Construction and forward kinematics of a novel reconfigurable parallel mechanism

Abstract

In this paper, a kind of hybrid kinematics chain with variable constraints is constructed by using a 6R spatial bifurcated chain and 4-DOF serial limbs, by using them, a 3-DOF Reconfigurable Parallel Mechanisms (RPM) was constructed, which has four motion modes: 3T, 2T1R, 2R1T, and 3R motion modes. Using screw theory, the change of wrench system in the hybrid kinematics chain caused by the reconfiguration of the 6R bifurcated chain is analyzed, which affects the wrench system of the moving platform (MP), and thus causes the reconfiguration of the parallel mechanism (PM). The triangular pyramid fixed to the MP was found as auxiliary geometry and used to intuitively describe the constraint relationship between joint axes in limbs. The latter was used to establish a unified forward kinematics model of the RPM in four motion modes. The general forward kinematics solution procedure for this type of RPM is given. The overall Jacobian matrix was obtained by screw theory for singularity analysis. The condition number of the Jacobian matrix measures the degree to which the mechanism is close to the singular configuration. Based on the Monte Carlo simulation, point cloud images representing the workspace of RPM were obtained.