Abstract
Properties of a swept-volume defined by a solid object moving in a three-dimensional space are theoretically discussed in this paper. First, the generation mechanism of the boundary of a swept-volume is formulated based on a concept of 'forehead' and 'rearend' faces on the object boundary. Next, the geometric necessary condition on the generation mechanism is derived using the minimal analysis theory under an object expression as a set-theoretical combination of volumes with C∞-class boundaries. Moreover, the geometric necessary condition is used for classification of swept-volume boundaries. The discussion in this paper gives fundamental knowledge for engineering applications such as NC machining simulation, optimization of cutter path, kinematic simulation and so on.
