An Automatic Approach to Handling Inequality Constraints in an Interactive Design Environment

Abstract

Abstract A general mechanical design can be characterized by a set of equality and inequality constraints. Constraint Management algorithms have been successfully applied for the satisfaction of equality constraints. The goal of this paper is to extend the ideas of constraint management to handle inequality constraints. Past research shows that the handling of inequality constraints has been restricted to optimization and symbolic frameworks. As opposed to the traditional optimization schemes in which all the inequality constraints are converted to equalities, our approach introduces slack variables for only those inequalities that are active at that particular stage of the design process. The basic premise governing the algorithm presented in this paper is to satisfy a set of inequality constraints while deviating as little as possible from the given design specifications. An occurrence matrix formulation is used to represent both the equality and inequality constraints that govern the design. A linear model of the design, based on sensitivity computations, is used to automate the procedure. The work is illustrated for the classical weldment design problem.