CN106529066A - Dynamic modelling method for connection process of indexing mechanism capture connection device - Google Patents

Abstract

The invention discloses a dynamic modeling method for the connection process of a capture connection device of an indexing mechanism, and belongs to the technical field of space station orbit services. First, determine the structure and parameters of the capture connection device of the indexing mechanism; determine the motion constraints of the mutual contact and slippage between the capture head and the index base during the connection process; secondly, determine the contact point between the capture head and the index base The relative sliding velocity on the connecting device is captured in the indexing mechanism; again, according to the constraint dynamic equation of the connection process between the capture head and the index base; finally, the constraint dynamic equation is analyzed. The complex motion mode of the connecting process captured by the indexing mechanism is transformed into a movement form of contact and sliding between the straight line and the straight line and between the straight line and the support in any space, which greatly reduces the capture and connection of the indexing mechanism. Difficulty in kinetic analysis of device connection process.

Description

Dynamic modeling method for the connection process of the indexing mechanism capture connection device

technical field

The invention relates to a dynamic modeling method, in particular to a dynamic modeling method for the connection process of an indexing mechanism capturing a connecting device, and belongs to the technical field of space station orbit services.

Background technique

The capture and connection device of the space station indexing mechanism can be used for the assembly, docking and separation required for the on-orbit operation of large spacecraft after docking with the space station, and is one of the important components of manned spaceflight. The indexing mechanism consists of a rotating arm and a rotating base. The rotating arm is installed on the body to be turned, and the indexing base is installed on the node module of the space station. The two can realize docking, locking, unlocking and reset. The dynamics and kinematics characteristics of the connection process between the capture head of the rotating arm and the indexing base are complex, and there are spatial motion constraints when the guide flap comes into contact. Conventional modeling methods based on Newtonian mechanics cannot be directly applied to the modeling of motion processes with sliding constraints, which restricts the research and development of indexing mechanism capture connection devices.

Contents of the invention

The technical problem to be solved by the present invention is to overcome the defects of the prior art and provide a modeling method capable of accurately describing the dynamic relationship of the indexing mechanism capturing the interaction between the various components of the connection device during the connection process.

In order to solve the above-mentioned technical problems, the dynamic modeling method for the connection process of the indexing mechanism capture connection device provided by the present invention includes the following steps:

Step 1: Determine the structure and parameters of the capture and connection device of the indexing mechanism. The capture and connection device of the indexing mechanism includes a capture head, a capture rod and an index base, the capture head is connected with the capture rod, and the capture head is connected with the capture rod. The indexing base can be moved relatively; the guide device on the end face of the capturing head and the indexing base are circular structures, and three trapezoidal guide lobes are evenly spaced along the outer circumference, and the capturing head and the indexing The positions of the guide petals between the bases are in one-to-one correspondence;

Step 2: Determine the motion constraints of the mutual contact slip between the capture head and the indexing base during the connection process;

Step 3: Determine the relative sliding speed of the contact point between the capturing head and the indexing base on the capturing connection device of the indexing mechanism;

Step 4: According to steps 2 and 3, determine the constraint dynamic equation of the connection process between the capture head and the indexing base;

Step 5: Solve the constrained dynamic equations.

In the present invention, the step 2 is: when the capture head is in contact with the indexing base, the absolute speeds of the i-th contact point are respectively:

in, represents the absolute velocity of the i-th contact point of the capture head, Indicates the absolute velocity of the i-th contact point of the indexing base, ω ₁ indicates the rotational angular velocity of the guide lobe of the capture head relative to the coordinate system of the interface of the capture head, ω ₂ indicates that the guide lobe of the index base is on the interface of the index base The angular velocity of rotation in the coordinate system, ω ₃ represents the angular velocity of rotation of the local coordinate system formed by the connecting surface of the capture head and the connecting surface of the indexing base relative to the inertial system, The position vector from the center of the connecting surface of the capture head to the i-th contact point, The position vector from the center of the connecting surface of the indexing base to the i-th contact point; Indicates the absolute velocity of the capture head and the guide lobe of the indexing base at the contact point 1,3, Indicates the absolute velocity of the capture head at the point of contact with the guide lobe of the indexing base2,4.

