Stiffness Analysis of Spherical Parallel Mechanism UP+R with 2-DOF

As one of the typical less-mobility parallel mechanisms, the spherical parallel mechanism Up.s with two degrees of freedom （2-DOF） possess high order overconstraints, and the calculation of its stiffness is partly different with general parallel mechanisms owing to the bars in each branch are assumed to be arc-shaped. By means of small deformation superposition principle, the relationship between the angle displacement and line displacement of moving platform and the forces acted on the branches were derived out. Based on the results of static analysis, the relationship between the applied force, the line displacement and the angle displacement of the mechanism was set up. And then the stiffness matrix was obtained. The six principal stiffness of the mechanism and the corresponding directions were achieved by the orthogonal transformation. The numerical calculation was performed and the results showed that the principal stiffness and directions are varied with the pose-position of the mechanism, and the principal stiffness is gradually enlarged when it is far away from the anigin. In addition, the torsion stiffness is much greater and the line deformation stiffness is smaller, the difference between the two parts is huge. The research content of this paper supplies the theoretical foundation for the further engineering design and application of the spherical parallel mechanism.

Stiffness Analysis of Spherical Parallel Mechanism Up+R with 2-DOF