GEOMETRIC REPRESENTATION OF THE SWEPT VOLUME USING JACOBIAN RANK DEFICIENCY CONDITIONS

A broadly applicable formulation for representing the boundary of swep t geometric entities is presented. Geometric entities of multiple para meters are considered. A constraint function is defined as one entity is swept along another. Boundaries in terms of inequality constraints imposed on each entity are considered which gives rise to an ability o f modeling complex solids. A rank-deficiency condition is imposed on t he constraint Jacobian of the sweep to determine singular sets. Becaus e of the generality of the rank-deficiency condition, the formulation is applicable to entities of any dimension. The boundary to the result ing swept volume, in terms of enveloping surfaces, is generated by sub stituting the resulting singularities into the constraint equation. Si ngular entities (hyperentities) are then intersected to determine sub- entities that may exist on the boundary of the generated swept volume. Physical behavior of singular entities is discussed. A perturbation m ethod is used to identify the boundary envelope. Numerical examples il lustrating this formulation are presented. Applications to NC part geo metry verification, robotic manipulators, and computer modeling are di scussed. (C) 1997 Elsevier Science Ltd.