Exactly constrained (EC) design is a robust design method which can be used for mechanical assemblies. It entails using the minimum number of constraints to eliminate all desired motion. While found by some engineers in industry to have many benefits (including robust assembly, no binding or play, ease of assembly, and the ability to tolerate the wear of parts), EC designs remain somewhat unrecognized by academia. One reason for this minimal exposure may be the lack of a quantitative foundation for such designs. This thesis describes the history and current background for EC designs, and it also begins to develop a quantitative foundation for EC design based on several mathematical methods. EC designs can be analyzed quite simply by understanding that they are statically determinate. Because of this, the equations of equilibrium can be used to validate the rules and the nesting force window that have been defined by Blanding [1999]. In addition, a generalized method using the equations of equilibrium has been developed in this thesis to analyze an EC design based on the locations of the constraints and to find the nesting force window. The direct linearization method (DLM) is another mathematical method used to quantify information in an EC design. While EC designs provide many advantages, some EC assemblies may be "better" than others. A quantitative measure of goodness is developed in this thesis using the DLM. The goodness value assigned to each design through this process can either be used to make a decision on an individual design, or it can be used to compare similar EC designs. Finally, the robust nature of EC design is examined using a Monte Carlo simulation. In general, the results show that EC designs have a higher rate of assembly than similar designs that are over-constrained. They are more robust. In addition, EC designs have lower assembly error than the similarly over-constrained assemblies.