Analysis of the Velocity of Two-Layer Generalized Parallel Manipulators

This paper presents a methodology for analyzing the input-output velocity equations of two-layer generalized parallel manipulators that have interconnected coupling sub-chains. These manipulators have velocity equations that are influenced by additional coupling sub-chains. For planar generalized parallel manipulators, constraint equations and loop closure are used to derive velocity matrices. Velocity matrices for spatial mechanisms, including spherical mechanisms, are derived from velocity loop equations. Using screw theory, the velocities of passive joints are eliminated to obtain the overall velocity matrix of inputs and outputs. For planar mechanisms, iterative Jacobian calculations are conducted, while constraint wrenches are modified for spatial mechanisms during Jacobian matrix derivation. Finally, the velocities of a series of generalized parallel manipulators are enumerated to demonstrate the feasibility and effectiveness of this proposed approach.