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

Abstract

The invention discloses a dynamic modelling method for the connection process of an indexing mechanism capture connection device, and belongs to the technical field of space station on-orbit servicing. The method comprises the following steps of: firstly, determining the structure and the parameter of the indexing mechanism capture connection device; secondly, determining the constraint of motion of mutual contact slippage between a capture head and an indexing substrate in a connection process; thirdly, determining the relative slippage speed of a contact point between the capture head and the indexing substrate on the indexing mechanism capture connection device; fourthly, according to the second step and the third step, determining a constrained dynamic equation of the connection process of the capture head and the indexing substrate; and finally, analyzing the constrained dynamic equation. The complex movement modality of the connection process of the indexing mechanism capture connection device is converted into a motion form of the mutual contact slippage between straight lines which carry out spatial arbitrary motion as well as between the straight line and a bracket, and the difficulty of the dynamic analysis of the connection process of the indexing mechanism capture connection device is greatly lowered.

Description

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

Technical Field

The invention relates to a dynamics modeling method, in particular to a dynamics modeling method for a connection process of a capture connection device of an indexing mechanism, and belongs to the technical field of space station on-orbit service.

Background

The space station indexing mechanism capturing and connecting device can be used for assembly, butt joint, separation and other operation activities required by in-orbit operation of a large spacecraft after butt joint with a space station, and is one of important components of manned spaceflight. The indexing mechanism consists of a rotating arm and a rotating base. The rotating arm is installed on the cabin body to be rotated, the rotating base is installed on the space station node cabin, and the rotating arm and the rotating base can be in butt joint, locked, unlocked and reset. Dynamics and kinematics characteristics of the connection process of the rotating arm capturing head and the rotating base are complex, and when the guide valve is contacted, spatial movement constraint exists. The conventional modeling method based on Newton mechanics cannot be directly applied to modeling of a motion process containing sliding constraint, and research and development of capturing and connecting devices of the indexing mechanism are restricted.

Disclosure of Invention

The invention aims to overcome the defects of the prior art and provides a modeling method capable of accurately describing the dynamic relationship of components of an indexing mechanism capturing and connecting device under the interaction in the connecting process.

In order to solve the technical problem, the invention provides a dynamic modeling method for a connection process of a capturing and connecting device of an indexing mechanism, which comprises 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.

In the invention, the step 2 is as follows: when the capture head is in contact with the indexing base, the absolute speed of the ith contact point is respectively as follows:

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 head₂Indicating that the guide lobe of the indexing base is seated on the connecting surface of the indexing baseAngular velocity of rotation, omega, within the system₃Represents 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.

In the invention, the step 3 is as follows: when capturing the head edge g₇,q₇When the direction of the water is clockwise,

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:

in the invention, the step 4 is as follows:

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_ctrl is an active control force acting on the indexing base, 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:

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,

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

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)

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

Can write formula (16) into

X＝CZ” (22)

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

Optional availability of binding Z ″)

The orthogonal complement equation system of constraint dynamics is

The invention simplifies the dynamic model of the indexing mechanism capturing connection device into a multi-body system consisting of three bodies, namely a capturing head, a capturing rod and an indexing base. When a dynamic model is established, the complexity and uncertainty of contact slip constraint between the capture head and the indexing base are considered, the capture head and the indexing base are considered separately, and the constraint force of a contact point is used as an external force to act on the connection surfaces of the capture head and the indexing base respectively. In addition, the connection process of the steering mechanism capturing connection device is dynamically modeled by using a virtual work principle (a journal-Bertrand principle) without considering the elastic deformation of the guide flap during the correction process.

The invention has the beneficial effects that: (1) the motion mode that the connection process of the indexing mechanism capturing and connecting device is complex is converted into the motion modes that the straight line and the straight line which move randomly in space and the straight line and the bracket slide in a mutual contact mode, and the difficulty of dynamic analysis in the connection process of the indexing mechanism capturing and connecting device is greatly reduced; (2) and by analyzing the motion constraints of the two motion modes, an analytic expression of the relative sliding speed of the mutual contact points of the two motion modes is given, and the analytic description of the dynamic characteristics of the indexing mechanism capturing and connecting device in the connecting process is solved.

Drawings

FIG. 1 is a schematic view of an indexing mechanism capture link;

FIG. 2 is a schematic view of the capture head end guide configuration; (a) is a top view, and (b) is a side view;

FIG. 3 is a schematic view of a 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 with reference to the accompanying drawings.

As shown in fig. 1, the indexing mechanism capture link capture head 12, capture bar 11, and indexing base 14 used in the inventive indexing mechanism capture link connection process dynamics modeling method. The catch head 12 is connected to the catch lever 11, a guide 13 is attached to a front end surface of the catch head 12, and the catch head 12 and the index base 14 are relatively movable and brought into contact with each other. The outer periphery of the guide 13 and the indexing base 14 mounts flared guide lobes 14.

