Assembling and Disassembling Planar Structures With Divisible and Atomic Components

This paper considers an assembly problem. Let there be two interlocking parts, only one of which may be cut into pieces. How many pieces should we cut the divisible part into to separate the parts using a sequence of rigid-body motions? In this initial exploration, we primarily consider 2-D polygonal parts. This paper presents an algorithm that computes a lower bound on the number of pieces that the divisible part must be cut into. This paper also presents a complete algorithm that constructs a set of cuts and a motion plan for disassembly, yielding an upper bound on the required number of pieces. Applications of the future extension of this paper to 3-D may include robot self-assembly, interlocking 3-D model design, search-and-rescue, packaging, and robotic surgery.