Abstract:

By the dismantle-bar method, the statics equilibrium equations of the mechanism were set up, considering the elasticity of member and then utilizing the micro-deformation and superposition principle, the deformation equations of compatibility were derived and then the statics analysis of the spherical parallel mechanism UP+R with 2-DOF was fulfilled. As a numerical example, some figures which showed the relationship between input torque, each force on each member and the position and posture of the mechanism were drawn under three kinds of external loads, respectively. The results show that, under the external force only, the input torque of the mechanism is vanishing identically and the variation of forces acting on members with the position and orientation of the mechanism in whole space is gentler slope. Under the external torque only, the variations of the input torques and the forces with the position and orientation of the mechanism are associated with the characteristic of the mechanism. The two portions of force jointly produced by external force and external torque are independent and detachable. The research provides the theoretical basis of statics for structure design and application of the mechanism in engineering．

Key words: spherical parallel mechanism, overconstraint, statics, deformation equation of compatibility

摘要：

采用拆杆法建立了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了机构的变形协调补充方程，进而完成了二自由度球面并联机构UP+R的静力学分析。通过计算，得到在三种载荷下构件上各力、输入转矩与机构位姿的关系图。结果表明，仅在外力作用下，机构的输入力矩恒等于零,构件上的力随机构位姿的变化比较平缓，仅在外力矩作用下，机构的输入力矩、构件上的力随着机构位姿的变化与机构的特性相关。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。研究结果为该机构在工程中的结构设计与应用提供了静力学理论基础和依据。

关键词: 球面并联机构, 过约束, 静力学, 变形协调方程