This paper describes the following two kinds of dynamic optimization problems applied to mechanisms and their solution by using the spectral theory of random processes: (1) One has to choose such parameters of three-mass vibrating system which will insure the minimum vibration of the most important element. (2) The possibility is envisioned of achieving output motion with minimal errors in a gearing mechanism, without increasing the accuracy of the wheels. It is suggested to achieve this effect by the choice of optimal teeth number combination. A randomized optimization algorithm is considered for these aims.

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