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

Abstract

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.