Application of Screw Theory to the Extended Congruence Transformation for Serial Manipulators

• Main Author: 陳啟修
• Other Authors: Huang,Chintien
• Format: Others
• Language: zh-TW
• Published: 2000
• Online Access: http://ndltd.ncl.edu.tw/handle/38731441241219784617

碩士 === 國立成功大學 === 機械工程學系 === 88 === The end-effectors of serial manipulators are likely to deviate from their goal positions due to inertia forces and external loads. The position errors aggravate in high-speed or heavy-duty applications. Many control algorithms have been developed to cope with position and velocity deviations of the end-effectors. Among them is the stiffness control algorithm, which relies on the congruence transformation of the stiffness matrices. The congruence transformation relates the joint stiffness matrix and the Cartesian stiffness matrix of a serial manipulator. Although the congruence transformation has been developed for about two decades, the stiffness control has not been very precise. Kao (1999) developed the extended congruence transformation to result in a satisfactory performance of the stiffness control. The main idea is to introduce an extra matrix called geometric stiffness matrix. This thesis aims to provide geometrical insights to the extended congruence transformation by using screw theory. This thesis demonstrates that the geometric stiffness matrix is related to the changes of joint screw coordinates due to small joint displacements. And the geometric stiffness matrix can thus be easily obtained without differentiating the Jacobian matrix of the manipulator. Planar 3R manipulators are studied in detail to illustrate the concepts; furthermore, the concepts and equations given in this thesis are readily applicable to three-dimensional manipulators.