In the present invention, the step 3 is: when the edges g ₇ and q ₇ of the capture head are both clockwise,

in, denote the variables associated with the capture head and the indexing base, respectively, where the subscript numbers denote the edges of contact;

Therefore, the velocity constraint equation of the i-th contact slip point is:

in, Indicates the rotational angular velocity of the capture head connection surface coordinate system relative to the local coordinates formed by the capture head connection surface and the index base seat connection surface, Indicates the absolute velocity of the capture head and the indexing base at the second contact point, and indicates the rotational angular velocity of the guide lobe of the indexing base in the coordinate system of the connecting surface of the indexing base;

The acceleration constraint of the i-th contact point between the guide flap of the capture head and the base is:

In the present invention, the step 4 is:

Among them, m ₁ represents the mass of the rotating arm, m ₂ represents the mass of the mechanism where the indexing base is located, m ₃ represents the mass of the capturing head of the rotating arm, m ₄ represents the mass of the indexing base, and A ^I1 represents the inertial system towards the capturing head The rotation matrix of the connection surface coordinate system transformation, A ^1I represents the rotation matrix of the capture head connection surface coordinate system to the inertial system transformation, m represents the number of contact points, the binding force at the i-th contact point, represents the equivalent tensor matrix of the arm in the inertial system, Indicates the acceleration of the capture head and the indexing base at the contact point 1, The acceleration of the guide lobe of the capture head and the guide lobe of the indexing base at the contact points 1 and 3, A ^I3 represents the rotational moment transformed from the inertial system to the local coordinate system, is the force between the capture head and the indexing base, the rotation matrix of A ^1I transformation from the coordinate system of the connection surface of the capture head to the inertial system, is the acting moment between the capture head and the indexing base, A ^3I represents the rotation matrix transformed from the local coordinate system to the inertial system, Indicates the acceleration of the capture head and the indexing base at the contact point 2, A ²⁴ indicates the transformation matrix from the coordinate system of the joint surface of the indexing base to the inertial system, and A ⁴² indicates the transformation from the inertial system transformation to the coordinate system of the joint surface of the base Matrix, A ^2I is the same as A ²⁴ , F _ctrl is the active control force acting on the indexing base, p _i is the position vector described by the indexing base and the capture head in the e ₃ coordinate system, a _i is the indexing The contact point between the base and the capture head is the vector position of the second speed in the e ₄ coordinate system, I ₃ is the equivalent inertia tensor described by the indexing base in the e ₃ coordinate system, and I ₁ is the indexing base in the e ₁ The equivalent inertial tensor described in the coordinate system.

5. The dynamic modeling method for the connection process of the indexing mechanism capture connection device according to any one of claims 1 to 4, characterized in that the step 5 is:

Step 51: Set the constraint dynamic equation of the capture head and the indexing base in step 4 as a matrix:

Among them, M represents the mass of the whole formed by the connection between the capture head and the indexing base, and the transpose matrix of the coefficients of the A ^T constraint equation;

Kinematic constraints for the contact slip between the capture head and the indexing base,

In the formula, is the first-order reciprocal array of the configuration coordinates of the entire system, F represents the constraint force between the indexing base and the capture head, f=(f ₁ ,f ₂ …f _m ) is the contact constraint between the capture head and the indexing base Force, A is the constraint equation coefficient matrix;

Step 52: Construct the orthogonal complement matrix of the A matrix constraining the dynamic equation:

G＝A ^T A (14)

In the formula, ^AT is the transposed matrix of A, from formula (9), it can be obtained that G is an n×n square matrix, and its rank is m;

