CGA Approach to Kinematic Analysis of a 2-DoF Parallel Positioning Mechanism

This paper proposes CGA based approach to determine motions and constraints, analyze mobility, identify singularity of parallel mechanisms, which is perfectly demonstrated by taking 3-RSR&SS parallel positioning mechanism as an example. By introducing CGA, which combining elements of geometry and algebra, the motions and constraints are expressed as simple formulas and their relations are calculated by means of outer product with clear physical meaning, these lead to the motions and constraints are determined in a visual, concise and efficient way, and the number and type of DoF and accessible motions are obtained readily. The inverse and forward position solutions are obtained easily utilizing special geometric relations of 3-RSR&SS parallel positioning mechanism, which are proven by calculating relations among point, line and plane in virtue of CGA operation rules. Two indices of singularity are defined to identify singular configurations of 3-RSR&SS parallel positioning mechanism in the light of the shuffle and outer products. The work of this paper lay a solid theoretical and technical foundation for the prototype design and manufacture of 3-RSR&SS parallel positioning mechanism.