Unlocking complex motion in one DoF higher pairs: Concept, constraint, and form closure for varying instantaneous center of rotation (VICR) joints

This paper investigates one degree of freedom (DoF) higher pairs enabling the complex motion with a varying instantaneous center of rotation (VICR), referred to as VICR joints. Firstly, the conceptual framework and classification for 1-DoF higher pairs with multi-point contact are proposed, introducing the innovative concept of VICR joints that incorporate one DoF to achieve complex motion. A profile synthesis method is further introduced for the geometric design of joint elements. Then, the constraint characteristics of VICR joints are analyzed, and the constraint performance evaluation index based on the generalized pressure angle is proposed, further revealing the geometric nature of constraint performance. Subsequently, the form closure criteria of VICR joints are derived by combining the directionality of constraint forces and restricted motion, ensuring persistent element contact solely through geometric profiles of joint elements. Finally, case studies are conducted to verify the effectiveness of the proposed concepts and methods. This research complements the design possibilities of planar joints by proposing a novel type of 1-DoF higher pair that enables complex motion, providing an innovative joint solution for modern mechanical systems.