Get the eigenvalue of G by |λΕ-G|=0, use the eigenvalue to construct the matrix

In the formula, E represents the eigenvalue of the matrix G, C' and C represent the matrix composed of the eigenvectors corresponding to the non-zero eigenvalues and the eigenvectors corresponding to the zero eigenvalues, respectively, and the matrix L is full rank

δX=LδZ (16)

in, There is a single-value one-to-one correspondence between δX and δZ, thus

Since each column of the C matrix is composed of the eigenvectors of the eigenvalues of the matrix G respectively, so

GC=0 (18)

Substitute into (14) formula

From this you can get

AC = 0 (20)

Matrix C is the orthogonal complement matrix of matrix A, so any value of δZ” in Equation (19) is valid, and we have

Formula (16) can be written as

δX=CδZ" (22)

Substitute (22) into (12) to get

Combined with the arbitrariness of δZ", we get

The orthogonal complementary equations for constrained dynamics are

The invention simplifies the dynamic model of the capture connection device of the index mechanism into a multi-body system composed of three individuals, that is, the capture head, the capture rod and the index base. When establishing the dynamic model, considering the complexity and uncertainty of the contact slip constraint between the capture head and the indexing base, the capture head and the indexing base are considered separately, and the constraint force at the contact point is taken as an external force, respectively It acts on the connecting surface of the capture head and the indexing base. In addition, without considering the elastic deformation of the guide flap during the correction process, and using the principle of virtual work (Jourdain-Bertrand principle), the dynamic modeling of the connection process of the indexing mechanism capturing the connecting device is carried out.

The beneficial effects of the present invention are as follows: (1), the complex motion mode of the connection process captured by the indexing mechanism is transformed into a movement form of mutual contact and sliding between straight lines and between straight lines and supports in any space. , which greatly reduces the difficulty of dynamic analysis of the connection process of the indexing mechanism to capture the connection device; (2), through the analysis of the motion constraints of the above two motion modes, the analysis of the relative slip velocity of their mutual contact points is given The expression solves the analytical description of the indexing mechanism capturing the dynamic characteristics of the connection device during the connection process.

Description of drawings

Fig. 1 is a schematic diagram of the structure of the capture and connection device of the indexing mechanism;

Fig. 2 is a schematic diagram of the structure of the end surface guide device of the capture head; (a) is a top view, (b) is a side view;

Fig. 3 is a schematic diagram of the base structure of the indexing mechanism; (a) is a top view, and b) is a side view.

detailed description

The present invention will be described in further detail below in conjunction with the accompanying drawings.

As shown in FIG. 1 , the indexing mechanism used in the dynamic modeling method for the connection process of the indexing mechanism capturing connecting device of the present invention captures the capturing head 12 , the capturing rod 11 and the indexing base 14 of the connecting device. The capture head 12 is connected with the capture rod 11, the front end of the capture head 12 is equipped with a guide device 13, and the capture head 12 and the indexing base 14 can move relatively and make contact. The outer periphery of the guide device 13 and the indexing base 14 is equipped with guide petals 14 that expand outwards.

As shown in Fig. 2, the guide device of the capture head of the present invention is a circular structure, and the guide device of the capture head is provided with three outwardly expanding guide petals evenly spaced along the outer circumference, and the guide petals are trapezoidal structures. Coordinate system e ₁ of the guide device of the capture head, D in the figure is the diameter of the inner ring of the guide device, R _k is the radius of the outer ring of the guide device, β is the installation angle of the guide flap relative to the end face of the guide device, H is the height of the guide flap, and L is the guide petal length. The numbering of the guide flap edge of the capture head guide device is 1, 2, 3, ... 6 in sequence, and the number of the edge of the end face is 7. In the figure, x1, y1 and z1 represent the direction of the coordinate system of the connection surface of the capture head.

As shown in FIG. 3 , the structure of the indexing base of the present invention is consistent with the guide device of the capture head, which is the coordinate system e ₂ (that is, the coordinate system of the connecting surface of the indexing base). The positions of the three guide petals on the indexing base correspond to the positions of the three guide petals on the guide device of the capture head. The numbering of the edge of the guide flap on the transposition base is 1, 2, 3, ... 6, and the number of the edge of the end face is 7. In the figure, x2, y2 and z2 represent the coordinate system of the connecting surface of the indexing base.

