Design of a static balancer with equivalent mapping

•We propose a design method of a static balancer with N-dof unit gravity compensators.•The space mapping method is extended to a N-dof gravity compensator space.•A N-dof gravity compensator can be represented with one-dof gravity compensators.

This paper proposes a design method of a static balancer with multi-dof unit gravity compensators. The design method based on the space mapping method is extended to a multi-dof gravity compensator space. A multi-dof gravity compensator can be equivalently represented with one-dof gravity compensators applying the design method. An equivalent mapping matrix is determined between rotation angles of a multi-dof gravity compensator and those of one-dof gravity compensators. That is, characteristics of a multi-dof gravity compensator are described in the one-dof gravity compensator space. Complexity and variety originated from the multi-dof can be overcome using the equivalent mapping matrix during designing a static balancer with multi-dof gravity compensators. The design of a static balancer with multi-dof gravity compensators is conducted: 1. perform the design only with the one-dof gravity compensator space to determine the base mapping matrix between the joint and the one-dof gravity compensator space, 2. applying the equivalent mapping matrix to the base mapping matrix. Various designs are obtained. Results of simulations show that the total potential energy is invariant for all poses.