The generation of swept volumes and its application in spatial mechanism design

Sweep is a constructive paradigm in which a geometric object called the generator undergoes a continuous motion. The set of total points traversed by the generator during that motion is called the swept volume of the generator. Swept volumes can find important applications in modern design and manufacturing. This thesis addresses the problem of determining the boundary of the swept volume of a solid generator undergoing a general sweep motion described by the instantaneous screw motion.; The classic envelope theory has been used to solve the swept surfaces of CSG primitives and deduce the candidate boundary set of a swept volume. The candidate boundary set of a swept volume consists of the swept surfaces of the surfaces and edges of the generator and the partial boundaries of the generator at the initial and final sweep positions. The candidate boundary set guarantees to contain the boundary of a swept volume. However, it may include the trim set due to the self-intersection of the swept volume. The trim set is located to the interior of a swept volume, and must be trimmed off in constructing the boundary representation of the swept volume. In this thesis, a multiple-step method has been used to construct the approximation model of a swept volume. These steps include the parallel sectioning operation to the candidate boundary set, constructing the simple contours in sectioning planes, and triangulating a sequence of parallel contours.; Swept volumes can serve as geometric constraints in designing link geometries of a mechanism. The top-down design method has been employed to design link geometries of a spatial mechanism which is guaranteed to be free of interference and collision.