The specific steps of the dynamic modeling method for the connection process of the indexing mechanism capture connection device of the present invention are as follows:

Step 1: Determine the structure and structural parameters of the indexing mechanism capture connection device, specifically combined with Figures 1-3.

Step 2: Determine the motion constraints of the mutual contact and slippage between the capture head and the index base during the connection process: when the capture head and the index base of the connection device are captured by the index mechanism during the capture connection process, the capture head and the index After the base is locked and retrieved, due to the structural characteristics of the guide flap, the contact point slides in the direction of reducing the relative position and attitude deviation between the capture head and the indexing base. Therefore, the establishment of dynamic constraints under such contact constraints is the first prerequisite for establishing the dynamic model of the capture connection process of the indexing mechanism capture connection device.

According to the structural characteristics of the capture and connection device of the indexing mechanism, the contact constraint between the capture head and the guide lobe of the index base is simplified as the mutual contact and sliding of two moving straight lines in space. Assuming that when the capture head is in contact with the indexing base, the absolute velocities of the i-th contact point are:

in, and Respectively represent the absolute velocity of the i-th contact point between the capture head and the indexing base, ω ₁ represents the rotational angular velocity of the guide lobe of the capture head relative to the coordinate system of the connection surface of the capture head, and ω ₂ represents the guide lobe of the index base when indexing The angular velocity of rotation in the coordinate system of the base connecting surface, ω ₃ represents the angular velocity of rotation of the local coordinate system formed by the connecting surface of the capture head and the connecting surface of the indexing base relative to the inertial system, The position vector from the center of the connecting surface of the capture head to the i-th contact point, The position vector from the center of the connecting surface of the indexing base to the i-th contact point; Indicates the absolute velocity of the capture head and the guide lobe of the indexing base at the contact point 1,3, Indicates the absolute velocity of the capture head at the point of contact with the guide lobe of the indexing base2,4.

Step 3: Determine the relative slip velocity of the constrained contact point on the indexing mechanism capture linkage:

When the edges g ₇ and q ₇ of the capture head are both clockwise,

in, Denote the variables associated with the capture head and base, respectively, where the subscript numbers indicate the edge of contact.

Therefore, the velocity constraint equation of the i-th contact slip point is:

in, Indicates the rotational angular velocity of the capture head connection surface coordinate system relative to the local coordinates formed by the capture head connection surface and the index base seat connection surface, Indicates the absolute speed of the capture head and the indexing base at the second contact point;

The acceleration constraint of the i-th contact point between the guide flap and the indexing base is:

Step 4: Determine the kinetic equation of the connection process of the indexing mechanism capture connection device

