6R关节式机器人奇异性分析

Singularity analysis of 6R articulated robot

针对6个转动关节(6R)关节式机器人奇异构型的问题,采用代数理论法对机器人处于奇异位形时末端执行器的可行运动及其方向进行了研究。首先,以IRB 4600—40/2.55型工业机器人为研究对象,采用连杆速度递推法,构建了以腕部为参考点的机器人物体雅可比矩阵,经过求解得到了机器人全部奇异构型;然后,对机器人奇异构型的几何性质进行了分析,得到了含转动和移动关节的6自由度(6-DOF)开链机器人在2个转动副共轴、3个平面转动副轴线平行、4个转动副轴线共点时产生的运动学奇异;最后,基于可操作度椭球提出了机器人灵活度指标,运用MATLAB中的Robotics工具箱对机器人灵活度指标进行了可视化仿真分析。研究结果表明:仿真结果与理论结果一致,6R关节机器人存在3种奇异构型,以及3种奇异情况之间的组合奇异构型;该结果验证了机器人灵活性指标的合理性及前期奇异构型求解的正确性,可为后续对奇异构型的规避及其路径规划研究提供理论依据。

Aiming at the singular shape problem of the 6 revolute joints(6R)robot,the feasible motion and direction of the end effector were studied by algebraic theory when the robot was in the singular configuration.Firstly,the IRB 4600—40/2.55 industrial robot was taken as the research object,the Jacobian matrix of the robot object with the wrist as the reference point was constructed by using the link speed recursion method,and all the singular forms of the robot were obtained.Then,by analyzing the geometrical properties of the robot s odd shape,the kinematic singularity of the 6 degree of freedom(6-DOF)open chain robot with revolute and prismatic joints would occur when two rotational pairs were coaxial,three planar rotational pairs were parallel,and four rotational pairs were co-pointed.Finally,based on the operability ellipsoid,the robot flexibility index was proposed,and the Robotics toolbox in MATLAB was used to carry out a visual simulation analysis of the robot flexibility index.The results show that the simulation results are consistent with theoretical results,the 6R robot has three singular configurations and combinatorial singular configurations among three singular cases,which can verify the rationality of the proposed robot flexibility index and the correctness of the previous singular configuration,and provide a theoretical basis for the follow-up research on the avoidance of the singular configuration and its path planning.