An incremental constraint-based approach to support engineering design.

Constraint-based systems are increasingly being used to support the design of products. Several commercial design systems based on constraints allow the geometry of a product to be specified and modified in a more natural and efficient way. However, it is now widely recognised the needs to have a close coupling of geometric constraints (i.e. parallel, tangent, etc) and engineering constraints (Le. performance, costs, weight, etc) to effectively support the preliminary design stages. This is an active research topic which is the subject of this thesis. As the design evolves, the size of the quation set which captures the constraints can get very large depending on the complexity of the product being designed. These constraints are expected to be solved efficiently to guarantee immediate feedback to the designer. Such requirement is also necessary to support constraint-based design within Virtual Environments, where it is necessary to have interactive speed. However, the majority of constraint-based design systems re-satisfy all constraints from scratch after the insertion of a new design constraint. This process is time consuming and therefore hinders interactive design performance when dealing with large constraint sets. This thesis reports research into the investigation of techniques to support interactive constraint-based design. The main focus of this work is on the development of incremental graph-based algorithms for satisfying a coupled set of engineering and geometric constraints. In this research, the design constraints, represented as simultaneous sets of linear and non-linear equations, are stored in a directed graph called Equation Graph. When a new constraint is imposed, local constraint propagation techniques are used to satisfy the constraint and update the current graph solution, incrementally. Constraint cycles are locally identified and satisfied within the Equation Graph. Therefore, these algorithms efiiciently solve large constraint sets to support interactive design. Techniques to support under-constrained geometry are also considered in this research. The concept of soft constraints is introduced to represent the degrees of freedom of the geometric entities. This is used to allow the incremental satisfaction of newly imposed constraints by exploiting under-constrained space. These soft constraints are also used to support direct manipulation of under-constrained geometric entities, enabling the designers to test the kinematic behaviour of the current assembly. A prototype constraint-based design system has been developed to demonstrate the feasibility of these algorithms to support preliminary desig