CN112507474A - Precision analysis method for space two-degree-of-freedom parallel vector adjusting mechanism - Google Patents

Abstract

A precision analysis method for a space two-degree-of-freedom parallel vector adjusting mechanism comprises the steps of selecting an annular motion chain through degree-of-freedom analysis, converting the annular motion chain into a series structure, establishing a kinematics model containing parameters such as a driving angle, a rod piece length and a kinematic pair gap, supplementing annular motion constraint to realize equivalence between the series mechanism and the parallel mechanism, obtaining motion precision of the two-degree-of-freedom parallel vector adjusting mechanism under different scales and assembly errors through analysis of influence of error parameters on the motion precision of a platform, and providing theoretical basis for configuration design, motor type selection, assembly process and the like.

Description

Precision analysis method for space two-degree-of-freedom parallel vector adjusting mechanism

Technical Field

The invention relates to a precision analysis method for a space two-degree-of-freedom parallel vector adjusting mechanism, and belongs to the technical field of space parallel vector adjusting mechanism control.

Background

The parallel vector adjusting system has the characteristics of small volume, simple structure and quick control, provides necessary thrust for the transfer, intersection and fly-around of the asteroid probe, and directly determines the working quality of the mechanism by the pointing accuracy of the system. Among them, the driving joint motion error, the connecting rod manufacturing error and the assembling error are the key factors influencing the motion precision of the parallel mechanism. Therefore, for a space two-degree-of-freedom parallel vector adjusting mechanism, a kinematics model containing physical parameter information such as active and passive joint kinematic pairs and a connecting rod needs to be established, so that the mechanism motion precision under different motions, scales and assembly errors is obtained, and a theoretical basis is provided for motor model selection, configuration design, assembly process and the like.

The precision analysis methods are mainly classified into two types. The first method is to establish a mechanism kinematics model, and analyze the influence of error quantity on the precision of the dynamic platform by comparing with the operation result of a theoretical model by utilizing the positive and negative kinematics relationship. The kinematic conversion relationship between the movable platform and the fixed platform is generally established according to the structural geometric characteristics, such as the length of a connecting rod. However, the constraint equation does not usually include a system passive kinematic pair, and the influence of assembly or clearance errors on the motion precision of the system is difficult to analyze. The second method is to establish the conversion relation between the mechanism moving platform pose and the error parameter, and obtain the functional relation between the mechanism precision and the error term by solving the differential equation related to the error term, such as a loop incremental method, a matrix method, a vector method and the like. The method has complex calculation results, needs to further simplify or degrade the Jacobian matrix, needs to obtain compensation errors by utilizing a conversion relation between a movable platform and a fixed platform, and is not suitable for a strong-coupling two-degree-of-freedom parallel mechanism with more error parameters and multiple annular loops.

Disclosure of Invention

The technical problem solved by the invention is as follows: aiming at the problems that the influence of the error parameters of the passive kinematic pair on the motion precision of the system and the establishment of the conversion relation between the pose of the moving platform and the error parameters are complex are difficult to analyze by a traditional kinematic model in the prior art, the precision analysis method for the space two-degree-of-freedom parallel vector adjusting mechanism is provided.

The technical scheme for solving the technical problems is as follows:

a precision analysis method for a space two-degree-of-freedom parallel vector adjusting mechanism comprises the following steps:

(1) selecting an annular motion chain by taking any one of the driving joint fixed connection points as an initial node of the two-degree-of-freedom electric propulsion vector adjusting mechanism needing precision analysis, and analyzing the degrees of freedom of all the annular motion chains;

(2) breaking chains at the fixed connecting points of the driving joints selected in the step (1), performing branched chain decomposition on the broken serial kinematic chains, and establishing branched chain kinematic models according to the obtained branched chains and branched chain DH parameters;

(3) determining a constraint function of each annular motion chain according to the motion constraint relation at the fixed connection point of the broken chain in the step (2);

(4) calculating the passive joint angle of the two-degree-of-freedom electric propulsion vector adjusting mechanism according to the preset angle of the driving joint and the constraint function of the annular motion chain obtained in the step (3) to obtain the attitude of the moving platform;

(5) respectively changing the length of a driven connecting rod, the angle of a driving joint and the radial clearance of a driven ball pair in the two-degree-of-freedom electric propulsion vector adjusting mechanism, repeating the steps (1) to (4), calculating the sum of pointing attitude errors of a moving platform of the two-degree-of-freedom electric propulsion vector adjusting mechanism under different conditions, and performing precision analysis.

In the step (1), the method for analyzing the degrees of freedom of all the circular motion chains specifically comprises the following steps:

the specific link structure of the two-degree-of-freedom electric propulsion vector adjusting mechanism is determined and specifically comprises a fixed platform, a movable platform, a driving joint, a driven ball pair, a driving connecting rod and a driven connecting rod, wherein the driving connecting rod is connected with the driving joint, two ends of the driven connecting rod are connected with the driven ball pair, the position and posture of the connecting point of the fixed platform, the driven ball pair and the driving joint are fixed relative to the fixed platform and serve as the fixed connecting point of the mechanism, the connecting points are B1, B2, B3, B4, B5 and B6 in sequence, and the connecting points of the movable platform and the driven ball pair are respectively B1, B2, B3, B4, B5 and B6. Wherein, B1, B2, B3 and B4, B5 and B6 are symmetrical about the X axis of the fixed platform coordinate system { A }, and B1, B2, B3 and B4, B5 and B6 are symmetrical about the X axis of the moving platform coordinate system { C }. Randomly selecting a driving joint, and determining all circular motion chain paths by taking a fixed connection point of the driving joint as an initial node of a circular motion chain;

and simplifying the degrees of freedom of the ball pairs at the two ends of the driven connecting rod, and eliminating the degrees of freedom rotating around the axis of the connecting rod from the ball pairs at the one ends of the connecting rods, so that the driven ball pairs are equivalent to two revolute pairs with axes intersecting at the center of a sphere and perpendicular to the axis direction of the connecting rod to determine the number of driven joints of each annular motion chain.

