A Geometric Method for Static Balancing of Spatial Mechanisms Using Springs

This paper presents a geometric method for static balancing of spatial mechanisms using only springs. The method applies to mechanisms composed of revolute (R) joints with arbitrary parameters. This method leads to systems with constant potential energy, including the potential energy associated with gravity and the elastic potential energy stored in the springs, hence make the systems more energy-efficient. In the literature, the static balancing of the 1-link manipulator and spatial manipulators without the consideration of the intermediate link weights has been discussed, using the algebraic method which needs lots of derivations or auxiliary parallelograms. This paper is to provide an efficient way to construct statically balanced spatial mechanisms with all the link weights considered. The proposed method is a geometric approach and can achieve static balancing without or with few derivations. In addition, an auxiliary mechanism with 3-degree of freedom (DOF) translational motions is introduced for the accommodation of the springs. In addition, the method can be applied to mechanisms with multiple modes. An 8R linkage and a 3-4R parallel mechanism with multiple motion modes are presented as examples to illustrate the proposed method. The method of equivalent virtual center of mass is also adopted for the 3-4R parallel mechanism to reduce the number of springs.