Understanding Linkages

Howard E. Shrobe

Mechanical linkages are used to transmit and transform motion. In this paper we investigate what it might mean to "understand" a linkage, i.e. how one would explain the functioning of the system. We present a system capable of understanding a variety of relatively simple linkage mechanisms found in standard references. Our system extracts its understanding by analyzing the results of a numerical simulation of the mechanism. It proceeds through several stages: The simulator builds a trace of its reasoning which is parsed and analyzed, leading to a structuring of the mechanism into driving and driven components. The trajectories of the coupling points are then analyzed to find interesting qualitative features, aa are the curves representing the histories of angular deflections of rocker arms. Next the system looks for symbolic relationships between the features and conjectures a causal relationship between them. Finally, this causal relationship is verified by geometric reasoning. This process produces explanations very much like those in standard texts.

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