In the step (2), the chain is broken at the fixed connecting point of the driving joint selected in the step (1), and the series kinematic chain after chain breaking is connected with the movable platform according to the connecting point b of the passive ball pair and the movable platform_iAnd i is 1 and 2 … 6, the method is divided into two branched chains which are connected in series, branched chain kinematics models are respectively established, and branched chain DH parameters comprise selected driving joint angles, driven joint angles, driving connecting rod lengths, driven connecting rod lengths and spherical pair radial clearance information.

In the step (3), the driving joints comprise a driving joint M1 and a driving joint M2 which are respectively fixed at the connection points B5 and B2 and are symmetrical about the X axis of the fixed platform coordinate system { A };

when the fixed connection point Bn of the driving joint is disconnected, the corresponding motion constraint relation of the annular motion chain Bn-Bn-Bm-Bm-Bn containing only one driving joint at the fixed connection point Bn is as follows:

I_4×4＝^BnT_0(n).⁰⁽ⁿ⁾T_1(n)····⁵⁽ⁿ⁾T_6(n)·⁶⁽ⁿ⁾T_bn·^bnT_bm·^bmT_0(m)·····^4(m)T_5(m)·^5(m)T_Bm·^BmT_Bn

wherein n is 2 or 5, m is 1 or 3 or 4 or 6;

the constraint function of the circular motion chain under the fixed platform coordinate system { A } is as follows:

^AT_Bn·(^BmT_Bn)^-1＝^AT_Bn·^BnT_0(n)·⁰⁽ⁿ⁾T_1(n)····⁵⁽ⁿ⁾T_6(n)·⁶⁽ⁿ⁾T_bn·^bnT_bm·^bmT_0(m)·····^4(m)T_5(m)·^5(m)T_Bm

^AT_Bm＝^Af_m(q1⁽ⁿ⁾,…,q6⁽ⁿ⁾,q1^(m),…,q5^(m),L_i,e_j)

when the fixed connection point Bn of the driving joint is disconnected, the corresponding motion constraint relation at the fixed connection point Bn of the circular motion chain Bn-Bn-Bp-Bp-Bn containing the two driving joints is as follows:

I_4×4＝^BnT_0(n)·⁰⁽ⁿ⁾T_1(n)····⁵⁽ⁿ⁾T_6(n)·⁶⁽ⁿ⁾T_bn·^bnT_bp·^bpT_0(p)·····^5(p)T_6(p)·^6(p)T_Bp ^BpT_Bn

wherein n is 2 or 5, p is 5 or 2;

the constraint function of the circular motion chain under the fixed platform coordinate system { A } is as follows:

^AT_Bn·(^BpT_Bn)^-1＝^AT_Bn·^BnT_0(n)·⁰⁽ⁿ⁾T_1(n)····⁵⁽ⁿ⁾T_6(n)·⁶⁽ⁿ⁾T_bn·^bnT_bp·^bpT_0(p)·····^5(p)T_6(p)·^6(p)T_Bp

^AT_Bp＝^Af_p(q1⁽ⁿ⁾,…,q6⁽ⁿ⁾,q1^(p),…,q6^(p),L_i,e_j)

in the formula (I), the compound is shown in the specification,^k-1(q)T_k(q)is the conversion of the coordinate system { k } in the series branched Bq-Bq or Bq-Bq with respect to the coordinate system { k-1}, wherein q is 1, …, 6; as the branched chains Bn-Bn, Bm-Bm and Bp-Bp are connected with the movable platform and the fixed platform through spherical hinges at the positions of Bn, Bm and Bp, the error is avoided⁶⁽ⁿ⁾T_bn、^5(m)T_BmAnd^6(p)T_Bpthe size is an identity matrix;^BnT_0(n)、^bmT_0(m)and^bpT_0(p)respectively are the conversion relations between the base coordinate systems of the tandem type kinematic chains Bn-Bn, Bm-Bm and Bp-Bp and the connecting points Bn, Bm and Bp of the moving platform and the fixed platform,^BnT_0(n)＝troty(π/2)，^bmT_0(m)＝troty(-π/2)，^bpT_0(p)troty (-pi/2), troty (delta) is a homogeneous change matrix of rotation angle delta around the Y axis of the coordinate system; l is_iThe lengths of the connecting rods i are respectively; e.g. of the type_jThe spherical hinge j is the offset generated in the radial direction of the connecting rod.

