There is no doubt that today’s mechanical systems are complex. Mechanical systems tend towards greater complexity as each component interacts with a larger number of neighboring components. This structure of interaction permits function-sharing of the components — one of the hallmarks of creative design. Function-sharing is one of the interesting ways in which mechanical design differs from, for example, solid state circuit design. Assembly models that require fixed contact between components at specified locations to determine their relative positions will also have gaps that provide clearance between the components. The complexity of these assembly models is linear in the number of gaps, as the clearance at each gap is dependent on a single set of dimensions. However, if the assembly model is defined in terms of potential (vs. required) contacts between components, the complexity of the analysis increases dramatically. In this paper we describe the complexity of assemblies analyzed in a single direction (i.e. one-dimensional analyses) and propose a means of characterizing different types of assemblies.

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