Among them, m ₁ represents the mass of the rotating arm, m ₂ represents the mass of the mechanism where the indexing base is located, m ₃ represents the mass of the capturing head of the rotating arm, m ₄ represents the mass of the indexing base, and A ^I1 represents the inertial system towards the capturing head The rotation matrix of the connection surface coordinate system transformation, A ^1I represents the rotation matrix of the capture head connection surface coordinate system to the inertial system transformation, m (without subscript) represents the number of contact points, the binding force at the i-th contact point, represents the equivalent tensor matrix of the arm in the inertial system, Indicates the acceleration of the capture head and the indexing base at the contact point 1, The acceleration of the guide lobe of the capture head and the guide lobe of the indexing base at the contact points 1 and 3, A ^I3 represents the rotational moment transformed from the inertial system to the local coordinate system, is the force between the capture head and the indexing base, the rotation matrix of A ^1I transformation from the coordinate system of the connection surface of the capture head to the inertial system, The binding force of the i-th contact point, is the acting moment between the capture head and the indexing base, A ^3I represents the rotation matrix transformed from the local coordinate system to the inertial system, Indicates the acceleration of the capture head and the indexing base at the contact point 2, A ²⁴ indicates the transformation matrix from the coordinate system of the joint surface of the indexing base to the inertial system, and A ⁴² indicates the transformation from the inertial system transformation to the coordinate system of the joint surface of the base Matrix, A ^2I is the same as A ²⁴ , F _ctrl is the active control force acting on the transposition base, p _i is the e ₃ coordinate system between the transposition base and the capture head (that is, the connecting surface of the capture head is connected to the transposition base The position vector described in the coordinate system formed by the surface); a _i is the vector position of the second speed of the contact point between the indexing base and the capture head in the e ₄ coordinate system (that is, the inertial coordinate system), and I ₃ the indexing base The equivalent inertia tensor described in the e ₃ coordinate system (that is, the coordinate system formed by the connecting surface of the capture head and the connecting surface of the indexing base), I ₁ is the index of the indexing base in the e ₁ coordinate system (that is, the connection surface of the capturing head The equivalent inertia tensor described in the surface coordinate system) is shown in Fig. 1.

Step 5: Determine the Analytical Form of the Constrained Kinetic Equations

Write the dynamic equations of the capturing head and the indexing base of the indexing mechanism in matrix form

Among them, M represents the mass of the whole formed by the connection between the capture head and the indexing base, and the transpose matrix of the coefficients of the A ^T constraint equation;

Contact-slip motion constraints between capture head and index base,

In the above formula, is the first-order reciprocal array of the configuration coordinates of the entire system, F represents the constraint force between the indexing base and the capture head, f=(f ₁ ,f ₂ …f _m ) is the contact constraint between the capture head and the indexing base Force, A is the constraint equation coefficient matrix. Since the capture head and the indexing base are in the process of capturing and connecting, the mutual movement between the capturing head and the indexing base is complex and the process of the space operation is complicated, the constraint equations of equations (10) and (11) are directly calculated solve. The invention uses the D'Alembert orthogonal complement principle to deal with the variable-dimensional constraint problem, and aims to convert the original variable-dimensional dynamic equations into fixed n-configuration space differential equations for solution. According to the principle of virtual work, the virtual position displacement of X needs to satisfy:

The constrained dynamic equations need to satisfy

AδX＝0 (13)

Considering that the system is constrained by dynamic motion, X is not independent. Therefore, it is necessary to solve it through the orthogonal complement matrix of the A matrix of the constraint equation. First, the orthogonal complement matrix of the A matrix of the constraint equation is constrained

G＝A ^T A (14)

Among them, ^AT is the transposed matrix of A, and G can be obtained from formula (9) as n×n square matrix, and its rank is m. Therefore, the eigenvalue of G can be obtained by |λΕ-G|=0, and the matrix is constructed using the eigenvalue

Among them, E represents the eigenvalue of the matrix G, and C' and C represent the matrix formed by the eigenvectors corresponding to the non-zero eigenvalues and the eigenvectors corresponding to the zero eigenvalues, respectively. So the matrix L must be full rank

δX=LδZ (16)

in, δZ and δX are constructed matrices, which have only mathematical meaning and no physical meaning. There is a single-value one-to-one correspondence between δX and δZ, thus

Since each column of the C matrix is composed of the eigenvectors of the eigenvalues of the matrix G respectively, so

GC=0 (18)

Substitute into (14) formula

From this you can get

AC = 0 (20)

Matrix C is the orthogonal complement matrix of matrix A, so any value of δZ” in Equation (19) is valid, and we have

Formula (16) can be written as

δX=CδZ" (22)

Substituting the above formula into (12) can get

Due to the arbitrariness of δZ", we can get

Therefore, the system of orthogonal complement equations for constrained dynamics

Equation (25) is the basic equation of constraint dynamics described in n-dimensional configuration space, and the constraint force f does not appear in the equation.

