Kinematic Analysis And Optimization Of A Six-dimensional Stewart Platform

Stewart platform, invented in 1965, is a typical kind of parallel robot with six degrees of freedom, including three translational degrees of freedom and three rotational ones. Kinematic optimization of a Stewart platform was carried out in this paper and the optimal parameters were obtained. Firstly, basic theory for kinematics of industrial robots was presented. Kinematic analysis of a Stewart platform was performed, including derivation of forward kinematics and inverse kinematics as well as analysis of Jacobian matrix, which laid the foundation of kinematic optimization. This paper accomplished the following research contents:(1) A six dimensional desired workspace of the Stewart platform, including three translational DOFs and three rotational ones, was defined and mathematically interpreted.(2) A new concept, called relative physical size, was defined. It was defined as the ratio of the physical size of the Stewart platform and the volume of the desired workspace. This new concept effectively reflects the relationship between the size of the desired workspace and that of the Stewart platform.(3) Condition number was chosen as a dexterity index. The cost function was defined as linear combination of two contradictory optimization criteria, the dexterity index and relative physical size. Different weighting factors can be assigned in different applications and corresponding optimal design parameters were obtained.(4) Relationships between changes of the design parameters and those of the two performance indices were obtained.(5) A numerical example was utilized to illustrate the presented methodology with MATLAB.