On the inertia duality of parallel-series connections of two robots in operational space

The inertias of the parallel and serial connections of two robots in the operational space are studied in this paper. First, it is reviewed that the symmetry between the velocity and force in a robotic chain results in velocity-force duality of the parallel and serial connections. The possible duality in the operational inertia matrix is then investigated. From the dynamic equations of the two connections, it is found that there does not exist a real duality in the operational inertia matrix. However, the real duality becomes possible when the coupling effects between the two robots are negligible. This conditional duality is called "quasi-duality" in this paper. As a result of this study, the duality behaviors of the two connections in velocity, force and inertia are completely obtained.<
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