There are many specific application approaches of the present invention, and the above description is only a preferred embodiment of the present invention. It should be pointed out that for those of ordinary skill in the art, some improvements can also be made without departing from the principles of the present invention. Improvements should also be regarded as the protection scope of the present invention.

Claims (5)

1. A dynamic modeling method for a connection process of a capture connection device of an indexing mechanism is characterized by comprising the following steps:

step 1: determining the structure and parameters of an indexing mechanism capturing connection device, wherein the indexing mechanism capturing connection device comprises a capturing head, a capturing rod and an indexing base, the capturing head is connected with the capturing rod, and the capturing head and the indexing base can move relatively; the guide device on the end face of the capturing head and the transposition base are both in circular structures, 3 trapezoidal guide flaps which are unfolded outwards are uniformly arranged at intervals along the outer periphery, and the positions of the guide flaps between the capturing head and the transposition base correspond to each other one by one;

step 2: determining the motion constraint of mutual contact and slippage between the capture head and the indexing base in the connection process;

and step 3: determining a relative sliding speed of a contact point between the capture head and the indexing base on the indexing mechanism capture connection device;

and 4, step 4: determining a constraint kinetic equation of the connection process of the capture head and the transposition base according to the steps 2 and 3;

and 5: and (6) resolving a constraint kinetic equation.

2. The method for modeling the dynamics of an indexing mechanism capture link assembly attachment process according to claim 1, wherein step 2 is:

when the capture head is in contact with the indexing base, the absolute speed of the ith contact point is respectively as follows:

$\begin{array}{c}{\stackrel{\→}{R}}_{ip}={\stackrel{\→}{R}}_1+{\stackrel{\→}{\mathrm{\ω}}}_1\×\left({\stackrel{\→}{R}}_{13}+{\stackrel{\→}{p}}_i\right)+{\stackrel{\→}{R}}_{13}+{\stackrel{\→}{\mathrm{\ω}}}_3\×{\stackrel{\→}{p}}_i+{\stackrel{\→}{p}}_i\\ {\stackrel{\→}{R}}_{ia}={\stackrel{\→}{R}}_1+{\stackrel{\→}{\mathrm{\ω}}}_2\×\left({\stackrel{\→}{a}}_i+{\stackrel{\→}{R}}_{24}\right)+{\stackrel{\→}{a}}_i\end{array}---\left(1\right)$

wherein,representing the absolute velocity of the ith contact point of the capture head,indicating the absolute speed, ω, of the ith contact point of the indexing carriage₁Representing the angular velocity, ω, of rotation of the guide lobe of the capture head relative to the coordinate system of the connection face of the capture head₂Representing the angular velocity, omega, of the guide lobe of the indexing base in the coordinate system of the surface of the indexing base connection₃Represents the rotation angular velocity of a local coordinate system formed by the connecting surface of the capturing head and the connecting surface of the indexing base relative to the inertial system,capturing the position vector of the center of the head connection surface to the ith contact point,a position vector from the center of the connecting surface of the indexing base to the ith contact point;indicating the absolute velocity of the capture head and indexing base guide lobe at contact points 1,3,indicating the absolute velocity of the capture head at the contact points 2,4 with the indexing base guide lobes.

3. The method for modeling the dynamics of an indexing mechanism capture link assembly attachment process according to claim 2, wherein step 3 is:

when capturing the head edge g₇,q₇When the direction of the water is clockwise,

$\begin{array}{c}\left({\stackrel{\&RightArrow;}{R}}_{ip}-{\stackrel{\&RightArrow;}{R}}_{ia}\right)\&CenterDot;\left({\stackrel{\&RightArrow;}{g}}_i\&times;{\stackrel{\&RightArrow;}{q}}_i\right)<0,(i=1,3,5,7...12)\\ \left({\stackrel{\&RightArrow;}{R}}_{ip}-{\stackrel{\&RightArrow;}{R}}_{ia}\right)\&CenterDot;\left({\stackrel{\&RightArrow;}{g}}_i\&times;{\stackrel{\&RightArrow;}{q}}_i\right)>0,(i=2,4,6,8...18)\end{array}---\left(2\right)$

