Self Dual Topology of Parallel Mechanisms with Configurable Platforms

This paper presents first an analysis of the topology of mechanisms via Graph Theory and Screw Theory and next the principle of dual mechanisms in terms of their mobility and overconstraints. Using dual graphs, the graph representations of the mechanisms that are dual to hybrid and Delta mechanisms are revealed. The concept of parallel mechanisms with configurable platforms (PMCPs) is introduced and it is shown that the graph reduction of PMCPs always results in a wheel graph, which has the interesting property of being self-dual. In case of self dual topology, it is then possible to directly convert any method developed for their mobilty analysis into an overconstraint analysis method and vice versa. This self dual topology property can also be exploited to create new PMCPs and is an important aspect in the future development of a type synthesis method that includes PMCPs.