Analysis of the ways of assembling a product requires an effective method of representing the motion of other components. This paper introduces the nondirectional blocking graph as a means to do this. For each direction in space, one can define a directional blocking graph whose nodes are the components of the assembly. There is an arc for each pair of nodes such that the corresponding components interfere with each other’s movement in the given direction. The key observation is that, for a given assembly, the directional blocking graphs can only have a finite number of different topological types. Indexing this finite set of graphs by subsets of the unit sphere in the space of motions gives the nondirectional blocking graph.

The authors show how to compute the nondirectional blocking graph in polynomial time. Various measures of complexity for an assembly problem are defined and related to the graph. The ideas are illustrated using a 23-part engine as an example.