Design and Modeling of a Compliant Underactuated 3-DOF CMC Joint Using a Parametric Spiral Spring

Abstract

Replicating the kinematic complexity of the human thumb carpometacarpal (CMC) joint in robotic hands requires a careful balance between dexterity and mechanical simplicity. Most existing designs approximate the CMC joint with only two degrees of freedom (DOFs), which limits thumb opposition and grasp stability. This paper presents a compliant underactuated CMC joint that enables three rotational DOFs motion, specifically flexion, adduction, and passive internal rotation, using only two independently actuated tendons. A parametric spiral spring is integrated along the internal rotation axis to introduce controllable compliance, while a spatial V-groove tendon routing scheme generates motion coupling between the active and passive DOFs. Unlike rigid kinematic designs, the proposed compliant architecture allows the thumb to passively reorient upon object contact, thereby enlarging the functional workspace and enhancing opposition without requiring complex control strategies. A static model based on the principle of virtual work is developed to characterize the equilibrium behavior of the coupled mechanism. Experimental results confirm that the proposed joint achieves the desired 3-DOF motion with reduced actuation complexity, validating the effectiveness of the passive opposition mechanism.