Singularity and path-planning with the working mode conversion of a 3-DOF 3-RRR planar parallel manipulator

This paper presents singularity analysis and path planning with the working mode conversion of a three-degrees-of-freedom (3-DOF) 3-RRR planar parallel manipulator (PPM). Firstly, the kinematics constraint equation of the manipulator is established, the velocity Jacobian matrix is obtained by differentiating the equation with respect to time, and comparisons of singular characteristics of eight working modes are made. Secondly, an algorithm is proposed for singularity-free path planning with the working mode conversion of the 3-RRR PPM. The path maintains a minimum distance with respect to the forward singular curve at all points, which guarantees the controllability of the manipulator everywhere along the path. Finally, three experiments are carried out: positioning close to the forward singular configuration, passing through the singular curve, and path-planning with working mode conversion. Experimental results demonstrate that the proposed approach for switching working modes is feasible and that the combination of workspaces of eight working modes is valid for expanding the workspace of the manipulator.