• First solution to the inverse kinematics of 2(3RPS) and 2(3SPR) serial-parallel manipulators, resolving a long-standing challenge.
• Decouples the coupling relationships of middle platform kinematic parameters layer by layer, enabling analytical solution via Sylvester’s elimination method.
• Reveals the essence of inverse kinematics for general (3-DOF)+(3-DOF) 6-DOF serial-parallel manipulators, providing a systematic solution framework.
• Enhances the practical applicability of these manipulators in robotics and mechanical systems by enabling precise position control.