When millions of years of evolution suggest a particular design solution, we may be tempted to abandon traditional design methods and copy the biological example. However, biological solutions do not often translate directly into the engineering domain, and even when they do, copying eliminates the opportunity to improve. A better approach is to extract design principles relevant to the task of interest, incorporate them in engineering designs, and vet these candidates against others. This paper presents the first general framework for determining whether biologically inspired relationships between design input variables and output objectives and constraints are applicable to a variety of engineering systems. Using optimization and statistics to generalize the results beyond a particular system, the framework overcomes shortcomings observed of ad hoc methods, particularly those used in the challenging study of legged locomotion. The utility of the framework is demonstrated in a case study of the relative running efficiency of rotary-kneed and telescoping-legged robots.