基于旋量理论的上肢康复机器人Kane动力学方程

Kane Dynamic Equations Based on Screw Theory for Upper Limb Rehabilitation Robot

引入基于旋量理论的运动旋量、力旋量及偏速度旋量等概念,推导得出五自由度上肢康复机器人的Kane动力学方程.结果表明,采用旋量理论分析机器人更加简明有效,比建立局部坐标系的D-H法更简易.Kane方程的求解只需加、减、乘运算,与拉格朗日、牛顿-欧拉等非线性动力学方程相比,计算效率更高,更易于实现实时控制.通过仿真研究了机器人各关节从初始位形到准备位形的角位移、角速度、角加速度以及驱动力矩,验证了基于旋量理论的Kane方程的正确性和有效性.

Based on the screw theory, the concepts of motion screw, force screw and partial velocity screw were introduced. Then Kane dynamic equations were derived for an upper limb rehabilitation robot with 5 DOF. Simulation results show that dynamics analysis for the robot based on the screw theory is more concise and explicit than that based on the D-H method in which local coordinate systems are used. The solution of Kane equations only involves addition, subtraction and multiplication, so the method has higher calculation efficiency than nonlinear Lagrange and Newton-Euler dynamic equations and is easier to implement real time control. The robotic joint curves of angular displacements, angular velocities, angular accelerations were studied by simulation from initial configuration to ready configuration. The conclusion validates the correctness and effectiveness of Kane equations based on the screw theory.