Inverse kinematics analysis of 6 – DOF Stewart platform based on homogeneous coordinate transformation

Abstract

ABSTRACTAt present, the mainstream method is directly reduced the platform of the six series branch to six drive rods for analysis and modeling refers to inverse kinematic of the parallel six-degree-of-freedom (6-DOF) Stewart platform, and ignored the influence of the joints that excluded the driving leg on the Stewart platform, resulted in the mathematical model lack of accuracy, there is error in the actual platform. In this paper, the mathematical analysis method of inverse kinematic of the parallel six-degree-of-freedom Stewart platform based on homogeneous coordinate transformation is studied. The relationship of spatial coordinate system is worked up by using the Denavit-Hartenberg (DH) method on the upper and lower platforms and each branch of parallel 6-DOF Stewart platform. Considering the influence among the series branch joints, the transfer relationship is established by using the three-dimensional vector and the homogeneous coordinate transformation matrix between the adjacent joint coordinate systems. The length of the branch drive lever is treated as a variable, the vector equation of the platform system is deduced based on the geometric relation of the parallel 6–DOF Stewart platform. The application of this method in the kinematic inverse solution of parallel 6–DOF Stewart platform is given, verified the correctness of this method. Thinks to the data validation of the actual Stewart platform, it is proved that the proposed method can be applied to the kinematic inverse of parallel 6–DOF Stewart platform that composed of series branch.