Disassembly sequences for objects built from unit cubes

TL;DR: A working program has been implemented in pop -11, which finds a disassembly sequence for an object defined by a 3D cube map, and the idea of coupling between two faces is introduced, which helps determine the global geometric feasibility of a motion.

Abstract: The geometrical problem of finding a possible disassembly sequence for an object is considered for a limited class of objects: those whose parts can be made from collections of unit cubes. For such objects, we consider motions of their component parts which are translations in one of three orthogonal directions. A working program has been implemented in pop -11, which finds a disassembly sequence for an object defined by a 3D cube map. Each disassembly step may consist of either one or two linear motions of single parts. Removal of subassemblies consisting of more than one part is not considered. To ensure properly the validity of a disassembly motion, both local and global geometric information must be considered. The local geometric feasibility of a motion relates to whether an infinitesimal motion can be made, and it is determined by the surface contacts (mates) between a part and other parts. The global geometric feasibility of a motion relates to whether a finite (or infinite) motion can be made in a particular direction. It depends not only on the relationship between the part to be moved and those that it touches, but also on its relationship with, potentially, all the other parts in the assembly. To determine the global geometric feasibility of a motion, the idea of coupling between two faces is introduced. Coupling is a directional quantity which gives the finite limit on the relative motion between two faces. By considering the coupling information for all the faces of a part, it is easy to determine the finite motions that are possible in any direction.