Constraint Stiffness Construction and Decomposition of a SPS Orthogonal Parallel Mechanism

This paper investigates both stiffness analysis and synthesis problems using a physical prototype of one SPS orthogonal parallel mechanism. This parallel mechanism is supported with line-type constraint limbs. In the stiffness analysis, a reciprocal relationship between motions and wrenches is used to design layouts of constraint limbs and construct the corresponding stiffness matrix. In the stiffness synthesis, the developed stiffness matrix is decomposed to obtain configurations of constraint limbs based on existing synthesis algorithms, including direct-recursion and matrix-partition approaches. It is revealed the line-vector based matrix-partition approach can establish an one-to-one correspondence between synthesized results and constraint limbs of the parallel mechanism. Subsequently both types of synthesis approaches are applied to decomposing the developed constraint stiffness matrix. The comparison results suggest the modified matrix-partition approach can obtain decomposed constraint limbs exactly the same as those used to construct the stiffness matrix.