中文摘要：

采用传统的拆杆法建立机构的静力学平衡方程，考虑构件弹性，利用小变形叠加原理建立机构的变形协调补充方程，进而完成3自由度球面并联机构的静力学分析。求得包括机构输入与输出载荷关系的每个构件上的全部力、力矩。通过计算，得到在三种外载荷下构件上的全部（各）力、输入转矩与机构运动位姿的关系图。结果表明，当作用在机构的外力（仅）F通过球心时，机构的输入力矩恒等于零，而构件上的力在全空间内随着机构位姿的变化比较平缓，机构等价一般结构架体而与机构的特性无关。仅在外力矩M作用下，机构的输入力矩、构件上的作用力随着机构位姿的变化与机构的特性相关（与雅可比矩阵的奇异性一致），力与力矩在构件上所产生的两部分力是独立的，并可以分离。研究为该机构在工程中的结构设计与应用提供静力学理论基础和依据。

英文摘要：

By the traditional dismantle-bar method, the static equilibrium equations of the mechanism are set up, considering the elasticity of member and then utilizing the micro-deformation and superposition principle, the deformation equations of compatibility are derived and then the static analysis of the spherical parallel mechanism with 3-DOF is fulfilled. All torques and forces acting on each member are obtained, including the relationship between input torques and output load. As a numerical example, some figures which show the relationship between input torque, each force on each member and the position and posture of the mechanism are drawn under three kinds of external loads, respectively. The results show that, when the external force （only） F acting on the mechanism overpasses the spherical center, the input torque of the mechanism is identically vanishing and the variation of forces acting on members with the position and orientation of the mechanism in whole space is gentler slope, meanwhile, the mechanism has been equivalent to a common frame-structure and the forces are not related to the properties of the mechanism. Under the external torque M only, the variations of the input torques and the forces with the position and orientation of the mechanism are associated with the characteristic （coincided with singularity of the Jacobian matrix） of the mechanism. The two portions of force jointly produced by F and M are independent and detachable. The research provides the theoretical basis of statics for structure design and application of the mechanism in engineering.