Geometric Tolerancing for Assembly with Maximum Material Parts

This paper introduces the ‘maximum material part’ (MMP) in higher dimensions, extending the 1-D MMP introduced in [9]. Given a toleranced object, an MMP is an ‘in-tolerance’ part that contains (as in set containment) all other in-tolerance parts, under suitable rigid motions. We show how tolerances leading to MMPs may be defined and how these lead to elegant solutions for the analysis of ‘floating’ assemblies of rigid toleranced objects. MMPs are also useful in motion planning with toleranced objects.