Synthesis method of a mapping matrix for gravity compensators

Abstract

This paper presents a synthesis method of a mapping matrix for gravity compensators. For the space mapping method the mapping matrix indicates the number of unit gravity compensators and their locations simultaneously. To enable the synthesis of the mapping matrix we newly suggest the motion matrix, which is originated from the concept of mobility and connectivity and represents possible joint motions of a target mechanism. We showed that a motion matrix can be synthesized by merging several motion matrices. The motion matrix is modified considering features of static balancing (e.g., absolute motion, mobility and potential energy) and, therefore, the mapping matrix is derived from the motion matrix with no computations. Thus, the synthesis of a gravity compensator is enabled with the motion matrix. The syntheses are conducted for a six-DOF and three-link manipulator.