基于螺旋理论的6R串联工业机器人奇异位形分析

摘要

Aiming at the 6-DOF series robot, the singularity in the working space was analysed. Based on the screw theory, the kinematic modeling of the robot is carried out by using the screw product of exponen-tials ( POE) method to obtain the positive kinematics equation, and the velocity Jacobian matrix is deduced based on the screw product of exponentials method. According to the condition that the robot is in the singu-larity, the determinant of the Jacobian matrix is solved, and all the cases when the robot is in the singularity are obtained, and the configurations of the robot when the singularity occurs are given. On this basis, the singularity of the cutting robot is simulated using MATLAB based on the dexterity index:Operability, Jaco-bian condition and minimum singular value, the simulation results show that the robot is in singularity in three cases, the simulation results are in agreement with the analytical results, the correctness of this method is verified.%针对6自由度串联工业机器人,对其工作空间中的奇异位形进行了分析.基于旋量理论,运用旋量指数积(POE)方法对机器人进行运动学建模,得到正运动学方程,并基于旋量指数积法对速度雅克比矩阵进行了推导.根据机器人处于奇异位形时的条件,对雅克比矩阵的行列式进行求解,从而得到机器人处于奇异位形时的所有情况,并给出了发生奇异时的机器人的构型.在此基础上,基于可操作度、雅克比条件数及最小奇异值等灵巧度指标使用MATLAB对机器人的奇异位形进行了仿真,仿真结果表明该机器人在3种情况下处于奇异位形,与分析结果一致,验证了文中方法的正确性.