Kinematic Modelling and Virtual-Prototype Analysis of a Modular 3-UPU Hybrid Serial–Parallel Manipulator

Kinematic modelling is essential for evaluating hybrid manipulators that require both stiffness and spatial adaptability. This paper proposes a modular 3-UPU (universal joint–prismatic joint–universal joint) hybrid serial–parallel manipulator for confined-space tool operations, with offshore jacket tubular-joint maintenance used as a representative application background. The mechanism connects several 3-UPU parallel units in series; each unit provides two rotational degrees of freedom and one translational degree of freedom for local steering and axial adjustment. Screw theory and the modified Grübler–Kutzbach formula are used to analyze module mobility, and a geometric kinematic model is established to map module pose to actuator displacement. Actuator commands are generated for cylindrical and planar surface-following trajectories and verified using a CAD-based Simscape Multibody virtual prototype. The maximum model-to-model relative position discrepancies are 1.07% and 1.45%, showing consistency between the analytical actuation model and the rigid-body virtual prototype under the considered conditions.