COMPLETE JACOBIAN MATRIX OF A CLASS OF INCOMPLETELY SYMMETRICAL PARALLEL

MECHANISMS WITH 4-DOF

LI Yonggang  SONG Yimin  FENG Zhiyou  ZHANG Ce

(School of Mechanical Engineering, Tianjin University, Tianjin 300072 )

Abstract: The complete Jacobian matrix of a lower-mobility parallel mechanism is a six by six matrix that consists of the actuation sub-matrix and the constraint sub-matrix. As the algebraic feature of the former one cannot account for the related constraint characteristics, modeling complete six by six Jacobian matrix becomes necessary in the kinematic analysis and optimal design of geometric parameters of this kind of parallel mechanisms. A method for deducing the complete Jacobian matrix of an incompletely symmetrical lower-mobility parallel mechanism is illustrated by taking 2RPS-2UPS as an example based on the theory of reciprocal screw. Firstly, the systems of twists and reciprocal screws of the constraint limbs are established based on the screw theory, then the constraint submatrix is obtained through the orthogonal product. Secondly, by locking active joints of each limb, the system of additional reciprocal screws of both constraint and unconstraint limbs is established, then the actuation sub-matrix is also obtained through the orthogonal product. By integrating these two sub-matrices properly, the complete Jacobian matrix of an incompletely symmetrical lower-mobility parallel mechanism can be finally set up. In the end, the singular conditions of 2RPS-2UPS parallel mechanism are analyzed by investigating the ranks of the Jacobian matrices.

Key words: Parallel mechanism Lower-mobility Incompletely symmetrical Jacobian matrix Screw theory

CLC No: TH112.1

国家自然科学基金(50535010, 50675151)和教育部高校博士点基金(20060056018)资助项目. Received 20060604, received in revised form 20061216