Compliant joint design and flexure finger dynamic analysis using an equivalent pin model

Adaptable to nonstructural environment, compliant joints are competent candidates for flexure fingers in humanoid robotic hands. This paper presents an equivalent pin model (EPM), which provides an in-depth understanding on flexure finger dynamics by accounting for the moving rotation center and varying radius of a compliant joint. Distinguished from other lumped-parameter formulations based on constant-axis pin-joint approximation, the large deformation of a compliant joint is characterized by closed-form solutions obtained from a distributed Euler–Bernoulli (E–B) beam model. Modeling tolerance guidelines derived by comparing the E–B model against finite element analysis (FEA) without neglecting shear distortions are provided for designing dimensions of a compliant joint. Design evaluation is illustrated with a flexure finger consisting of three phalanxes by comparing the maximum stress among different configurations. The EPM reveals critical effects of rotational center-offset and varying radius on the dynamic response of a flexure finger, showing that the negligence of these effects yields an out-of-phase prediction in joint rotation. Although presented in the scope of finger manipulation, the method is expected to have potential applications for multi-body dynamics involving compliant mechanisms.