Automated design and parametrization of mechanical part geometry

Variational methods for evaluating the design of mechanisms were first introduced by this group in the form of mathematical formulations generally applicable to open- and closed-loop mechanisms. This method is extended here, and demonstrated on the design of mechanical parts in the context of automatic parametrization of the geometry. The formulation is based on the development of constraint equations that govern the relationships between geometry in mechanical part as dictated by a designer. Instead of the tedious method of specifying mathematical relations between any two geometries of the part, it is proposed to use the notion kinematic relations inherent in the formulation relating the connectivity between joints and links. Cut-joint constraints are introduced, kinematic joints in the formulation are combined, their variations evaluated, and a Jacobian is determined. Constraint violations are then compensated to compute an assembled mechanism, hence redesigning the part. It is shown that this kinematically-driven formulation is broadly applicable to 2D and 3D models. The method and algorithm are illustrated through a number of examples.