Continuous Analysis of Cutter-Workpiece Engagement Based on Four-Dimensional Geometric Models

Geometric simulations are typically used to represent modern machining processes. However, most strategies rely on three-dimensional geometric models, which represent movements as a series of discrete snapshots. Physical laws and real-time interpolations are often used to estimate the state of motion at specific moments. To address this limitation, this study introduces a four-dimensional (4D) geometric model that simulates the tool-workpiece contact process within the spatiotemporal space. This article presents the fundamental concept of representing tools and workpieces in 4D space, followed by the proposal and implementation of two 4D cutter-workpiece engagement methods.