wherein,representing variables associated with the capture head and the index base, respectively, where subscript numbers represent the edges of the contacts;

therefore, the ith contact slip point velocity constraint equation is:

wherein,representing the angular velocity of rotation of the capture head joint plane coordinate system relative to the local coordinate formed by the capture head joint plane and the indexing base joint plane,the absolute speed of the capture head and the indexing base at the 2 nd contact point is shown, and the rotation angular speed of the indexing base guide lobe in the indexing base connection surface coordinate system is shown;

the acceleration constraint of the guide lobe of the capture head to the ith contact point of the base is:

4. the method for modeling the dynamics of an indexing mechanism capture link assembly attachment process according to claim 3, wherein step 4 is:

$(m_1+m_2){\stackrel{\&CenterDot;\&CenterDot;}{\stackrel{\&RightArrow;}{R}}}_1-m_3{A}^{I1}{\tilde{R}}_{13}{\stackrel{\&CenterDot;}{\stackrel{\&RightArrow;}{\mathrm{\&omega;}}}}_1+m_3{A}^{I1}{\tilde{R}}_{13}=-\underset{i=1}{\overset{m}{\&Sigma;}}{\stackrel{\&RightArrow;}{F}}_i-m_3{A}^{I1}{\widetilde{\mathrm{\&omega;}}}_1{\widetilde{\mathrm{\&omega;}}}_1{\tilde{R}}_{13}-2m_3{A}^{I1}{\widetilde{\mathrm{\&omega;}}}_1{\tilde{R}}_{13}+A^{I1}{F}_{Ctrl}$

$(m_2+m_4){\stackrel{\&CenterDot;\&CenterDot;}{\stackrel{\&RightArrow;}{R}}}_2=\underset{i}{\overset{m}{\&Sigma;}}{\stackrel{\&RightArrow;}{F}}_i---\left(8\right)$

wherein m is₁Representing the mass of the arm, m₂Denotes the mass of the mechanism in which the index base is located, m₃Representing the mass of the pivoted-arm catch head, m₄Denotes the mass of the index pedestal, A^I1Rotation matrix representing the transformation of the inertial system into the plane of coordinates of the attachment surface of the capture head, A^1IA rotation matrix representing the conversion of the coordinate system of the connection surface of the capturing head to the inertial system, m represents the number of contact points,the restraining force of the ith point of contact,an equivalent tensor matrix representing the rotating arm under the inertial system,Representing the acceleration of the capture head at the contact point 1 with the indexing base,Acceleration of the Capture head guide lobe in contact with the indexing base guide lobe at contact points 1,3, A^I3Representing the rotational moment of the transformation of the inertial system into the local coordinate system,for the force between the catch head and the indexing base, A^1IA rotation matrix for transforming the coordinate system of the connection surface of the capture head to the inertial system,For the moment of action between the catch head and the indexing base, A^3IA rotation matrix representing a transformation of the local coordinate system into the inertial system,representing the acceleration of the capture head at the contact point 2 with the indexing base, A²⁴Transformation matrix representing transformation from coordinate system of connection surface of indexing base to inertial system, A⁴²A transformation matrix representing the transformation of the inertial system into the coordinate system of the base connection surface, A^2ISame as A²⁴，F_ctrlFor active control forces acting on the indexing table, p_iFor indexing the base and the capture head at e₃Position vector described in a coordinate system, a_iFor the contact point between the indexing base and the capture head at e₄Vector position in the coordinate system at second speed, I₃The indexing base is at₃Equivalent inertia tensor, I, described in a coordinate system₁For indexing the base at e₁An equivalent inertia tensor described in a coordinate system.

