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Mechanical gyroscopes are actuators used for balancing and steering purposes due to their ability to generate torque, fast dynamic responses, high efficiency and control linearity. Analytical methods are available for their mechanical designs. Also optimization can be made thanks to simulations. In this study, the optima of the dimension and rotational speed, which are the basis for the design of a mechanical gyroscope, were determined by using the flexible body dynamic simulation and optimization method. The effects of the main structural parameters on the vibration frequency were also determined. The gyroscope has a flywheel and produces torque owing to its own weight. Classical (Newtonian) mechanics principles were followed. As a result, suitable gyroscope dimension and rotational velocity were determined. Thanks to the response function of the optimization, the relationships between the parameters were also determined. Initially, the disc thickness is 10 mm, the radius is 100 mm, the rotor diameter is 20 mm, and the length is 115 mm, while the optimum rotor length is 30 mm, the rotor radius is 30 mm, the disc radius is 265 mm, the thickness is 12 mm, and the operating speed is 400 rad/s. By using the optima, it has been ensured that the nutation, mass, energy consumption are minimized, the torque is maximized, thus it has a service life of more than one million cycle. [ABSTRACT FROM AUTHOR]