solves displacement transducer of kinematics; Adjustment upper mounting plate and the distance value of lower platform or the length of displacement transducer make up 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 ₁Be the sensitivity (unit is mv/um) of stay-supported displacement transducer, L ₂Be the space geometry sensitivity (unit is um/um) of measuring mechanism,

Generally, the sensitivity of six stay-supported displacement transducers is identical, then this moment L ₁Also be the sensitivity of single displacement transducer.

Claims (2)

1. six displacement transducer dynamic measuring methods of a space six-freedom motion is characterized in that may further comprise the steps:

1) build six displacement transducers parallel connection measuring mechanism:

The six displacement transducers parallel connection measuring mechanism of building comprises upper mounting plate, lower platform and six stay-supported displacement transducers; Respectively there are six mounting points to be used to install the stay-supported displacement transducer on upper mounting plate and the lower platform; Six mounting points on the identical platform are on a circle or place, hexagonal six angles, and 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 connection stay-supported displacement transducer; Six stay-supported displacement transducer touchless; Said lower platform is fixed on the pedestal, fixing testee on the upper mounting plate, and move with testee;

2) set up coordinate system:

On upper mounting plate, set up moving coordinate system o '-x ' y ' z ', set up quiet coordinate system o-xyz on the lower platform, A _i, B _iBe respectively the contact point of six stay-supported displacement transducers 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 _iExpression A _iB _iBetween displacement, in the 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 is separated:

When upper mounting plate changes, obtain the coordinate figure A of this stylish point based on the relation of putting on plane and the plane,

A＝T*A _i′+P

T is the direction cosine matrix of upper mounting plate attitude, A _i' be A _iPoint is in the position vector of moving coordinate system, and P is that moving coordinate system on the 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 two platforms is l up and down _I0, i=1,26; Line between each corresponding mounting points of two platforms is as six branches up and down, and the real-time measurement length of each branch can be expressed as the function of tested moving object location parameter:

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

In the formula, A _Ix, A _Iy, A _IzBe the position of termination contact on the stay-supported displacement transducer in position fixing system, B _Ix, B _Iy, B _IzBe the position of termination contact under the stay-supported displacement transducer in position fixing system, because tested moving object is the length variations amount that the stay-supported displacement transducer records contrary the separating of the pose of upper mounting plate:

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

With six pose parameter substitution formulas (1.3) of tested moving object, can obtain the length variations amount that the stay-supported displacement transducer records when measuring testee, then according to formula l _I0=l _i-Δ l _iThe distance between the lower platform is gone up in adjustment again;

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 _iBe the coordinate of stay-supported displacement transducer lower extreme point in the quiet coordinate system of lower platform, l _iThe length that records for the stay-supported displacement transducer

Order $\underset{i=1}{\overset{6}{\mathrm{\&Sigma;}}}{f}_i(x,y,z,{\mathrm{\&theta;}}_x,{\mathrm{\&theta;}}_y,{\mathrm{\&theta;}}_z)=(T_i*{A^{\&prime;}}_i+P_i-B_i){(T_i*{A^{\&prime;}}_i+P_i-B_i)}^T-l_i^2=0---\left(1.4\right)$

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

$f_i\left(A_i\right)+\underset{k=1}{\overset{6}{\mathrm{\&Sigma;}}}(x_k-x_k)\frac{\&PartialD;f_i\left(A_i\right)}{\&PartialD;x_k}=0$

Formula (1.4) can be regarded as with A _iBe the system of linear equations of unknown number, its Jacobi's system matrix number is:

$J=\left[\begin{array}{cc}\frac{\&PartialD;f_1}{\&PartialD;x_1}\frac{\&PartialD;f_1}{\&PartialD;x_2}\&CenterDot;& \frac{\&PartialD;f_1}{\&PartialD;x_6}\\ \frac{\&PartialD;f_2}{\&PartialD;x_1}\frac{\&PartialD;f_2}{\&PartialD;x_2}\&CenterDot;& \frac{\&PartialD;f_2}{\&PartialD;x_6}\\ \&CenterDot;& \\ \frac{\&PartialD;f_6}{\&PartialD;x_1}\frac{\&PartialD;f_6}{\&PartialD;x_2}\&CenterDot;& \frac{\&PartialD;f_6}{\&PartialD;x_6}\end{array}\right]$

Ask the inverse matrix of Jacobi matrix through the elementary row conversion, be converted into plus-minus and the multiplying of asking matrix so fully; (x wherein 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, it is characterized in that: said upper mounting plate and lower platform are regular hexagon or circle, upper mounting plate be positioned at lower platform directly over.

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