Design of a static balancer for constrained joint space

Abstract

We propose a design method for a gravity compensator using the space mapping method and joint constraints. The pose of a mechanism can be described with various joint angle sets (i.e., joint spaces). When constraints exist between joint angle sets, a gravity compensator for a mechanism can be derived from the gravity compensator of a base joint space using constraints. Thus, it is not necessary to recompute the whole design equation. A slider-crank mechanism was adopted as an example and various gravity compensators were obtained using the space mapping method. Investigations of various gravity compensators proved that their design equations can be derived from the base joint space by applying mapping relations between joint spaces (i.e., constraints). The results of simulations show that the obtained gravity compensators effectively counterbalance the gravitational force and the total potential energy is invariant for all poses.