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Engineering design is an iterative process with a fundamental need for the consistent management and propagation of product dependencies. Constraint-based design provides a unified framework to meet this critical need, but there are known issues due to the complexity of the problem within three-dimensional space. This paper presents results from a decade of research into graph theory and numerical solution techniques to address issues such as user comprehension and multiplicity of solutions. The proposed solution, Extended Variational Design Technology (VGX), utilizes an innovative Drag and Drop user interaction paradigm to improve comprehension performance, and usability. It is also demonstrated that VGX technology can provide common mathematical foundation to support flexible and integrated product design, assembly and analysis.