Swept volumes: void and boundary identification

A general formulation for determining complex sweeps comprising a multiple of parameters has been presented by the authors in recent work. This paper investigates the boundaries to swept volumes, and in specific, addresses the problem of determination of voids in the volume. The determination of voids has become of major concern in CAD software, where the accurate calculation of the swept volume is used in computing solid properties such as mass and moments of inertia. A mathematical formulation based on the concept of a normal acceleration function on singular surfaces is introduced. Criteria are derived regarding the identification of a boundary from the definiteness properties of the normal acceleration function. Numerical examples are illustrated in detail and represent the first treatment of void identification in complex sweeps.