In the step (4), the method for calculating the attitude of the moving platform of the two-degree-of-freedom electric propulsion vector adjusting mechanism comprises the following steps:

compared with the prior art, the invention has the advantages that:

(1) according to the precision analysis method for the space two-degree-of-freedom parallel vector adjusting mechanism, the parallel mechanism is converted into the equivalent series kinematic chain by disconnecting the plurality of annular loop fixed hinges and supplementing the motion constraint, and then the kinematic solution and precision analysis are performed on the equivalent series kinematic chain, so that the problem that the parallel mechanism is difficult to be subjected to precision analysis by directly adopting a series mechanism kinematic modeling method is solved, the method is not limited by the number and the configuration of the parallel mechanism degree-of-freedom annular loops, and the method has good application and popularization performance;

(2) the invention adopts a kinematic model for simplifying adjacent spherical hinges in the selection process of the annular loop, so that the angle of the passive joint to be solved is consistent with the number of constraint equations, thereby avoiding the generation of local optimum and multiple solutions in the solving process, simultaneously, in the modeling process of the annular kinematics, error parameters such as connecting rod processing errors, kinematic pair clearances, driving precision and the like are included, the influence of the error parameters on the system precision is solved and analyzed through the kinematics, the structure of an error item differential equation and the simplification process thereof are avoided, and the problems that the kinematic information of the passive joint is lacked and the influence of the kinematic pair clearances on the system precision is difficult to analyze in the existing parallel mechanism kinematic modeling method are solved.

Drawings

FIG. 1 is a schematic structural view of a two-degree-of-freedom electric propulsion vector adjusting mechanism provided by the invention;

FIG. 2 is a simplified schematic diagram of an adjacent ball pair connecting rod model provided by the invention;

FIG. 3 is a schematic structural view of a two-degree-of-freedom electric thrust vector adjusting mechanism of a degenerated spherical pair provided by the invention;

FIG. 4 is a schematic diagram of a serial equivalent model of the circular kinematic chain provided by the present invention;

FIG. 5 is a schematic diagram of the angle error of the driving joint and the attitude error and distribution of the moving platform provided by the invention;

FIG. 6 is a schematic diagram of the length processing accuracy of the passive connecting rod and the attitude error and distribution of the movable platform provided by the invention;

FIG. 7 is a schematic diagram of the radial clearance error of the passive ball pair and the attitude error and distribution of the movable platform provided by the invention;

Detailed Description

A precision analysis method for a space two-degree-of-freedom parallel vector adjusting mechanism is characterized in that for an existing two-degree-of-freedom electric propulsion vector adjusting mechanism, an annular motion chain is selected through degree-of-freedom analysis, the annular motion chain is converted into a series structure, a kinematic model comprising parameters such as driving joint precision, lengths of driving and driven rods, kinematic pair radial gaps and the like is established, annular motion constraint is supplemented to achieve equivalence between the series mechanism and the parallel mechanism, and the method specifically comprises the following steps:

(1) selecting an annular motion chain by taking any one of the driving joint fixed connection points as an initial node of the two-degree-of-freedom electric propulsion vector adjusting mechanism needing precision analysis, and analyzing the degrees of freedom of all the annular motion chains;

the two-degree-of-freedom electric propulsion vector adjusting mechanism comprises a fixed platform, a movable platform, a driving joint, a driven ball pair, a driving connecting rod and a driven connecting rod, wherein the driving connecting rod is connected with the driving joint, two ends of the driven connecting rod are connected with the driven ball pair, the connecting points of the fixed platform, the driven ball pair and the driving joint are fixed relative to the fixed platform and serve as fixed connecting points of the mechanism, the connecting points are B1, B2, B3, B4, B5 and B6 in sequence, and the connecting points of the movable platform and the driven ball pair are B1, B2, B3, B4, B5 and B6 respectively. Wherein, B1, B2, B3 and B4, B5 and B6 are symmetrical about the X axis of the fixed platform coordinate system { A }, and B1, B2, B3 and B4, B5 and B6 are symmetrical about the X axis of the moving platform coordinate system { C }. Randomly selecting a driving joint, and determining all circular motion chain paths by taking a fixed connection point of the driving joint as an initial node of a circular motion chain;

simplifying the degrees of freedom of the ball pairs at the two ends of the passive connecting rod, and eliminating the degrees of freedom which rotates around the axis of the connecting rod in the ball pair at one end of the connecting rod to ensure that the passive ball pairs are equivalent to two revolute pairs of which the axes are intersected at the center of a sphere and are vertical to the axis direction of the connecting rod;

determining the number of passive joints of each annular motion chain;

(2) breaking the chain at the fixed connecting point of the driving joint selected in the step (1), and connecting the broken chain with the series kinematic chain according to the connecting point b of the passive ball pair and the movable platform_iI is 1, 2 … 6, which is decomposed into two branches connected in series, and each branch movement model is established according to the obtained branch chain and the branch chain DH parameter; wherein, the branched chain DH parameters comprise the selected driving joint angle, the passive joint angle and the length of the driving connecting rodPassive link length and ball pair radial clearance information. (ii) a

(3) Determining a constraint function of each annular motion chain under a fixed platform coordinate system according to the motion constraint relation at the fixed connection point of the broken chain in the step (2);

in the step (3), each broken ring-shaped motion chain corresponds to a single motion constraint relation,

the driving joint comprises a driving joint M1 and a driving joint M2 which are respectively fixed at the connecting points B5 and B2 and are symmetrical about the X axis of the fixed platform coordinate system { A };

when the fixed connection point Bn (n ═ 2 or 5) of the driving joint is disconnected, the corresponding motion constraint relation formula at the fixed connection point Bn (m ═ 1, 3, 4, 6) of the circular kinematic chain Bn-Bm-Bn (m ═ 1, 3, 4, 6) containing only one driving joint is as follows:

I_4×4＝^BnT_0(n)·⁰⁽ⁿ⁾T_1(n)····⁵⁽ⁿ⁾T_6(n)·⁶⁽ⁿ⁾T_bn·^bnT_bm·^bmT_0(m)·····^4(m)T_5(m)·^5(m)T_Bm·^BmT_Bn

the constraint function of the circular motion chain under the fixed platform coordinate system { A } is as follows:

