中文摘要：

根据Kutzbach-Grübler修正公式分析了球面3-RRR并联机构的自由度个数以及性质,采用哈密顿＂四元数＂对关节矢量进行描述并建立了逆运动学数学模型,找出了动平台运动时连杆之间、连杆与电机主轴相互之间的碰撞干涉条件。根据运动学逆解以及碰撞干涉条件,基于Mathematica软件完成了可达工作空间的分析,绘制了球面并联机构的工作空间形状,给出了工作空间的极限位置。以工作空间的最大化为目标对并联机构进行了结构优化设计,使动平台实现了完整的球面工作空间。

英文摘要：

The degree of freedom of 3-RRR spherical parallel mechanism is calculated according to corrected Kutzbach- Griibler equation.The inverse kinematics equation is established by using Hamilton quaternion to describe the vectors of joint. The condition when collision and interference of linkages and axes of drive motors happens is found out. The reachable workspace analysis is finished according to the inverse kinematics equation and the condition of collision and interference with Mathematicca The shape of workspace is plotted and the extreme position of workspace is figured out. The parallel mechanism obtains the maximum workspace by structure optimization The platform obtains the complete spherical workspace.