This article presents a nonlinear gear-spring design for gravity balancing of robotic manipulators with variable payloads. Three design methods based on the compact gear-spring mechanism are proposed for serial manipulators: (i) direct installation, (ii) integration with parallelogram linkages, and (iii) integration with a pulley-belt system. The significance of the proposed methods is that they enable compact designs with high performance, accommodate variable payloads, and incorporate gear friction losses into the performance analysis. In this work, numerical examples are illustrated to demonstrate the effectiveness of the proposed methods, showing that both the parallelogram and pulley-belt configurations can fully eliminate the actuator torques of the robotic manipulators under varying payloads, while the direct installation achieves partial gravity compensation. Furthermore, a prototype of a robot arm with a 1-kg payload capacity and 540-mm reach has also been developed by adopting a pulley-belt system. Experimental results showed average reductions of 72.8% in torque, 57.5% in power, and 89.3% in energy consumption.
