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. A planar three-revolute (3R) serial chain is an importantpart of many mechanisms. The classical approach in motion generation of aplanar 3R serial chain is to construct closed-loop equations based oncomplex numbers, which yields a large-scale polynomial system. In thisstudy, a new approach of planar 3R serial chain motion generation byestablishing the relative kinematics model based on conformal geometricalgebra (CGA) is proposed. The simpler design equations are obtained, whichcan be used to design a planar 3R serial chain that can accurately achievethe N poses. In the numerical examples, the number of different poses is used to verify the correctness and efficiency of the proposed method byusing polyhedral homotopy continuation. The results indicate that the designequations obtained via CGA are more concise for improving the solving efficiency compared with the previous method. Finally, a geared five-barmechanism with a seven-pose motion generation example is considered.

Motion generation of a planar 3R serial chain based on conformal geometric algebra with applications to planar linkages