Design of Statically Balanced Planar Articulated Manipulators With Spring Suspension

This paper proposes a design methodology for the synthesis of statically balanced planar articulated manipulators through direct spring installation. The proposed method can determine all admissible configurations of spring installation with a given planar articulated manipulator. The fundamental principle for gravity balance of a conservative system of spring-gravity is formulated by a stiffness block matrix, wherein each component matrix implies interacting forces among the links. The distribution of nonzero-component matrices can be related to a type of spring configuration. The minimum number of springs that are required for a statically balanced manipulator can be further determined, based on the number of design parameters and the number of simultaneous equations derived from the zero-component matrices of stiffness block matrix. By the representation of conventional adjacency matrix for connectivity of springs among the links, five characteristics are identified to enumerate all admissible spring configurations with a minimum number of springs. Spring configurations for the statically balanced articulated manipulators with up to four degrees of freedom are obtained and illustrated schematically. An index function for the evaluation of the robustness of such a statically balanced articulated manipulator with respect to each spring configuration is also proposed.