Noncircular rolling contact joints enable programmed behavior in robotic linkages.

Rolling contact joints (RCJs) guide motion in robotic linkages, including manipulators, surgical devices, prosthetics, and more. In this work, we present a generalized optimization method to tailor the kinematic properties of RCJs by simultaneously optimizing both noncircular surface geometries and internal actuation pulley shapes. Our approach accommodates multiple joint types, including passively coupled systems with programmable spring stiffness as well as actuated single or multilink mechanisms. We explicitly incorporate common and practical manufacturing constraints into our optimization framework, such as size and convexity constraints. To demonstrate this approach, we optimize an RCJ designed to replicate the trajectory of a human knee, achieving a 99.6% reduction in alignment error compared to revolute joints and a 99.3% error reduction compared to circular RCJs. Additionally, we show that optimized RCJs increase the load-carrying capacity of a two-finger gripper by more than 3.5 times compared to a comparable circular-jointed design, showcasing how joint optimization can enhance robotic performance.