Gravity balancing of a spatial serial 4-DOF arm without auxiliary links using minimum number of springs

The principle of gravity balancing has been studied for a long time. It allows a system to be in indifferent equilibrium regardless of the configuration. In the literature, gravity balancing has often been achieved using appropriate combinations of springs and auxiliary links. Some papers address potential layouts without auxiliary links, but limited to planar mechanisms. This paper proposes a method to passively balance an anthropomorphic arm, with spatial kinematics, avoiding the use of auxiliary links. The approach used in this paper includes the analysis of all the contributions to the potential energy of the arm. It is shown that they are proportional (according to geometrical and inertial parameters) to scalar products between configuration-dependent unit vectors and/or configuration-independent unit vectors. Analysing the potential energy contributions for each combination of unit vectors, it is shown how to minimize the number of springs required to balance the mechanism without additional links. As a result, four possible layouts are developed, all of them using only two springs. Features and design issues of the four layouts are discussed. Finally, one of them is chosen for actual implementation.