Automatic Reasoning for Design Under Geometric Constraints

Parametric design is very stable but requires a predefined dimensioning and ordering scheme, thus limiting flexibility and precluding sketch input. Variational geometry design, while general and flexible, necessitates intensive use of numerical solvers to solve many simultaneous nonlinear equations. Frequently the solvers cannot solve these equations. A new system, based on an original theory for automatic constraint analysis, has been developed for solving sets of two-dimensional geometric constraints in product design. The proposed system offers the flexibility of variational based design along with the stability of parametric design. The solution strategy is based upon breaking down the problem into a sequence of construction steps. When no sequential construction is found, auxiliary geometrical constructions are automatically generated based on rules for relocating constraints. Thus, an apparently simultaneous constraint set is converted into a set that can be constructed sequentially by decomposing strongly connected components of the original constraint graph. This new approach has been implemented in a system for designing sheet metal parts.