A novel spring gravity-balance method for spatial articulated manipulators without auxiliary links

Abstract

Previous studies developed spring-gravity balancing methods for articulated manipulators using auxiliary links. However, these links caused extra inertia and motion interference. To address these issues, a spring balancing method based on the quadratic form was proposed. In this form, matrix components represent the energy change due to the manipulator's posture, i.e., stiffnesses. Gravity balancing can be simplified as the summation of matrices that remain unchanged. However, the matrix component contains the polar angles, which can only describe the links’ direction on a plane, thus making this form applicable only to planar manipulators. To extend its applicability to spatial manipulators, we have reformulated it using local coordinates to describe the manipulator's posture in space. The improved quadratic form can be applied to both planar and spatial manipulators, unifying energy representations of articulated manipulators. By arranging the springs to maintain a constant summation of matrices, energy balance is achieved. The criteria of spring attachment and the rules of using springs are proposed. Simulation of a spatial four-link manipulator show perfect balance can be achieved without auxiliary links using our approach.