Kinematic and dynamic analysis of a double parallel manipulator for enlarging workspace and avoiding singularities

For enlarging workspace and avoiding singularities, a double parallel manipulator has been designed by combining two parallel mechanisms with a central axis. The motion of the device is decoupled and constrained by the central axis. This leads to simplicity in geometric constraints but needs a novel strategy for the mechanism analysis. Based on the geometric constraints, the paper develops the formulation for inverse/forward kinematics and Jacobian to be implemented in real time position and velocity controls. These are used for propeller grinding to measure the surface of a casting blade and to grind the removal depth. A dynamic formulation for the parallel mechanism composed of one passive and n-active link trains is derived from motor algebra and a virtual coefficient. The formulation can compute the forces and moments acting at the passive joints as well as the active ones. Workspace and singularities are also analyzed to prove the advantage of the device