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

Abstract

Abstract. A planar three-revolute (3R) serial chain is an important part of many mechanisms. The classical approach in motion generation of a planar 3R serial chain is to construct closed-loop equations based on complex numbers, which yields a large-scale polynomial system. In this study, a new approach of planar 3R serial chain motion generation by establishing the relative kinematics model based on conformal geometric algebra (CGA) is proposed. The simpler design equations are obtained, which can be used to design a planar 3R serial chain that can accurately achieve the N poses. In the numerical examples, the number of different poses is used to verify the correctness and efficiency of the proposed method by using polyhedral homotopy continuation. The results indicate that the design equations obtained via CGA are more concise for improving the solving efficiency compared with the previous method. Finally, a geared five-bar mechanism with a seven-pose motion generation example is considered.

Survey of New Applications of Geometric Algebra

“…Jesús Medrano-Hermosilo et al 95 for 6-DOF serial robot's forward kinematics, or Edgar Macias-Garcia et al 96 solving the inverse position kinematics for 𝑛-degrees-of-freedom kinematic chains with revolving joints and, similarly, Lechuga-Gutierrez et al 97 present a set of generalized iterative algorithms for these mechanisms. A planar three-revolute (3R) serial chain motion generation by establishing the relative kinematics model based on CGA is introduced in Lei Wang et al 98 . Finally, a new coordinate-invariant geometric constraint equation for 3-RPR planar parallel mechanisms is elaborated by Ganmin Zhu et al in 99 .…”