^AT_Bn·(^BmT_Bn)^-1＝^AT_Bn·^BnT_0(n)·⁰⁽ⁿ⁾T_1(n)····⁵⁽ⁿ⁾T_6(n)·⁶⁽ⁿ⁾T_bn·^bnT_bm·^bmT_0(m)·····^4(m)T_5(m)·^5(m)T_Bm

^AT_Bm＝f_m(q1⁽ⁿ⁾,…,q6⁽ⁿ⁾,q1^(m),…,q5^(m),L_i,e_j)

when the fixed connection point Bn (n ═ 2 or 5) of the driving joint is disconnected, the corresponding motion constraint relation at the fixed connection point Bn of the circular kinematic chain Bn-Bp-Bn (p ═ 5 or 2) containing the two driving joints is as follows:

I_4×4＝^BnT_0(n)·⁰⁽ⁿ⁾T_1(n)····⁵⁽ⁿ⁾T_6(n)·⁶⁽ⁿ⁾T_bn·^bnT_bp·^bpT_0(p)·····^5(p)T_6(p)·^6(p)T_Bp·^BpT_Bn

the constraint function of the circular motion chain under the fixed platform coordinate system { A } is as follows:

^AT_Bn·(^BpT_Bn)^-1＝^BnT_0(n)·⁰⁽ⁿ⁾T_1(n)····⁵⁽ⁿ⁾T_6(n)·⁶⁽ⁿ⁾T_bn·^bnT_bp·^bpT_0(p)·····^5(p)T_6(p)·^6(p)T_Bp

^AT_Bp＝f_p(q1⁽ⁿ⁾,…,q6⁽ⁿ⁾,q1^(p),…,q6^(p),L_i,e_j)

in the formula (I), the compound is shown in the specification,^k-1(q)T_k(q)is the conversion of the coordinate system { k } in the series branch Bq-Bq or Bq-Bq (q ═ 1, …, 6) relative to the coordinate system { k-1 }; as the branched chains Bn-Bn, Bm-Bm and Bp-Bp are connected with the movable platform and the fixed platform through spherical hinges at the positions of Bn, Bm and Bp, the error is avoided⁶⁽ⁿ⁾T_bn、^5(m)T_BmAnd^6(p)T_Bpthe size is an identity matrix;^BnT_0(n)、^bmT_0(m)and^bpT_0(p)respectively are the conversion relations between the base coordinate systems of the tandem type kinematic chains Bn-Bn, Bm-Bm and Bp-Bp and the connecting points Bn, Bm and Bp of the moving platform and the fixed platform,^BnT_0(n)＝troty(π/2)，^bmT_0(m)＝troty(-π/2)，^bpT_0(p)troty (-pi/2), troty (delta) is a homogeneous change matrix of rotation angle delta around the Y axis of the coordinate system; l is_iThe lengths of the connecting rods i are respectively; e.g. of the type_jThe spherical hinge j is the offset generated in the radial direction of the connecting rod.

(4) Calculating the passive joint angle of the two-degree-of-freedom electric propulsion vector adjusting mechanism according to the preset angle of the driving joint and the constraint function of the annular motion chain obtained in the step (3) to obtain the attitude of the moving platform;

firstly, determining a preset angle range of a driving joint, determining a design target of precision analysis, simultaneously determining the lengths of driving and driven connecting rods, pose information of a fixed platform and a movable platform relative to a connecting point of a two-degree-of-freedom electric propulsion vector adjusting mechanism, angle information of a driven joint, and calculating the posture of the movable platform of the two-degree-of-freedom electric propulsion vector adjusting mechanism according to the data, wherein the specific calculation method comprises the following steps:

(5) respectively changing the length of a passive connecting rod, the angle of a driving joint and the radial clearance of a passive ball pair in the two-degree-of-freedom electric propulsion vector adjusting mechanism, repeating the steps (1) to (4), calculating the attitude error sum of a moving platform of the two-degree-of-freedom electric propulsion vector adjusting mechanism under different conditions, and performing precision analysis;

the method comprises the following steps of obtaining attitude motion precision data of the moving platform by changing the physical quantity and repeating the calculation step, and determining attitude errors of the moving platform of the two-degree-of-freedom electric propulsion vector adjusting mechanism under different conditions and taking the attitude errors as final data;

the following is further illustrated with reference to specific examples:

as shown in fig. 1, a two-degree-of-freedom electric propulsion vector adjusting mechanism is selected, the mechanism is connected with adjacent linear connecting rods through a rotating pair and a ball pair, B1-B6 and B1-B6 are respectively connecting points of the connecting rods with a fixed platform and a movable platform, wherein B1-B6 are fixed connecting points, driving joints M1 and M2 are respectively fixed at the connecting points B2 and B5, and the position and the posture of the movable platform are adjusted by controlling the rotation of the driving joints;

b1, B2, B3, B4, B5 and B6 are symmetrical about the X axis of a fixed platform coordinate system { A }, B1, B2, B3, B4, B5 and B6 are symmetrical about the X axis of a movable platform coordinate system { C }, the whole mechanism has better symmetry, and the accuracy analysis method of the vector adjustment mechanism is explained by taking a fixed connection point B5 of a driving joint M1 as an example.

