A Screw Theory Approach for Instantaneous Kinematic Analysis of Parallel-Serial Manipulators

The paper presents an approach to perform an instantaneous kinematic analysis of parallel-serial (hybrid) manipulators using screw theory. In this study, we focus on non-kinematically redundant manipulators that include a single parallel mechanism. The proposed systematic procedure allows deriving Jacobian matrices for such manipulators, which provide mathematical relations between the end-effector velocities and speeds in the actuated joints. A generalized structure of the obtained matrices also reflects the constrained motions of the end-effector and the parallel mechanism. To illustrate the developed techniques, we consider three examples where we analyze three well-known parallel-serial manipulators with six, five, and four degrees-of-freedom. Following the proposed method, we determine Jacobian matrices for each manipulator. Next, we apply the presented approach for velocity analysis of a novel parallel-serial manipulator with five degrees-of-freedom. Numerical simulations validate the proposed theoretical techniques. The suggested approach represents the basis for subsequent singularity and performance analysis, and it can be adapted to hybrid manipulators with other architectures.