四自由度机械手臂运动学分析及雅可比矩阵求解

Kinematics Analysis and the Jacobian Matrix Solution for a Four Degree of Freedom (4-DOF) Mechanical Arm

为了降低机械手臂正、逆运动学方程求解过程的复杂度,准确快捷求出逆运动学方程封闭的解析解,使控制更加精确,根据机器人四自由度机械手臂分析理论,提出一种优化的建立坐标系方法,建立了基于该坐标系的四自由度机械手臂正、逆运动学方程,给出了机器人各运动构件与末端执行器在空间的位置、姿态间的关系,使机器人在执行任务时能够按照预定的位置序列运动。并方便地求解出其雅可比矩阵,为实现机械手臂末端在笛卡尔空间的速度控制程序设计提供了理论依据。

In order to reduce the complexity of kinematics and inverse kinematics equation solving process, improve the accuracy of control, and calculate the inverse kinematics equation＇s analytical solution fast and precisely, an optimal method of setting the coordinate system has been put forward according to the theory of a robot＇s 4-DOF mechanical ann. The kinematics and inverse kinematics equations of the 4-DOF mechanical ann were established based on this coordinate system. The positions of its moving elements and end-effectors with their relationship were presented; these made the robot move in accordance with a scheduled program. Finally, the Jacobian matrix was solved, providing theoretical basis for realizing the mechanical ann＇s program design of velocity control in the Cartesian space.