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The report contains a new approach to the design of mechanical systems and elements. The classical idea of mechanical design being an iterative trial and error process is replaced by a procedure to first determine the characteristics of the best possible design and then to use this information in the conception of the optimum fabricable mechanical design. Mechanical systems for which the optimum design is distinguished by minimum peak response functions are selected for consideration, with special emphasis being given to shock isolation and absorption systems. Several techniques, including control theory computational approaches such as dynamic programming, have been explored in considerable detail to contribute to their development or applicability for mechanical design and to determine the promise or difficulties to be expected in future use. Description of the techniques appropriate for the new approach are presented in handbook form. Recommendations are made as to the course ensuing efforts should take in the field of optimal mechanical design synthesis. (Author)