On the Robustness of Exactly Constrained Mechanical Assemblies

In recent years a number of practicing engineers have discussed the virtues of exactly constrained (EC) mechanical assemblies. While found by engineers in industry to have many benefits, EC designs remain somewhat unrecognized by academia. One reason for this minimal exposure may be the lack of a mathematical foundation for such designs. EC designs can be analyzed quite simply by understanding that they are statically determinate. This paper describes the history and current background for EC designs. It also begins to develop the mathematical foundation for EC design based on equations of equilibrium. Finally, it examines a Monte Carlo simulation of the effects of variation on EC assemblies vs. over-constrained assemblies. The EC design assembles 100% of the time, while the over-constrained design assembles only 50% of the time with greater error.