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. In this paper, 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. A reliability-based design optimization (RBDO) method is also developed to seek reliable spring setting parameters 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.

This paper presents the static balancing design of a special reconfigurable linkage that can switch between two one-degree-of-freedom (DoF) working configurations. We will show that the studied dual-mode linkage only requires one mechanical spring or one counterweight for completely balancing its gravitational effect in theory at both modes. First, the theoretical models of the spring-based and the counterweight-based designs are derived. The proposed design concepts were then demonstrated by a numerical example and validated by software simulation. Experimental tests on both designs were also performed. The result of this study shows that a reconfigurable mechanism with N working configurations can be completely statically balanced by using less than N passive energy elements.

This paper presents a method for realizing a gear-spring balancer (GSB) that can cope with variable payloads and its application to serial robots. The GSB is constructed with a three-gear train articulating a nonzero-free-length spring to a rotating link with a mass to be statically balanced. In the proposed method, the parameters of the GSB are derived from solving the identity problem of perfect static balancing. The significance of this method is that it enables the GSB to handle variable payloads via energy-free adjustment and allows the selection of spring stiffness. The effectiveness of the proposed method was demonstrated through a numerical example and experimental tests. The analytical results showed that the GSB theoretically achieved perfect static balancing even when the payload varied. The peak actuator torque of the GSB was practically reduced by more than 90% with different payloads. In this work, the application of the GSB to serial robots is described to underline the significance of the payload variability of the GSB in pick-and-place operations. A theoretical model illustrated that the peak actuator torques of a serial robot were reduced by an average of 93.4% during operation.