A 1-DoF Mechanism Using a Cam and a Compliant Beam for Gravity Compensation in Robotic Arms

Gravity balancing is a classic concept in robotics, especially for serial arms, as it can improve their efficiency, accuracy, and safety. Often, balancers with a single Degree-of-Freedom are combined to form more complex linkages. The existing literature offers many designs, but mechanism complexity and size limit applications in robots. We present a proof-of-concept for a passive, partial gravity-balancing system with a rigid circular cam acting on a compliant beam with fixed ends. The cam is attached to a rotating link and applies a vertical contact force to the beam through a bearing, to reduce friction. The elastic and gravitational potential energy compensate each other as the link moves. An analytical model is derived from Euler–Bernoulli’s beam theory, enforcing compatibility and equilibrium conditions at the contact point. Combined with the kinematic constraints due to the cam geometry and the tangency condition, we obtain a nonlinear system of equations; the contact force is thus a function of the link rotation angle. The design parameters are optimized, to minimize the unbalanced joint torque over a prescribed angular range. We show that this simple, compact and low-friction architecture, suited for robotic systems, can achieve quasi-exact balancing.