Maintaining a Consistent Configuration in a Constraint-Based Mechanical Design System

We consider here the class of mechanical designs that can be expressed as systems of nonlinear equations that describe the dimensions of the feature(s) being created. Systems of nonlinear equations typically have multiple possible solutions even though the designer usually has only one in mind. Iterative solution techniques used to solve systems of equations (e.g., Newton-Raphson) fall short due to their lack of control over which solution the system converges to. We introduce here an interval-based technique to efficiently solve this problem. Variational design is a powerful paradigm for design, but has been limited in its application by the inability to characterize multiple solutions resulting from systems of nonlinear equations. Previous research efforts in variational design have introduced numerous methods for increasing the stability of iterative methods in the presence of multiple competing solutions. These methods can be categorized as either 1) requiring the user to manually monitor and correct the convergence process, or 2) requiring the user to define additional constraints or other information about the system. Instead of these approaches, this paper introduces techniques for tracking a specific solution as the constraints are modified by the user. In this scenario, the user only has to help guide the search the first time the systems of constraints are solved. During subsequent modifications (as occur often in design), the techniques are able to automatically follow the trajectory of the solution as the parameters change so as to maintain a consistent configuration. The incremental design of a cantilever beam is used to demonstrate the solution trajectory tracking technique.