Kinematics Analysis Of Two-platform Of Serial-parallel Manipulators Including 3-RPS And 3-SPR Manipulator

In this paper,four two-layer of serial-parallel manipulators including a 3-RPS manipulator and a 3-SPR manipulator are used as the object of study,and the inverse kinematics of this kind of manipulator is systematically analyzed.Aiming at(3-SPR)+(3-RPS)redundant serial-parallel manipulator,based on the Sylvester resultant elimination method,the constraint relation of end position and orientation parameters is obtained.The optimal position inverse kinematics of(3-SPR)+(3-RPS)redundant serial-parallel manipulator is obtained by optimizing the performance index of manipulability,and the velocity inverse kinematics of(3-SPR)+(3-RPS)redundant serial-parallel manipulator is optimized by gradient projection method.Aiming at three non-redundant serial-parallel manipulators,the position inverse kinematics of three manipulators are studied which verified by calculating examples.The main research work is as follows:The redundancy of(3-SPR)+(3-RPS)serial-parallel manipulator is analyzed.By using the Sylvester resultant elimination method,the position and orientation parameters of the middle platform in the geometric constraint equations are eliminated,and a coefficient matrix of the 8×8 form associated with the manipulator terminal position and orientation parameters is constructed.By using the position parameter calculating example and the orientation parameter calculating example,we get two linear equations of higher degree associated with the end position and orientation parameters.Comparing the solutions figured out by the Maple programming software with the data measured by the SolidWorks software,which verifies the correctness of the constraint relation of manipulator terminal position and orientation parameters.Based on the constraint relation of the terminal position and orientation parameters of(3-SPR)+(3-RPS)redundant serial-parallel manipulator,given position parameters of the manipulator terminal,the position inverse kinematics model is established according to the geometrical constraint equations of the manipulator,and the optimal position inverse kinematics of(3-SPR)+(3-RPS)redundant serial-parallel manipulator is obtained by optimizing the performance index of manipulability.The kinematic velocity model of serial-parallel manipulator is established based on the velocity constraint relation and velocity coupling relation of the upper and lower parallel manipulator,and the velocity inverse kinematics of(3-SPR)+(3-RPS)redundant serial-parallel manipulator is optimized by gradient projection method.The position inverse kinematics of three manipulators are studied,comparing the solutions figured out by the Maple programming software with the data measured by the SolidWorks software,which verifies the correctness of the position inverse kinematics of three manipulators.