Engineering Constraint Management Based on an Occurrence Matrix Approach

In many mechanical systems, the mathematical model can be characterized by m nonlinear equations in n unknowns. The m equations could be either equality constraints or active inequality constraints in a constrained optimization framework. In either case, the mathematical model consists of (n-m) degrees of freedom, and (n-m) unknowns must be specified before the system can be analyzed. In the past, designers have often fixed the set of (n-m) specification variables and computed the remaining n variables using the n equations. This paper presents constraint management algorithms that give the designer complete freedom in the choice of design specifications. An occurrence matrix is used to store relationships among design parameters and constraints, to identify dependencies among the variables, and to help prevent redundant specification. The interactive design of a torsion bar spring is used to illustrate constraint management concepts.