A Quotient Manifold Identification Method Based on the Chasles Decomposition Models for the Quotient Mechanism Available to Purchase

Kinematic synthesis design typically relies on predefined motion types, but traditional mechanism synthesis theories are primarily applied at the theoretical level, limiting their practical application in engineering. Therefore, a novel rigid-body motion identification method is developed to identify the quotient manifold $G/H$ (in the coordinated motion of two mechanism modules used to realize the left-and-right hand system of the Lie group $G$⁠, $G/H$ is defined by one of the modules realizing the complement of the Lie subgroup H in $G$⁠). First, based on the synthesis of the quotient mechanism $MG/H$⁠, a Lie subgroup motion generator synthesis theorem is introduced. Second, based on the finite screw displacement motion theory, Chasles decomposition models for $MG/H$ are developed. Finally, utilizing the transversality conditions and normalizer subgroups, an effective $G/H$ identification method is proposed, where the $SO(3)$ submanifold is identified first, followed by the preselection of the product of exponential (POE) cross-sectional submanifold containing the $T(3)$ submanifold, using the hierarchical relationship of $G/H$⁠. This method successfully relates rigid-body motion to $G/H$⁠, advancing the development of mechanism synthesis theory in engineering practice.