Dimension driven Computer Aided Design (CAD) systems hold great promise for enhancing productivity and competitiveness of the early conceptual stages of mechanical engineering design. Current systems suffer one of two sets of deficiencies. Variational Geometry systems suffer from speed problems and problems controlling which solutions their geometry solution mechanism converges to. Constructional or "parametric" systems, while fast, have a less intuitive user interface and a less flexible geometry representation. The objective of the research is to develop a new graph-theory based technique to convert a variational geometry description to a constructional system. Preliminary research in two-dimensions has indicated the prospect of dramatically increasing the speed of variational geometry solution, and thus increasing the range of problems to which it may be applied. Successful implementation in a mechanical design package will greatly expand the utility of conceptual design software to the mechanical engineer.