3-RRR球面并联机器人逆向运动学分析

Inverse Kinematics Analysis of 3-RRR Spherical Parallel Robots

提出球面三自由度并联机器人构件之间运动学关系的算法。针对球面三自由度并联机器人所有关节均为转动关节且关节轴线汇交于一点的结构特点,借助球面上大圆弧与四元数代数的对应关系,将构件的位置用四元数表示出来。采用四元数表示的旋转变换来描述构件的相对运动,通过球面上大圆弧几何加法与四元数乘法之间的对应关系,得到关节轴线的方向余弦,从而建立了机器人约束方程,从中导出了机器人逆解方程。利用影响系数法,建立了机器人主动构件到末端构件上角锥的角速度和角加速度的传递关系。

An algorithm of kinematic relationship between components of spherical three DOF parallel robots was proposed in this study.In view of the structural characteristics that all joints of the spherical 3-DOF parallel robots are rotating and the joint axis intersects at one point,the position of the component was represented by quaternion with the help of the corresponding relationship between the large arc on the sphere and quaternion algebra.The rotation transformation of quaternion was used to describe the relative motion of the components.The direction cosine of the joint axis was obtained by the corresponding relationship between the geometric addition of the large arc on the sphere and the quaternion multiplication,thus the constraint equation of the robot was established and the inverse solution of the robot was derived.By using the influence coefficient method,the transfer relationship between the angular velocity and the angular acceleration of the corner cone from the active component to the end component of the robot was-built.