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This thesis presents the ideas underlying a computer program that takes as input a schematic of a mechanical or hydraulic power transmission system, plus specifications and a utility function, and returns catalog numbers from predefined catalogs for the optimal selection of components implementing the design. Unlike programs for designing single components or systems, the program provides the designer with a high level 'language' in which to compose new designs. It then performs some of the detailed design process. The process of 'compilation', or transformation from a high to a low level description, is based on a formalization of quantitative inferences about hierarchically organized sets of artifacts and operating conditions. This allows design compilation without the exhaustive enumeration of alternatives. The program has been tested on a wide variety of power transmission and temperature sensing problems. Key elements of the theory have been formally proven. It appears that the theory has applications outside design. (rrh)