A novel Schönflies-motion generator parallel manipulator with decoupled rotational freedom

This paper introduces a four-legged decoupled Schonflies-motion generator parallel manipulator, free of passive limbs, provided with three linear actuators and one rotary actuator. The displacement analysis problem leads to closed-form solutions, thus avoiding the application of numerical methods for their solution, an unusual feature for most parallel manipulators. Subsequently, the theory of screws allows for solving the velocity, acceleration, and jerk analyses. Canceling the passive joint rates of the limbs is an indisputable advantage of the reciprocal-screw algebra. Moreover, upon the velocity analysis, the singularity analysis of the parallel manipulator is carried out by investigating the nature of the Jacobian matrices of the parallel manipulator. Then, we conclude that the robot at hand is free of type I and III singularities. Numerical examples enhance the correctness of the kinematic analysis method employed in the contribution. As far as the authors are aware, the topology of the parallel manipulator investigated here is original.