5. The method for modeling dynamics of an indexing mechanism capture link assembly connection process according to any of claims 1-4, wherein the step 5 is:

step 51: and 4, setting a constraint kinetic equation of the capture head and the indexing base in the step 4 as a matrix:

$M\stackrel{\&CenterDot;\&CenterDot;}{\stackrel{\&RightArrow;}{X}}=F-A^{T}f---\left(10\right)$

wherein M represents the mass of the capture head as a whole when it is connected to the indexing base, A^TA transposed matrix of constraint equation coefficients;

the motion constraint of the contact slip between the capture head and the index base,

$\begin{array}{c}A\stackrel{\&CenterDot;\&CenterDot;}{\stackrel{\&RightArrow;}{X}}=0\\ A\stackrel{\&CenterDot;\&CenterDot;}{X}=-\stackrel{\&CenterDot;}{A}\stackrel{\&CenterDot;}{X}\end{array}---\left(11\right)$

in the formula,for the whole system position coordinate first order reciprocal array, F represents the restraining force between the indexing base and the capture head, and F ═ F (F ═ F)₁,f₂…f_m) A is a constraint equation coefficient matrix for the contact constraint force of the capture head and the transposition base;

step 52: constructing an orthogonal complement matrix of an A matrix of a constraint kinetic equation:

G＝A^TA (14)

in the formula, A^TIs a transposed matrix of A, G is a square matrix of n × n obtained from formula (9), and the rank is m;

obtaining the eigenvalue of G from | Lambda E-G | ═ 0, and constructing matrix by using the eigenvalue

In the formula, e represents the eigenvalue of matrix G, C' and C represent the matrix formed by eigenvector corresponding to non-zero eigenvalue and eigenvector corresponding to zero eigenvalue, respectively, and matrix L full rank

X＝LZ (16)

Wherein,there is a single value one-to-one correspondence between X and Z, whereby

$\begin{array}{c}AL\mathrm{\&delta;}Z=0\\ {\mathrm{AC}}^{\&prime;}{\mathrm{\&delta;Z}}^{\&prime;}+{\mathrm{ACZ}}^{\&prime;\&prime;}=0\end{array}---\left(17\right)$

Since each column of the C matrix is composed of the eigenvectors of the eigenvalues of the matrix G, respectively

GC＝0 (18)

Into formula (14)

$\begin{array}{c}{A}^{T}AC=0,\\ C^T{A}^{T}ACC={\left(AC\right)}^{T}AC=0\end{array}---\left(19\right)$

Thereby can obtain

AC＝0 (20)

The matrix C is an orthogonal complement of the matrix A, so that Z' in equation (19) holds for any value, some

$\begin{array}{c}{\mathrm{AC}}^{\&prime;}{\mathrm{\&delta;Z}}^{\&prime;\&prime;}=0\\ \underset{\&CenterDot;}{\&CenterDot;\&CenterDot;}\det \left({\mathrm{AC}}^{\&prime;}\right)\&NotEqual;0\\ \stackrel{\&CenterDot;}{\&CenterDot;\&CenterDot;}{\mathrm{\&delta;Z}}^{\&prime;}=0\end{array}---\left(21\right)$

Can write formula (16) into

X＝CZ” (22)

Substituting the formula (22) into the formula (12) to obtain

${\mathrm{\&delta;Z}}^{\&prime;\&prime;T}{C}^T(F-A^{T}f-m\stackrel{\&CenterDot;\&CenterDot;}{X})=0---\left(23\right)$

Optional availability of binding Z ″)

$C^T(F-A^{T}f-m\stackrel{\&CenterDot;\&CenterDot;}{X})=C^T(F-M\stackrel{\&CenterDot;\&CenterDot;}{X})=0---\left(24\right)$

The orthogonal complement equation system of constraint dynamics is

$\left[\begin{array}{c}{C}^{T}M\\ A\end{array}\right]\stackrel{\&CenterDot;\&CenterDot;}{X}=\left[\begin{array}{c}{C}^{T}F\\ -\stackrel{\&CenterDot;}{A}\stackrel{\&CenterDot;}{X}\end{array}\right]---\left(25\right).$