Design of Statically Balanced Spatial Mechanisms With Spring Suspensions

Abstract

This paper proposes a general approach for designing spatial statically balanced mechanisms with articular joints utilizing ideal zero-free-length springs. The proposed statically balanced mechanism can counterbalance the gravitational forces and provides a perfect static equilibrium at any configuration. The method of the paper is based on the energy approach, and a generalized coordinate system is developed to define the configuration of a spatial mechanism and to be a vector basis for the derivation of potential energy. By incorporating the gravitational forces and the spring forces into the system, the stiffness matrix of a spring-loaded mechanism is proposed. The perfect static balance is observed when the stiffness matrix is a diagonal matrix, from which, the design equations can be readily obtained. The closed-form solution of spring design parameters of a statically balanced, spatial, three-articular arm is obtained as a design example. The simulations of the conceptual design are performed by commercial computer software, and the static equilibrium of a quasi-static continuous motion is verified.