This paper presents the methodology of topological reconfigurations with composite Bennett linkages. A new family of diverse reconfigurable Bennett linkages is discovered. The framework is based on the parallel combination of Bennett chains. Two kinds of expansible frameworks are addressed in detail. The topological reconfigurations of Bennett-based linkage with multiple working-phases can be attained from the composite framework of the compositing Bennett chain by eliminating the revolute angle between its adjacent links. Several examples are provided not only to interpret the construction of extant ones but also to develop more complicated ones. The proposed method systematically discovers all possible permutations of number of joints and links for topological variants of the resultant linkages. The spatial linkage built based on the presented methodology may be either overconstrained or underconstrained because some of their DOFs may not follow the mobility as predicted by Chebychev-Grübler-Kutzbach criterion.

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