The angle of any one rotary joint in the parallel mechanism is affected by all father nodes and all child nodes, and the motion states of the joints are coupled with each other, so that the following 5 circular motion chains are selected from a fixed connection point B5 of a driving joint M1 to contain the motion states of all the joints, specifically:

the kinematic chain 1: B5-B5-B1-B1-B5

The kinematic chain 2: B5-B5-B2-B2-B5

The kinematic chain 3: B5-B5-B3-B3-B5

The kinematic chain 4: B5-B5-B4-B4-B5

The kinematic chain 5: B5-B5-B6-B6-B5

Simplifying the degrees of freedom of the ball pairs at the two ends of the passive connecting rod, and eliminating the degrees of freedom rotating around the axis of the connecting rod from the ball pairs at one end of the connecting rod to ensure that the passive ball pairs are equivalent to two revolute pairs with axes intersecting at the center of a sphere and perpendicular to the axis direction of the connecting rod, as shown in FIG. 2;

as shown in fig. 3, in the 5 endless kinematic chains, six ball pairs are degenerated into two revolute pairs whose axes intersect at the center of the sphere and are perpendicular to the axial direction of the connecting rod, the degenerated ball pair is denoted by "X", the parallel mechanism has 32 joints in total, wherein the degenerated ball pair includes 2 active joints, 6 passive ball pairs and 6 degenerated ball pairs, 6 × 2+6 × 3 is 30 passive joints in total, and the two independent degrees of freedom are provided;

the endless kinematic chain is disconnected at a fixed connection point, converted into a serial mechanism, and the equivalent serial mechanism is kinematically modeled, respectively with an endless kinematic chain 1 with one driving joint: B5-B5-B1-B1-B5 and a kinematic chain 2 with two drive joints: B5-B5-B2-B2-B5 is taken as an example, the position is broken at B5, and B5, B1 and B2 are fixed under a fixed platform, so that the circular motion chain 1 and the circular motion chain 2 are respectively decomposed into two branched chains of B5-B5, B1-B1, B5-B5 and B2-B2 which are connected in series according to the connection points B5, B1, B5 and B2 of the passive ball pair and the moving platform, and the two branched chains are connected through the fixed conversion relation of B5, B1 and B2 to form a closed loop;

the serial branches B3-B3, B4-B4, B5-B5 in the circular kinematic chain 3-5 are consistent with the kinematic models of the branches B1-B1, so that after the fixed connection point of the driving joint is disconnected, all the circular kinematic chain branches can be summarized into three types, namely a serial branch B5-B5, a serial branch B1-B1 and a serial branch B2-B2, and DH parameters of the three types of serial branch kinematic models are respectively as follows:

TABLE 1D-H parameters of equivalent tandem model branches B5-B5

Rod piece i	ai	αi	di	θi
					1	L1	π/2	L3	q1(5)
2	0	-π/2	0	q2(5)
					3	L2	π/2	0(e5)	q3 (5)
4	0	-π/2	0	q4 (5)
					5	0	π/2	0	q5(5)
6	0	0	0	q6(5)

Wherein, a_i，α_i，d_iAnd theta_iThe definition of the parameters is consistent with the standard D-H modeling method. q1⁽⁵⁾Is the angle of the driving joint M1 on the branched chain B5-B5; q2⁽⁵⁾-q6⁽⁵⁾Represents the angle of the passive joint on the branch B5-B5; l is₁、L₃The length of the drive link on the branch B5-B5, L₂The passive link length, as shown in fig. 4 (a); e.g. of the type₅The motion gap generated by the ball pair on the branch chain B5-B5 in the radial direction of the connecting rod is shown;

TABLE 2D-H parameters of equivalent tandem model branches B1-B1

Rod piece i	ai	αi	di	θi
					1	0	-π/2	0	q1(1)
2	-L4	π/2	0(e1)	q2 (1)
					3	0	-π/2	0	q3 (1)
4	0	π/2	0	q4 (1)
					5	0	0	0	q5(1)

Wherein, q1⁽¹⁾-q5⁽¹⁾Represents the angle of the passive joint on the branched chain B1-B1; l is₄Represents the length of the passive link on the branched chain B1-B1, as shown in FIG. 4 (B); e.g. of the type₁The motion gap generated by the ball pair on the branched chain B1-B1 in the radial direction of the connecting rod is shown;

TABLE 3D-H parameters of equivalent tandem model branches B2-B2

Wherein, q6⁽²⁾Is the angle of the driving joint M2 on the branched chain B2-B2; q1⁽²⁾-q5⁽²⁾Represents the angle of the passive joint of the branched chain B2-B2; l is₁、L₃The length of the drive link on the branch B2-B2, L₂The passive link length is as shown in fig. 4 (c); e.g. of the type₂The moving gap generated by the ball pair on the branched chain B2-B2 in the radial direction of the connecting rod is shown.

According to the branched chain motion model disconnected at the fixed connection point of the driving joint, supplementing circular motion constraint at the disconnected fixed connection point B5, and constructing an equivalent kinematics model, wherein the motion constraint relational expressions of the circular motion chain 1 and the circular motion chain 2 are respectively as follows:

I_4×4＝^B5T₀₍₅₎·⁰⁽⁵⁾T₁₍₅₎····⁵⁽⁵⁾T₆₍₅₎·⁶⁽⁵⁾T_b5·^b5T_b1·^b1T₀₍₁₎·····⁴⁽¹⁾T₅₍₁₎·⁵⁽¹⁾T_B1·^B1T_B5

