Assembling polyhedra with single translations

The problem of partitioning an assembly of polyhedral objects into two subassemblies that can be separated arises in assembly planning. The authors describe an algorithm to compute the set of all translations separating two polyhedra with n vertices in O(n⁴) steps and show that this is optimal. Given an assembly of k polyhedra with a total of n vertices, an extension of this algorithm identifies a valid translation and removable subassembly in O(k²n⁴) steps if one exists. Based on the second algorithm, a polynomial time method for finding a complete assembly sequence consisting of single translations is derived. An implementation incorporates several changes to achieve better average-case performances. Experimental results obtained for composite objects consisting of isothetic polyhedra are described.