Formulation of unified Jacobian for serial-parallel manipulators

• The unified form of the Jacobian for 6-DOF serial-parallel manipulators is derived.
• The inverse kinematics of a novel (3-RPS)+(3-SPS/UP) serial-parallel manipulator is derived in closed form.
• The Jacobian of the (3-RPS)+(3-SPS/UP) serial-parallel manipulator is established based on the unified Jacobian model.

This paper presents a general approach for Jacobian analysis of serial-parallel manipulators (S-PMs) formed by two lower mobility parallel manipulators (PMs) connected in serials. Based on the kinematic relation, coupling and constraint properties of each PM, the unified forward and inverse Jacobian matrices for S-PMs are derived in explicit form. It is shown that the Jacobian matrices of S-PMs have unified forms, which include the complete information of each PM. A (3-RPS)+(3-SPS/UP) S-PM is used as an example to demonstrate the proposed approach. The established model is applicable for S-PMs with various architectures.