Type synthesis of a class of parallel RCM manipulators based on concentric spherical surfaces geometric model

• A concentric spherical surfaces geometric model for RCM motion is presented. • A class of spatial parallel RCM manipulators is synthesized. • A universal error model is presented to analyze the accuracy of the manipulator. • The presented PM-RCM has a flat form feature, simple and analytical kinematics. Leveraging the intuitiveness of a geometric model to describe motion, this study proposed a design method for a novel class of spatial parallel manipulators with remote center of motion (RCM) based on a concentric spherical surfaces geometric model. First, the topological structures of the parallel RCM manipulator are constructed by integrating the characteristics of the single-loop closed chain (SLCC), multi-degree of freedom (DOF) drive unit (DU), and RCM motion. Subsequently, a geometric model based on concentric spherical surfaces is developed to reveal the principle of generating RCM motion. Building on the concentric spherical geometric model, the general topological arrangements of the parallel RCM manipulators are proposed, while the key constraint conditions are determined. Then, a class of parallel RCM manipulators is systematically synthesized based on the Lie group. Based on the structural characteristics of this class of parallel RCM manipulators, a generalized assembly error model is built to analyze the impact of assembly errors on mechanism accuracy. Finally, the application and analysis of a parallel RCM manipulator are discussed.