I_4×4＝^B5T₀₍₅₎·⁰⁽⁵⁾T₁₍₅₎····⁵⁽⁵⁾T₆₍₅₎·⁶⁽²⁾T_b2·^b2T_b2·^b2T₀₍₂₎·····⁵⁽²⁾T₆₍₂₎·⁶⁽²⁾T_B2·^B2T_B5

wherein, I_4×4Representing a 4-dimensional identity matrix. Due to the pose relations of the points B1, B2, B5, B1, B2 and B5 relative to the fixed platform { A } and the movable platform { C } respectively^AT_B1、^AT_B2、^AT_B5、^CT_b5、^CT_b1And^CT_b2is known, therefore^B1T_B5＝(^AT_B1)^-1·^AT_B5，^B2T_B5＝(^AT_B2)^-1·^AT_B5，^b5T_b1＝(^CT_b5)^-1·^CT_b1，^b5T_b2＝(^CT_b5)^-1·^CT_b2The constraint functions of the circular motion chain 1 and the circular motion chain 2 with one driving joint under the fixed platform coordinate system { A } can be obtained^Af₁，^Af₂：

^AT_B5·(^B1T_B5)^-1＝^AT_B5·^B5T₀₍₅₎·⁰⁽⁵⁾T₁₍₅₎····⁵⁽⁵⁾T₆₍₅₎·⁶⁽⁵⁾T_b5·^b5T_b1·^b1T₀₍₁₎·····⁴⁽¹⁾T₅₍₁₎·⁵⁽¹⁾T_B1

^AT_B1＝^Af₁(q1⁽⁵⁾,…,q6⁽⁵⁾,q1⁽¹⁾,…,q5⁽¹⁾,L_i,e_j)

^AT_B2·(^B2T_B5)^-1＝^AT_B5·^B5T₀₍₅₎·⁰⁽⁵⁾T₁₍₅₎····⁵⁽⁵⁾T₆₍₅₎·⁶⁽⁵⁾T_b5·^b5T_b2·^b2T₀₍₂₎·····⁵⁽²⁾T₆₍₂₎·⁶⁽²⁾T_B2

^AT_B2＝^Af₂(q1⁽⁵⁾,…,q6⁽⁵⁾,q1⁽²⁾,…,q6⁽²⁾,L_i,e_j)

Wherein the content of the first and second substances,^k-1(q)T_k(q)is the conversion of the coordinate system { k } in the series branch Bq-Bq or Bq-Bq (q ═ 1, …, 6) relative to the coordinate system { k-1 }; (ii) a As the branched chains B5-B5, B1-B1 and B2-B2 are connected with the movable and fixed platforms at the positions B5, B1 and B2 through spherical hinges, when no error occurs, the movable and fixed platforms are connected with each other⁶⁽⁵⁾T_b5、⁵⁽¹⁾T_B1And⁶⁽²⁾T_B2the size is an identity matrix;^B5T₀₍₅₎、^b1T₀₍₁₎and^b2T₀₍₂₎respectively shows the conversion relation of the base coordinate system of the serial kinematic chain B5-B5, B1-B1 and B2-B2 and the connection part of the moving platform and the fixed platform,^B5T₀₍₅₎＝troty(π/2)，^b1T₀₍₁₎＝troty(-π/2)，^b2T₀₍₂₎troty (-pi/2), troty (Δ) represents a homogeneous change matrix of the rotation angle Δ around the Y-axis of the coordinate system; l is_iRespectively representing the lengths of the connecting rods i; e.g. of the type_jRepresents a branch b_j-B_jOr B_j-b_jThe size of a movement gap generated by the upper spherical hinge j in the radial direction of the connecting rod is large;

the motion constraint function of the circular motion chain 3-5 can be obtained according to the steps,^Af₃、^Af₄、^Af₅The left side of each function represents the pose conversion relation of the fixed connection points B3, B4 and B6 under the fixed platform, the pose conversion relation comprises constraint functions related to 3 positions and 3 postures, the 5 annular motion chains totally comprise 5 multiplied by 3+5 multiplied by 3-30 independent constraint equations, when the driving joint angle is given, the total number of the constraint equations is equal to the number of the passive joint variables, and all the passive joint angles can be solved by adopting a Newton iteration method;

forward kinematics according to passive joint angle, branch B5-B5^AT_b5And b5 fixed position and posture relation relative to the movable platform C^CT_b5Calculating a predetermined drive joint angle q1⁽⁵⁾And q6⁽²⁾Moving platform position and posture^AT_CThe method specifically comprises the following steps:

and respectively determining the ranges of parameters such as the length processing error of the passive connecting rod, the angle error of the driving joint, the radial clearance of the passive ball pair and the like. The vector adjusting mechanism is designed to aim at the condition that the pointing accuracy of a movable platform of the vector adjusting mechanism is better than 0.2 degrees, and the motion range of a driving joint is [ -27.56; the method comprises the following steps of (1) comparing the motion state of a movable platform of a vector adjusting mechanism without parameter errors, analyzing the influence of the machining precision of a motor and a connecting rod and the motion precision of the movable platform caused by the clearance of a spherical hinge, further performing motor model selection, and providing theoretical basis for the process requirements of machining, assembly and the like, wherein the method specifically comprises the following steps:

the length of each connecting rod is L₀＝43mm，L₁＝115mm，L₂＝310mm，L₃＝14mm，L₄A 40mm vector adjustment mechanism is an example. The postures of B1-B6 are consistent with the fixed platform { A }, and the positions of the fixed platforms are B1 ═ 0.2253, 0.3305 and 0 respectively]m，B2＝[0.1735，0.3604，0]m，B3＝[-0.3989，0.0299，0]m，B4＝[-0.3989，-0.0299，0]m，B5＝[0.1735，-0.3604，0]m，B6＝[-0.2253，0.3305，0]m。

The postures of b1-b6 are consistent with that of a movable platform { C }, the positions of the relative movable platforms are b1 ═ 0.2336, 0.0278, 0] m, b2 [ -0.092, 0.2162, 0] m, b3 [ -0.1409, 0.1884, 0] m, b4 [ -0.1409, -0.1884, 0] m, b5 [ -0.2336, -0.0278, 0] m, b6 ═ 0.2336, 0.0278, 0] m;

the relationship between the angle error of the driving joint and the attitude motion precision of the movable platform is shown in table 4.

