Unified motion synthesis of spatial seven-bar platform mechanisms and planar-four bar mechanisms

A unified motion generation algorithm that combines Spatial and Planar mechanism synthesis has been a hard problem in kinematics. In this paper, we present a new method to generate planar RRRR mechanisms and spatial 5-SS mechanisms using a unified algorithm. For a generalized spatial pose problem where all the poses fall on a plane, we show that there exist 1-∞ plane constraint solutions and 3-∞ planar-spherical solution dyads. We also show that for a spatial five pose problem where all poses lie on a plane, there exists a 2-∞ solution space of spherical and planar constraints. This multiplicity of solutions are intelligently constrained to find up to four circle constraints representing planar four-bar mechanism. Finally, examples are presented testing the proposed algorithm and verified using results from past publications.