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中文摘要：
3自由度球面并联机构是重要的少自由度机构之一,各支链的构件为球面上的弧杆,其刚度计算十分复杂。基于此,采用计算杆件变形的方法,利用小变形叠加原理,推得机构动平台的角位移、球心点线位移与各支链两构件上力的关系。利用机构静力学分析的结果,即支链两构件上的力与动平台上的外力关系,建立机构动平台、球心点位移与外力的关系。进而得到机构的整体柔度、刚度矩阵。采用正交变换方法,得到机构的6个主刚度指标,最大、最小刚度及所在的方向。研究结果表明,机构的主刚度及主方向随着机构运动位姿的变化而变化,远离零点逐渐增大,其中3个主刚度（即扭转刚度）较大,另3个主刚度（线位移刚度）较小,两者差距巨大。研究成果为该机构的工程设计和应用提供了理论基础。
英文摘要：
The spherical parallel mechanism 3-RRR with 3-DOF rotations is one of the most important less-mobility mechanisms and it is very complicated and difficult to calculate the stiffness of 3-RRR mechanism where the bars in each branch are arc-shaped. Based on this, the angle displacement of mobile platform and line displacement of spherical center of the mechanism are derived by means of calculating deformation and superposition principle at small strain--the relationship between the displacements and forces acted on the members in each branch. And then the relationship between outer loads and the line displacement, the angle displacement of （spherical center） vertex of mobile platform is set up based on the result of static analysis--the relationship between external wrenches and forces acted on the members in each branch. Finally the flenibility, stiffness matrix are obtained. The 6 principal stiffness and directions of the mechanism are achieved by orthogonal transformation. The results show that the principal stiffness and directions are varied with the pose-position of the mechanism in which the principal stiffness is gradually enlarged away from the origin where 3 principal stiffness （torsional stiffness） are much greater and the others（line deformation stiffness） are smaller, the difference between the two parts are giant. This research is the important theoretical foundation and support for engineering design and application of 3-RRR mechanism in practice.
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