This article proposes a method for analyzing the gravity balancing reliability of spring-articulated serial robots with uncertainties. Gravity balancing reliability is defined as the probability that the torque reduction ratio (the ratio of the balanced torque to the unbalanced torque) is less than a specified threshold. The reliability analysis is performed by exploiting a Monte Carlo simulation (MCS) with consideration of the uncertainties in the link dimensions, masses, and compliance parameters. The gravity balancing begins with a simulation-based analysis of the gravitational torques of a typical serial robot. Based on the simulation results, a gravity balancing design for the robot using mechanical springs is realized. A reliability-based design optimization (RBDO) method is also developed to seek a reliable and robust design for maximized balancing performance under a prescribed uncertainty level. The RBDO is formulated with consideration of a probabilistic reliability constraint and solved by using a particle swarm optimization (PSO) algorithm. A numerical example is provided to illustrate the gravity balancing performance and reliability of a robot with uncertainties. A sensitivity analysis of the balancing design is also performed. Lastly, the effectiveness of the RBDO method is demonstrated through a case study in which the balancing performance and reliability of a robot with uncertainties are improved with the proposed method.

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