| Gyroscopes are one of the most widely used devices for measuring the angle of rotation or the rate of change of angular rotation. In the last few years, the advent of micromachining technology has made it possible to fabricate high performance Micromachined Electro-Mechanical Systems (MEMS) gyroscopes at a relatively low cost. Of the various types of MEMS gyroscopes, vibrating beam type, are the most commonly used, but they have a main drawback (cross-axis effect) which significantly affects their measurement and results in much error. In view of this, the present work focuses on a gyroscope, called rocking-mass gyroscope, which does not have that drawback at all and can give a very precise measurement.;The rocking-mass gyroscope consists of an assembly of four cantilever beams with a rigid mass attached to them in the middle subjected to base rotations. Due to the gyroscopic effect, the beams undergo coupled flexural-torsional vibrations. The main goal of the research is to develop an accurate model of such a system and along this line a detailed mathematical modeling of the gyroscope is developed for a macro-scaled system. The equations of motion clearly show the presence of the gyroscopic couplings in all cantilever beams. In order to analyze the effectiveness of this type of gyroscope a computer simulation model in its most general form has been developed. Before deriving the governing equations of motion for a rocking-mass gyroscope, a detailed mathematical model of a single beam gyroscope was considered to investigate the cross-axis effect in this type of gyroscopes.;The characteristic equation of a rocking-mass gyroscope, using an exact method, is derived, and the fundamental frequency of the vibration and the corresponding mode shape are obtained. Finally, the time history diagram of this system is presented to illustrate the dynamic response of the system. Simulation results show that the bending vibrations induced in the second and the forth beams are directly proportional to the magnitude of the base rotation. Therefore, the gyroscope can be widely used as a device for measuring the base rotation velocity.;Keywords. Rocking-mass gyroscope; Vibrating beam gyroscope; Extended Hamilton's principle; Frequency analysis; Mathematical modeling. |
