Design and Modeling of a Topology-Morphing Spherical Mechanism with Mobility and Compliance Switching

Remote center-of-motion (RCM) mechanisms are widely used in robotic palms and wrists, orientation platforms, and medical devices. A spherical mechanism provides a compact RCM realization by enforcing intersection of all joint axes at a common center. This paper introduces a topology-morphing 7R spherical mechanism that switches from a single-loop configuration with compliant motion into a double-loop spherical scissors configuration with substantially increased stiffness. The architecture is modeled using a graph-based description in which the mobility is expressed as a function of the numbers of links, holes, and tails. A unified kinematic and static formulation is then derived for both topology modes using a consistent joint coordinate set and Jacobian structure. Reconfiguration conditions are established from the pin-hole coincidence constraints, and an algorithm is provided to compute admissible reconfiguration configurations. The reachable orientation workspace and manipulability are evaluated by sampling on the unit sphere. Under identical end-effector loading (0-2N), rigid-body simulation predicts an equivalent stiffness increase from 0.3N/mm to 571N/mm. Prototype experiments further confirm compliance to rigid switching with stiffness increasing from 0.106N/mm to 0.525N/mm. These results indicate that topology-morphing on the sphere can provide a compact mechanism-level strategy for switching mobility and effective stiffness under the same actuation scheme.