Multi-level molecular representation

In the initial molecular representation proposal for kinematic reasoning (Gupta and Jakiela, 1994), object contours were represented using a list of touching circles each of equal diameter. Gupta and Jakiela characterise procedures by which: (1) kinematic analysis can be performed by advancing the driving contour through a small displacement and moving the driven object in such a manner as to minimise divergence in the spatial relationship between the two contours; and (2) kinematic synthesis can be effected by deforming a blank component with respect to the known half of a kinematic pair. We have further developed this approach and employed a multi-level molecular representation, and have considerably improved both the synthesis and analysis procedures. In this we paper we describe our kinematic synthesis and analysis algorithms, and give an account of how the multi-level representation can be maintained with minimum effort during the synthesis process.