Swept volumes generated from deformable objects application to NC verification

Abstract

The paper suggests a representation of swept volumes generated by the motion of deformable objects. This representation is based on the topological properties of n-dimensional manifolds. The algorithm developed for the evaluation of the boundary exploits these properties in such a way that the n-dimensional object (swept volume) is generated only from the (n-1)-dimensional components resulting from a family of deformations. The deformation, analytically expressed, integrates physical properties, especially the nonlinearities of deformable objects. The representation is applied to the modeling of the deformations of a milling cutter being fed into a workpiece and it constitutes an efficient tool for NC verification. Many other applications may be concerned by this work, especially in robotics (modeling of flexible robots, collision detection) or in mechanical engineering.