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CN-121997489-A - 3-RSS/S parallel equipment kinematics analysis method

CN121997489ACN 121997489 ACN121997489 ACN 121997489ACN-121997489-A

Abstract

The invention relates to a 3-RSS/S parallel equipment kinematics analysis method which comprises the following steps of S1, establishing a mechanism coordinate and a 3-RSS/S parallel equipment kinematics model, determining a geometric constraint relation and a motion transmission path between each component, S2, deriving a pose curve equation of a parallel equipment moving platform according to the 3-RSS/S parallel equipment kinematics model, and S3, obtaining pose curves of the moving platform in the x, y and z directions according to the pose curve equation. According to the method, the known structural parameters of the equipment are used as input variables, the structural parameters are substituted into the pose curve equation of the equipment, so that the pose state of the parallel equipment is calculated, the actual pose of the movable platform can be calculated in real time, and the influence of the structural parameters of the parallel equipment on the movable platform is better researched.

Inventors

  • HAN XINGHUI
  • MA TENG

Assignees

  • 武汉理工大学

Dates

Publication Date
20260508
Application Date
20260106

Claims (10)

  1. 1. The 3-RSS/S parallel equipment kinematics analysis method is characterized by comprising the following steps of: s1, establishing a mechanism coordinate and a kinematic model of 3-RSS/S parallel equipment, and determining a geometric constraint relation and a motion transmission path between all components; S2, deducing a pose curve equation of the parallel equipment moving platform according to the 3-RSS/S parallel equipment kinematic model; s3, acquiring pose curves of the movable platform in the x, y and z directions according to pose curve equations.
  2. 2. The kinematic analysis method of the 3-RSS/S parallel equipment according to claim 1, wherein the 3-RSS/S parallel equipment comprises a servo motor, a speed reducer, a coupler, a driving gear, a moving platform, a workpiece support frame and a feeding platform, the driving gear adopts four gear revolute pairs, an intermediate gear is rigidly connected with an output shaft of the servo motor, torque transmission is realized through meshed transmission with three peripheral driven gears, each driven gear forms hinged fit with a connecting rod through an upper ball pair, the other end of the connecting rod is connected with the moving platform through a lower ball pair in a ball hinge manner, the moving platform is driven to complete space attitude adjustment through the cooperation of a plurality of connecting rods, the central area of the moving platform forms a ball pair fit structure through an S-shaped joint and a bearing, and a passive constraint branched chain is formed, and can limit the translational freedom degree of the moving platform, so that the moving platform can only realize rotary motion around x, y and z three axes.
  3. 3. The method according to claim 2, wherein in the step S1, the passive branched chain is simplified into a link with two ends having S joints, the fixed coordinate system B and the movable coordinate system P are fixed at the centers of the upper joint of the intermediate branched chain and the lower joint of the intermediate branched chain, a i and C i respectively represent the center of the upper joint of the i-th active link and the center of the lower joint of the i-th active link, D i is the geometric center of the driving gear rotating pair, a i and D i are located in the plane of the fixed coordinate system B, and C i is located in the plane of the movable coordinate system P.
  4. 4. A3-RSS/S parallel equipment kinematics analysis method according to claim 3, characterized in that in said step S2 the position vector of the upper joint center a i in the B coordinate system is noted as (I=1, 2, 3), the position vector of the lower joint center C i in the P coordinate system is noted as (I=1, 2, 3), position vector (I=1, 2, 3) and The expression (i=1, 2, 3) is expressed as: (1) (2) in the formula, Is a dot Relative to the point Is a distance of (2); And Respectively are And Polar angles corresponding to the coordinate system B and the coordinate system P; Is a dot Relative to the point Is included in the eccentric angle of (a).
  5. 5. The method for kinematics analysis of 3-RSS/S parallel equipment according to claim 4, wherein in the step S2, euler angles of the moving platform around x, y, and z axes are set to be respectively 、 、 The pose of the movable platform Expressed as: (3)。
  6. 6. The method for kinematic analysis of 3-RSS/S parallel equipment according to claim 5, wherein in the step S2, the pose of the 3-RSS/S parallel equipment platform is solved by: (4) in the formula, The vector denoted as the i-th link, Represented as a rotation matrix from the P-coordinate system to the B-coordinate system, Represented as a position vector of the inferior articular center C i in the P-coordinate system, Represented as a position vector of the origin of the P coordinate system in the B coordinate system, Represented by the length of the link, Expressed as the axial deflection of the ith connecting rod, wherein the position vector of the origin of the P coordinate system in the B coordinate system Expressed as: (5) Where h represents the vertical distance between the origins of coordinate system P and coordinate system B.
  7. 7. The 3-RSS/S parallel equipment kinematics analysis method according to claim 6, characterized in that in the step S2, a rotation matrix of P-coordinate system to B-coordinate system Expressed as: (6) Wherein: (7) then a rotation matrix of the P coordinate system to the B coordinate system is calculated according to the formula (7) and the formula (6) The method comprises the following steps: (8)。
  8. 8. the method for kinematics analysis of 3-RSS/S parallel arrangement according to claim 7, characterized in that in said step S2, an input angular velocity is obtained With the pose of the movable platform The expression of the mapping relation between the two is: (9) (10)。
  9. 9. The method for kinematic analysis of 3-RSS/S parallel equipment according to claim 8, wherein in the step S3, the pose characteristics of the 3-RSS/S parallel equipment moving platform are determined by the rotation angles around the x, y, and z axes 、 、 The curve changing along with time and the space track are visually embodied, and the structural parameters of the parallel equipment are respectively substituted into the parameters corresponding to the pose curve equation, so that the pose curve of the 3-RSS/S parallel equipment moving platform, namely the rotation angle curve of the moving platform in the x, y and z directions, can be obtained.
  10. 10. The method for analyzing the kinematics of the 3-RSS/S parallel equipment according to claim 8, wherein in the step S3, the method for optimizing the pose in the step S3 comprises the steps of discretizing the independent variable time t in the pose equation into a plurality of uniform sampling points and substituting the uniform sampling points into the solution formula to obtain the corresponding sampling points 、 、 Performing curve fitting on the discrete data by using least square method to generate continuous smooth 、 、 And (3) rotating the angle curve, carrying out smoothness and precision verification on the fitted curve, and eliminating abnormal data points.

