Kinematics And Character Of Mechanisms Based On Geometric Algebra

The mathematic model of robot research is complex and various. The purpose of this paper is to make the analysis and calculation of kinematics, dynamics and work space etc. more compact, hence the control of robot more fast and accurate. Based on geometric algebra, the analysis of kinematics and singularity of mechanisms is made. In addition, the continuous motion judgment criterion of constrained rigid body is presented. by virtual coefficient.The screw motion of rigid body in 3dimensional space is presented by the special 4 dimensional geometric algebra-motor algebra. Based on the motion models of point, line and plane, the analysis of forward and backward kinematics of serial robot manipulator is presented.The backward kinematics model and analysis of SCARA robot and Steward parallel mechanism is presented by conformal geometric algebra.The singularity configuration analysis of 3-RPS parallel mechanism is represented in geometric algebra according to Merlet's singularity categories. The singular condition of deficient parallel robots is derived by geometric algebraic representation. Moreover, several singularity configurations of 3-RPS parallel mechanism are given.At last, the motion character of mechanism is analyzed by virtual coefficient, and the criterion for the instantaneous and continuous motion judgment is presented.This paper is useful for finding a unified mathematical language in mechanism analysis, hence reducing the nonlinearity and enhancing the geometric intuition.