: This paper presents a further analysis of the recently developed sweep-envelope differential equation (SEDE) method for the numerical computation of swept volume. An SEDEbased algorithm is described, analyzed and combined to calculate the swept volume generated by machining tools for a large class of sweeps. The SEDE approach reduces the swept volume computation to the determination of SEDE trajectories at the initial grazing points (the main portion of the swept volume boundary) of the tool and provides a natural connectivity for most points on the swept volume boundary. An example is given to illustrate the effectiveness of the SEDE algorithm. Keywords: Geometric Modeling; Swept Volume; Multi-Axis NC Machining; CAD/CAM INTRODUCTION Swept volume research arises from the construction of computer-based NC simulation and verification system and other applications in manufacturing automation processes. A great amount of work on swept volume has been devoted to developing new methods,..