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This paper presents a design concept for gravity compensation of planar articulated robotic arms using a series of gear-slider mechanisms with springs. The spring-attached gear-slider mechanism has one degree-of-freedom (DOF) of motion, which can serve as a gear-spring module (GSM) to be installed onto the robot joints for leveraging the gravitational energy of the robot arm. The proposing GSM-based design is featured by its structure compactness, less assemblage effort, ease of modularization, and high performance for gravity compensation of articulated robotic manipulators. As a key part of the design, the stiffness of the spring in the GSM can be determined through either a design optimization or an analytical approximation to perfect balancing. The analyses on several 1-, 2-, and 3-DOF GSM-based robot arms illustrate that the analytical approximation to perfect balancing can reach nearly the same performance as provided through the design optimization. The power loss due to the gear contact is considered when evaluating the gravity compensation performance. A formula for spring stiffness correction is suggested for taking the power loss into account. An experimental study on a one-DOF GSM-based robot arm was performed, which shows that a power reduction rate of 86.5% is attained by the actuation motor when the GSM is installed on the robot arm.

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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 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.