TABLE 4 relationship between angle error of driving joint and attitude motion precision of moving platform

Drive joint angle error (deg)	±0.05	±0.1	±0.15	±0.2
					Sum of attitude errors (deg) of moving platform	0.0063	0.1261	0.1858	0.2464

As can be seen from Table 4, the angle error of the driving joint and the maximum attitude error of the movable platform are approximately in a linear relationship. When the motion accuracy of the two driving joints is +/-0.15 degrees, the pointing accuracy of the movable platform of the vector adjusting mechanism is better than 0.2 degrees, the design requirement is met, and the error distribution curve is shown in figure 5.

The relationship between the length processing error of the connecting rod and the attitude motion precision of the movable platform is shown in table 5.

TABLE 5 relationship between passive link length processing error and moving platform attitude motion accuracy

L2Connecting rod length processing error (mm)	±0.1	±0.2	±0.5	±1
					Sum of attitude errors (deg) of moving platform	0.0197	0.0394	0.0974	0.2005

As can be seen from Table 5, the length error of the connecting rod and the maximum attitude error of the movable platform are approximately in a linear relationship. When the connecting rod L on the branched chain B5-B5 and the branched chain B2-B2₂When the processing precision is better than +/-1 mm, the pointing precision of the movable platform of the vector adjusting mechanism is better than 0.2 degrees, the design requirement is met, and the error distribution curve is shown in figure 6

The axial error of the driven ball pair can be equivalent to the length error of the connecting rod. Therefore, the influence of the radial error of the ball pair on the precision of the movable platform of the vector adjusting mechanism is analyzed. As shown in table 6.

TABLE 6 relationship between radial clearance error of passive ball pair and attitude motion accuracy of movable platform

Branched chain B5-B5 spherical pair radial clearance (mm)	±5	±10	±20	±30
					Sum of attitude errors (deg) of moving platform	0.0079	0.0317	0.1318	0.2807

As can be seen from Table 6, the radial clearance of the ball pair has a nonlinear relationship with the maximum attitude error of the movable platform, which mainly affects the rotation of the movable platform around the Z direction, when the error is less than 10mm, the influence of the error parameters on the pointing accuracy of the movable platform is not obvious, and when the error is greater than 10mm, the pointing accuracy is very sensitive to the change of the error direction. When the spherical hinge gap error on the branched chain B5-B5 is +/-10 mm, the error distribution curve is shown in FIG. 7.

Those skilled in the art will appreciate that those matters not described in detail in the present specification are well known in the art.

Claims (5)

1. A precision analysis method for a space two-degree-of-freedom parallel vector adjusting mechanism is characterized by comprising the following steps:

(1) selecting an annular motion chain by taking any one of the driving joint fixed connection points as an initial node of the two-degree-of-freedom electric propulsion vector adjusting mechanism needing precision analysis, and analyzing the degrees of freedom of all the annular motion chains;

(2) breaking chains at the fixed connecting points of the driving joints selected in the step (1), performing branched chain decomposition on the broken serial kinematic chains, and establishing branched chain kinematic models according to the obtained branched chains and branched chain DH parameters;

(3) determining a constraint function of each annular motion chain according to the motion constraint relation at the fixed connection point of the broken chain in the step (2);

(4) calculating the passive joint angle of the two-degree-of-freedom electric propulsion vector adjusting mechanism according to the preset angle of the driving joint and the constraint function of the annular motion chain obtained in the step (3) to obtain the attitude of the moving platform;

(5) respectively changing the length of a driven connecting rod, the angle of a driving joint and the radial clearance of a driven ball pair in the two-degree-of-freedom electric propulsion vector adjusting mechanism, repeating the steps (1) to (4), calculating the sum of pointing attitude errors of a moving platform of the two-degree-of-freedom electric propulsion vector adjusting mechanism under different conditions, and performing precision analysis.

2. The method for analyzing the accuracy of a spatial two-degree-of-freedom parallel vector adjustment mechanism according to claim 1, wherein:

in the step (1), the method for analyzing the degrees of freedom of all the circular motion chains specifically comprises the following steps:

the specific link structure of the two-degree-of-freedom electric propulsion vector adjusting mechanism is determined and specifically comprises a fixed platform, a movable platform, a driving joint, a driven ball pair, a driving connecting rod and a driven connecting rod, wherein the driving connecting rod is connected with the driving joint, two ends of the driven connecting rod are connected with the driven ball pair, the position and posture of the connecting point of the fixed platform, the driven ball pair and the driving joint are fixed relative to the fixed platform and serve as the fixed connecting point of the mechanism, the connecting points are B1, B2, B3, B4, B5 and B6 in sequence, and the connecting points of the movable platform and the driven ball pair are respectively B1, B2, B3, B4, B5 and B6. Wherein, B1, B2, B3 and B4, B5 and B6 are symmetrical about the X axis of the fixed platform coordinate system { A }, and B1, B2, B3 and B4, B5 and B6 are symmetrical about the X axis of the moving platform coordinate system { C }. Randomly selecting a driving joint, and determining all circular motion chain paths by taking a fixed connection point of the driving joint as an initial node of a circular motion chain;

and simplifying the degrees of freedom of the ball pairs at the two ends of the driven connecting rod, and eliminating the degrees of freedom rotating around the axis of the connecting rod from the ball pairs at the one ends of the connecting rods, so that the driven ball pairs are equivalent to two revolute pairs with axes intersecting at the center of a sphere and perpendicular to the axis direction of the connecting rod to determine the number of driven joints of each annular motion chain.