As shown in figure 2, the guiding device of the capturing head is of a circular structure, 3 guiding petals which are unfolded outwards are uniformly arranged on the guiding device of the capturing head along the outer circumference at intervals, and the guiding petals are of a trapezoidal structure. Capture head guide coordinate system e₁D in the figure is the inner ring of the guiding deviceDiameter, R_kβ is the installation angle of the guide flap relative to the guide end face, H is the height of the guide flap, L is the length of the guide flap, the guide flap edge of the capture head guide is numbered 1,2,3, … 6 in sequence, and the end face edge is numbered 7, wherein x1, y1 and z1 represent the direction of the capture head attachment face coordinate system.

As shown in FIG. 3, the indexing base of the present invention conforms to the guide structure of the capture head, which is a coordinate system e₂(i.e., representing the index base connection surface coordinate system). The 3 guide lobes on the indexing base correspond one-to-one with the position of the 3 guide lobes on the capture head guide. The guide lobe edges on the indexing base are numbered 1,2,3, … 6 in that order, and the end face edge is numbered 7. In the figure, x2, y2 and z2 represent the index base joint plane coordinate system.

The invention relates to a dynamic modeling method for a connection process of a capture connection device of an indexing mechanism, which comprises the following specific steps:

step 1: the structure and structural parameters of the indexing mechanism capture interface are determined as described in conjunction with figures 1-3.

Step 2: determining the motion constraint of mutual contact sliding between the capture head and the indexing base in the connection process: when the capture head and the indexing base of the indexing mechanism capture connection device are in the capture connection process, the capture head and the indexing base are locked and recovered, and due to the structural characteristics of the guide flaps, the contact point slides towards the direction of reducing the relative position and posture deviation between the capture head and the indexing base. Therefore, establishing the dynamic constraint under the contact constraint condition is the first prerequisite for establishing the dynamic model of the process of capturing the connection by the indexing mechanism capturing the connection device.

According to the structural characteristics of the indexing mechanism capturing and connecting device, the contact constraint between the capturing head and the indexing base guide valve and between the capturing head and the indexing base guide valve is simplified into the mutual contact sliding of two spatial motion straight lines. Assuming that the capture head is in contact with the index base, the absolute velocity of the ith contact point is:

wherein,andrepresenting the absolute velocity, ω, of the capture head at the ith contact point with the index base, respectively₁Representing 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.

And step 3: determining the relative sliding speed of the restraining contact point on the indexing mechanism capturing the connecting device:

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

wherein,variables associated with the capture head and the base are indicated, respectively, where subscript numbers indicate 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,representing the absolute velocity of the capture head at the 2 nd contact point with the index base;

the acceleration constraint of the guide flap and the ith contact point of the indexing base is as follows:

and 4, step 4: determining kinematic equation of connection process of capture connection device of indexing mechanism

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 (without subscript) representing 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,The restraining force of the ith point of contact,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 e₃A position vector described in a coordinate system (i.e., a coordinate system formed by the connection surface of the capture head and the connection surface of the indexing base); a is_iFor the contact point between the indexing base and the capture head at e₄Vector position in second speed, I, in a coordinate system (i.e. inertial coordinate system)₃The indexing base is at₃Equivalent inertia tensor, I, described in a coordinate system (i.e., the coordinate system formed by the coupling surface of the capture head and the coupling surface of the indexing table)₁For indexing the base at e₁The equivalent inertia tensor described in the coordinate system (i.e. the capture head connection surface coordinate system) as shown in figure 1.

And 5: determining an analytic form of a constrained kinetic equation

Writing a kinetic equation of a capture head and an indexing base of an indexing mechanism into a matrix form

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;

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

in the above formula, the first and second carbon atoms are,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) For the contact constraint force of the capture head and the indexing base, A is a constraint equation coefficient matrix. Because the capturing head and the indexing base are in the capturing connection process, the process of the space and the space operation of mutual movement between the capturing head and the indexing base is complex, the constraint equations of the equations (10) and (11) are directly solved. The invention uses the D' Alembert orthogonal complement principle to process the problem of dimension-changing constraint, and aims to convert an original dimension-changing kinetic equation set into a fixed n-bit space differential equation set for solution. The virtual bit displacement of X according to the virtual work principle needs to satisfy:

constraint kinetic equation needs to be satisfied

AX＝0 (13)

Considering that the system is constrained by dynamic motion, X is not independent, and solving by an orthogonal complement matrix of an A matrix of a constraint equation is needed for the purpose, wherein the orthogonal complement matrix of the A matrix of the dynamic equation is constrained firstly

G＝A^TA (14)

Wherein A is^TAs a transpose matrix of a, there is a matrix of n × n G obtained from equation (9) with rank m

Wherein e denotes the eigenvectors of the matrix G, and C' and C denote matrices formed by eigenvectors corresponding to non-zero eigenvalues and eigenvectors corresponding to zero eigenvalues, respectively. So the matrix L must be of full rank

X＝LZ (16)

Wherein,z, X is a constructed matrix with only mathematical meaning and no physical meaning, and a single-value one-to-one correspondence exists between X and Z, thereby

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)

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

Can write formula (16) into

X＝CZ” (22)

Substituting the above formula into formula (12) to obtain

Due to the arbitrary nature of Z', can be obtained

Therefore, an orthogonal complement system of constraint dynamics

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

While the invention has been described in terms of its preferred embodiments, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the 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

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