Closed Form Solutions for Connectivity and Connectivity of Motion in Mechanisms
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Abstract This paper presents a closed form solution for determining connectivity between any two links in mechanism. The formulation is based on graph theory and its modification. The proposed approach could be applied to both planar and spatial mechanisms including combined planar-spatial mechanisms. Further, the mechanism may have multiple closed loops and/or open-chain substructures. A new concept of Connectivity of Motion has been introduced to determine the connectivity between any two links when the mechanism under consideration has special arrangement of adjacent joints such as joints with parallel and/or intersecting axes. Four examples are presented to illustrate connectivity calculations in spatial mechanisms.