Many curves and surfaces in CAD are defined or constrained by the movement of points, curves or surfaces. Other surfaces have constraints such as points and curves with a prescribed curvature, minimization of some tension, requirement to be non-oscillating etc.
In general in mechanical engineering most of the interesting curves and shapes are given by an envelope of a movement, or by a movement without slipping (or with it) of a contact point (stock for a mechanical part, gears profiles for example). We want to address the potential of constrained modelling by combining parametric and algebraic representations and approaches for constraint geometries and the resulting surfaces. One has to take care of some penalty functions, in order to avoid specific areas of the space (collision prevention).
Kinematics-defined shapes will frequently result in degeneracies and singularities. Consequently they pose challenges to CAD-algorithms when we want to obtain a reliable and usable solid modelling with solids or surfaces defined as general moves of points, curves and surfaces.
For more details contact: Dominique Laffret
Published June 20, 2008