A study of velocity kinematics for hybrid manipulators with parallel-series configurations

The velocity kinematics of a hybrid robotic mechanism comprising both serial and parallel closed chains is studied. The hybrid manipulator has six degrees of freedom, which features a three-degree-of-freedom in-series actuated module mounted on the moving plate of a three-degree-of-freedom in-parallel actuated manipulator. Methods of solution for forward (direct) and inverse problems are established for each of the serial-chain and the parallel-chain components. Constant compatibility conditions necessary for arriving at meaningful velocity solutions are identified. A joint rate solution for the combined hybrid system is formulated and its validity demonstrated. The method is based on a velocity decomposition scheme that in effect decouples the interplay between the serial and the parallel structures. The condition of geometric singularity is addressed