Design of a Static Balancer with Space Mapping

Abstract

This paper proposes a general expression of the energy method for an n-dofs and n-links gravity compensator in the basis of space mapping. Joint space and gravity compensator space are determined and a mapping between the two spaces is considered. The mapping matrix is determined by mechanical constraints between two spaces. Potential energy in the joint space (i.e., the manipulator mass) and potential energy in the gravity compensator space (i.e., springs) are derived in generic forms. The design equation is obtained by partial differentiation of the potential energy in the both spaces and spring coefficients are determined with the design equation. Example studies are conducted to evaluate the mapping method. The bevel gravity compensator and a three-link spatial manipulator with the bevel gravity compensator are investigated. For the three-link spatial manipulator, the bevel gravity compensator and one-dof gravity compensator are equipped for link 3 and link 1 and the parallel constraint is adopted between the base and link 2 to obtain complete gravity compensation for all poses of the manipulator. Experimental results on gravity compensation indicate that gravitational torques are effectively counterbalanced.