Description

3-RSS/S parallel equipment kinematics analysis method Technical Field The invention relates to the field of parallel equipment kinematics analysis, in particular to a 3-RSS/S parallel equipment kinematics analysis method. Background With the development of equipment manufacturing technology, parallel equipment is widely applied to the fields of precision manufacture, aerospace, medical equipment and the like by virtue of the advantages of high rigidity, strong bearing capacity, high motion precision, good dynamic response and the like. The kinematic analysis is the basis of parallel equipment design, control and optimization, and the core task is to establish a mapping relation between joint input and end effector pose. For 3-RSS/S parallel equipment, due to the fact that the structure of the equipment has a coupling relation, the kinematic modeling difficulty is high, the traditional inverse kinematics analysis method often has the problems of complex calculation, poor real-time performance and the like, the requirement of high-precision motion control is difficult to meet, and the method is not suitable for single-drive parallel equipment with single-driver motion degree of freedom coupling. At present, systematic analysis on the influence of the length of a connecting rod on the pose of a moving platform of 3-RSS/S parallel equipment is imperfect, and an effective parameter optimization basis is lacked, so that the application of the equipment in high-end scenes such as precise positioning, pose adjustment and the like is limited. Disclosure of Invention The invention aims to solve the technical problem of providing an accurate and efficient 3-RSS/S parallel equipment kinematics analysis method, which can calculate the actual pose of a moving platform in real time and provide technical support for the design optimization and high-precision control of equipment. The invention solves the technical problems by adopting the technical scheme that a 3-RSS/S parallel equipment kinematics analysis method is constructed, and comprises the following steps: s1, establishing a mechanism coordinate and a kinematic model of 3-RSS/S parallel equipment, and determining a geometric constraint relation and a motion transmission path between all components; S2, deducing a pose curve equation of the parallel equipment moving platform according to the 3-RSS/S parallel equipment kinematic model; s3, acquiring pose curves of the movable platform in the x, y and z directions according to pose curve equations. According to the scheme, the 3-RSS/S parallel equipment comprises a servo motor, a speed reducer, a coupler, a driving gear, a movable platform, a workpiece support frame and a feeding platform, wherein the driving gear adopts four gear revolute pairs, an intermediate gear is rigidly connected with an output shaft of the servo motor, torque transmission is realized through meshing transmission with three peripheral driven gears, each driven gear is in hinged fit with a connecting rod through an upper ball pair, the other end of the connecting rod is connected with the movable platform through a ball pair in a ball hinge manner, the movable platform is driven by the cooperation of a plurality of connecting rods to complete space attitude adjustment, a ball pair matching structure is formed in the central area of the movable platform through an S-shaped joint and a bearing, and the translational freedom degree of the movable platform can be limited by the constraint branched chains, so that the movable platform can only realize rotational movement around x, y and z three axes. According to the scheme, the passive branched chain is simplified into the connecting rod with the joints S at the two ends, the fixed coordinate system B and the movable coordinate system P are respectively fixed at the centers of the upper joint of the middle branched chain and the lower joint of the middle branched chain, A i and C i respectively represent the center of the upper joint of the ith active connecting rod and the center of the lower joint of the ith active connecting rod, D i is the geometric center of the driving gear rotating pair, A i and D i are positioned on the plane where the fixed coordinate system B is positioned, and C i is positioned on the plane where the movable coordinate system P is positioned. According to the scheme, the position vector of the upper joint center A i in the B coordinate system is recorded as(I=1, 2, 3), the position vector of the lower joint center C i in the P coordinate system is noted as(I=1, 2, 3), position vector(I=1, 2, 3) andThe expression (i=1, 2, 3) is expressed as: (1) (2) in the formula, Is a dotRelative to the pointIs a distance of (2); And Respectively areAndPolar angles corresponding to the coordinate system B and the coordinate system P; Is a dot Relative to the pointIs included in the eccentric angle of (a). According to the scheme, euler angles of the movable platform around x, y and z a