On deciding 3D part disassemblability and surface machinability

Abstract

In this paper we consider two manufacturing-related problems: 3D part disassemblability and surface machinability. The former is to find a feasible direction along which a part can be separated from a given 3D assembly, and the latter is to find a feasible direction in which an NC machining tool can approach a given surface. We present a unified formulation of these problems by using a system of linear inequalities. We also show that a feasible direction can be found in O(n) time by transforming the formulation into the 2D linear separability problem, where n is the number of faces. All feasible directions can also be found in O(n log n) time. Furthermore, by transforming the formulation into the smallest enclosing sphere problem, an O(n) time algorithm is proposed to find the optimal direction, i.e., the direction minimizing the maximum angle to the normal vectors of 3D surfaces.