On tolerance problem of contacting polyhedral objects

This paper first presents the decision curve as an economical way that describes the correlations between scaling pairs (rho₁, rho₂), small relative motion conditions (type, direction and amount) and contact configurations (feature) of two scaled convex polyhedral objects where rho_i denotes the scaling factor of polyhedral object i = 1,2. Via Analytical Equations of contact feature, the new decision curves after an intended relative motion of any type within its coherent range could be immediately obtained by taking advantage of original decision curve. We illustrate via two examples this method allows users to systematically and efficiently search a lot of design of fine motions to reorient two nominally contacting convex or non-convex polyhedral objects with assigned tolerance of scaling factors that satisfy the requirements.