串联机构运动分析的D-H四元数变换方法

D-H Quaternion Transformation Method for Kinematics Analysis of Serial Mechanisms

提出了串联机构运动分析的Denavit-Hartenberg(D-H)四元数变换方法.给出了点的映射的四元数描述方法和相邻连杆间变换的D-H四元数变换方法,建立了D-H四元数变换的矩阵演算方法,构造出了机器人学中经典的D-H齐次变换矩阵,证明了D-H四元数变换方法与D-H齐次变换矩阵方法的运动分析结果是一致的,从而从理论上证明了所提出的D-H四元数变换方法的正确性.在相邻连杆变换的D-H四元数变换公式基础上进一步推广,提出了任意个连杆的串联机构运动分析的D-H四元数变换方法.以PUMA机器人的运动分析为实例,采用D-H四元数变换方法进行运动分析,并验证了该方法的正确性和有效性.D-H四元数变换方法是串联机构运动分析的一种新方法,具有几何意义明确和计算简单的优点.

A Denavit-Hartenberg （D-H） quaternion transformation method for kinematics analysis of serial mechanisms was presented. Firstly, the point mapping is described with quaternion. Then a D-H quaternion transformations method for motion transformation between adjacent linkages was proposed. Moreover, the matrix operation method of D-H quaternion transformations was illustrated to construct the classical D-H homogeneous transformation matrix in robotics, which can be theoretically proven that the pro- posed D-H quaternion transformation method is correct. Based on the above D-H quaternion transformation formula of motion transformation between adjacent linkages, the D-H quaternion transformation method for kinematics analysis of serial mechanisms with any number of linkages was further proposed. By analyzing the kinematics of PUMA robot, the effectiveness and correctness of the proposed method was vali- dated as well. The D-H quaternion transformation method has clear geometric meaning and the computation process is simple. The method is proved effective for kinematics analysis of serial mechanisms.