|M.Sc Thesis||Department of Applied Mathematics|
|Supervisor:||Prof. Elber Gershon|
In this work, we address several important problems in the field of verification of multi-axis NC-machining. We offer novel approaches for the problem of collision detection and avoidance in the context of multi-axis NC-machining, which are also extended to support continuous collision detection between the discrete tool locations.
The axial symmetry inherent in the tool's rotational motion is exploited to derive a highly precise polygonal surface—tool intersection algorithm. We radially project the 3-dimensional collision detection and avoidance problems onto a 2-dimensional space, reducing the complex interference tests to the intersection calculations between planar hyperbolic and linear segments. The latter can be performed in an exact and efficient way.
Due to the directional nature (tool axis) of multi-axis NC-machining, space subdivision techniques were adopted from ray-tracing algorithms and are extended to devise a highly efficient data structure and algorithms that further increase the overall efficiency of the proposed methods.
Other advantages of the proposed method are the separation of the entire computation into a preprocessing stage that is executed only once, allowing more than one tool-path to be efficiently verified thereafter. The method allows precise collision detection and avoidance of arbitrarily orientated tools, and introduces the ability to test for collisions against arbitrary shaped tools including flat- and ball-ends, or even test for interference with the tool holder or other parts of the NC-machine.
An additional research effort was directed into extending the collision detection algorithm to work with free-form surfaces.