An Assessment of Geometric Methods in Trajectory Synthesis for Shape-Creating Manufacturing Operations

This paper presents an assessment of the steps involved in trajectory synthesis (for example, trajectory layout, trajectory generation, trajectory spacing, trajectory postprocessing, and trajectory verification) for shape-creating manufacturing operations such as rapid prototyping, milling, and electrical discharge machining. The rationale for this paper is that trajectory plays an important role in determining productivity, as explained below. Shape-creating manufacturing operations are those that make use of a "tool" that operates on a "workpiece" to create the desired shape. The tool operates on the workpiece as dictated by the trajectory of the tool, resulting in the manufactured shape. Often, the geometric and functional properties of the end product are dependent on the trajectory of the tool. Moreover, the trajectory dictates the accuracy of the end product and the time taken to manufacture the product. Recognizing the important contribution of the trajectory in shape-creating operations, this paper therefore focuses on trajectory synthesis.