Abstract:

The 3-RRS mechanism is one of the latest architectures of the spherical parallel mechanism 3-RRR families with 3 DOF and it will be used as a prototype mechanism of bionic shoulder joints of humanoid robot. It is quite complex to calculate the stiffness of 3-RRS mechanism which the bar in each branch is arc-shaped. The angle displacement of mobile platform and line displacement of spherical center of the mechanism were derived by mean of calculation deformation and superposition principle at small strain; the relationships between outer loads and the displacements of (spherical center) vertex of mobile platform were set up based on the results of static analysis-the relationship between external wrenches and forces acted on the members in each branch. Flexibility，stiffness matrix were finally obtained herein. The 6 principal stiffness and principal directions of the mechanism was achieved by orthogonal transformation. It provides the important theoretical foundation and support for engineering design and application of 3-RRS mechanism in practice.

Key words: spherical parallel mechanism;static stiffness;orthogonal transformation;line displacement;angle displacement

摘要：

3-RRS机构是三自由度球面并联机构3-RRR的新构型之一，可作为人形机器人仿生肩关节的原型机构，因各支链的构件为球面上的曲杆，其刚度计算十分复杂。采用（杆件）变形法与小变形叠加原理，推得机构动平台的角位移、球心点线位移；利用机构静力学计算的结果，即各支链两构件上的力与动平台上外载荷的关系，建立了机构动平台上（球心点的）的位移与外载荷关系，进而求得机构的整体柔度、刚度矩阵；采用正交变换使刚度矩阵对角化，得到机构的6个主刚度指标及其所在的方向。研究结果为该机构的工程设计和应用提供了理论基础。

关键词: 球面并联机构, 静刚度, 正交变换, 线位移, 角位移