3. The method for analyzing the accuracy of a spatial two-degree-of-freedom parallel vector adjustment mechanism according to claim 1, wherein:

in the step (2), the chain is broken at the fixed connecting point of the driving joint selected in the step (1), and the series kinematic chain after chain breaking is connected with the movable platform according to the connecting point b of the passive ball pair and the movable platform_iI 1, 2 … 6, into two branched chainsAnd respectively establishing branched chain kinematics models, wherein branched chain DH parameters comprise selected driving joint angles, passive joint angles, driving connecting rod lengths, passive connecting rod lengths and spherical pair radial clearance information.

4. The method for analyzing the accuracy of a spatial two-degree-of-freedom parallel vector adjustment mechanism according to claim 1, wherein:

in the step (3), the driving joints comprise a driving joint M1 and a driving joint M2 which are respectively fixed at the connection points B5 and B2 and are symmetrical about the X axis of the fixed platform coordinate system { A };

when the fixed connection point Bn of the driving joint is disconnected, the corresponding motion constraint relation of the annular motion chain Bn-Bn-Bm-Bm-Bn containing only one driving joint at the fixed connection point Bn is as follows:

I_4×4＝^BnT_0(n)·⁰⁽ⁿ⁾T_1(n)…·⁵⁽ⁿ⁾T_6(n)·⁶⁽ⁿ⁾T_bn·^bnT_bm·^bmT_0(m)…··^4(m)T_5(m)·^5(m)T_Bm·^BmT_Bn

wherein n is 2 or 5, m is 1 or 3 or 4 or 6;

the constraint function of the circular motion chain under the fixed platform coordinate system { A } is as follows:

^AT_Bn·(^BmT_Bn)^-1＝^AT_Bn·^BnT_0(n)·⁰⁽ⁿ⁾T_1(n)…·⁵⁽ⁿ⁾T_6(n)·⁶⁽ⁿ⁾T_bn·^bnT_bm·^bmT_0(m)…··^4(m)T_5(m)·^5(m)T_Bm

^AT_Bm＝^Af_m(q1⁽ⁿ⁾,…,q6⁽ⁿ⁾,q1^(m),…,q5^(m),L_i,e_j)

when the fixed connection point Bn of the driving joint is disconnected, the corresponding motion constraint relation at the fixed connection point Bn of the circular motion chain Bn-Bn-Bp-Bp-Bn containing the two driving joints is as follows:

I_4×4＝^BnT_0(n).⁰⁽ⁿ⁾T_1(n)…·⁵⁽ⁿ⁾T_6(n)·⁶⁽ⁿ⁾T_bn·^bnT_bp·^bpT_0(p)…··^5(p)T_6(p)·^6(p)T_Bp ^BpT_Bn

wherein n is 2 or 5, p is 5 or 2;

the constraint function of the circular motion chain under the fixed platform coordinate system { A } is as follows:

^AT_Bn·(^BpT_Bn)^-1＝^AT_Bn·^BnT_0(n)·⁰⁽ⁿ⁾T_1(n)…·⁵⁽ⁿ⁾T_6(n).⁶⁽ⁿ⁾T_bn·^bnT_bp·^bpT_0(p)…··^5(p)T_6(p).^6(p)T_Bp

^AT_Bp＝^Af_p(q1⁽ⁿ⁾,…,q6⁽ⁿ⁾,q1^(p),…,q6^(p),L_i,e_j)

in the formula (I), the compound is shown in the specification,^k-1(q)T_k(q)is the conversion of the coordinate system { k } in the series branched Bq-Bq or Bq-Bq with respect to the coordinate system { k-1}, wherein q is 1, …, 6; as the branched chains Bn-Bn, Bm-Bm and Bp-Bp are connected with the movable platform and the fixed platform through spherical hinges at the positions of Bn, Bm and Bp, the error is avoided⁶⁽ⁿ⁾T_bn、^5(m)T_BmAnd^6(p)T_Bpthe size is an identity matrix;^BnT_0(n)、^bmT_0(m)and^bpT_0(p)respectively are the conversion relations between the base coordinate systems of the tandem type kinematic chains Bn-Bn, Bm-Bm and Bp-Bp and the connecting points Bn, Bm and Bp of the moving platform and the fixed platform,^BnT_0(n)＝troty(π/2)，^bmT_0(m)＝troty(-π/2)，^bpT_0(p)troty (-pi/2), troty (delta) is a homogeneous change matrix of rotation angle delta around the Y axis of the coordinate system; l is_iThe lengths of the connecting rods i are respectively; e.g. of the type_jIs a spherical hinge j formed by connecting rods in the radial directionThe magnitude of the offset generated.

5. The method for analyzing the accuracy of a spatial two-degree-of-freedom parallel vector adjustment mechanism according to claim 1, wherein:

in the step (4), the method for calculating the attitude of the moving platform of the two-degree-of-freedom electric propulsion vector adjusting mechanism comprises the following steps:

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