A two-wheeled self-balancing robot is considered for investigating the responses of a control moment gyroscope powered by a proportional controller to prevent the robot rollover against the constant inertia forces because of accelerations of the wheels of the robot. The amplitudes of the frequency equations related to the required angular momentum of flywheels with an optimum controller gain were also found. A simulation model of the robot using computer-aided engineering software (RecurDyn) is built to verify the equations of a Lagrangian model. The results of both obtained from the Lagrangian and that from RecurDyn simulations are analyzed comparatively, in which the proportional control loop reduces the required flywheel speeds Ω of gyros and keeps the robot in a very small amplitude of a stable sinusoidal motion in the upright position.

Inthispaper, the characteristics of a vibration control system utilizing a gyro and its effectiveness in the control of the motion subjected to a seismic ground motion acceleration were studied. A gyro design was presented as a vibration absorber for reduction of the column vibration, which has a potential for application to towers, high-rise buildings and other structures.Thenon-linear motions of the gyro-column system and the equations of motion for the system are derived following energy (Lagrange) based approaches and examples provided. On the otherhand, the effect of the angular velocity of thegyroscope is studied, and it is shown that the angular velocity (spin velocity) Ω of gyroscope has a significant effect on the behavior of the dynamic motion.It is also shown how the damper and spring due to the motion between the suporting gimbaland tip mass influence the dynamic behavior of the gyroscope

In this paper, an experimental model of a horizontal cantilever beam with a rotating/oscillating attached to the shaker for harmonic excitation at the one end and a gyrostabilizer at the other end is built to verify the equations of the Lagrangian model. The primary focus of the study was to investigate the parameters of excitation amplitude, natural frequency, rotating mass (disk mass), and disk speed of gyro that would minimize the amplitude of the beam to identify these effects. Numerical and experimental results indicate that the angular momentum of the gyrostabilizer is the most effective parameter in the reduction of beam displacement.

Two-wheeled robots are popular in transportation applications because of their high maneuverability. In this research, the oscillation attenuation performance of the control moment gyroscope (CMG) for the two-wheeled robot was studied. The stored kinetic energy of a CMG can offer a weight and volume saving compared to conventional vibration absorbers. This CMG is also more reactionless than other conventional absorbers by transforming the impact of angular momentum to unidirectional thrust along the center of gravity. The gimbals can precess while providing the angular momentum under the gravitational force. This study indicated that the CMG can operate in a wide range of excitation frequencies to balance the robot in a stable period. Because the flywheel speed is much easier changed to thrust against the unwanted oscillations disturbing the robot stability. There is a relation between the gimbal amplitude and the flywheel speed of CMG, in which the required flywheel speed can be reduced if the higher gimbal amplitude is chosen. It can be also concluded from the study that the oscillation amplitudes at the target frequency can decrease as much as flywheel speed increases. There was also a mathematical model using ANSYS software. The simulation results using ANSYS matched well with the theoretical results of the Lagrangian model.

This paper deals with the investigation of optimum values of the stiffness and damping which connect two gyroscopic systems formed by two rotors mounted in gimbal assuming negligible masses for the spring, damper, and gimbal support. These coupled gyroscopes use two gyroscopic flywheels, spinning in opposing directions to have reverse precessions to eliminate the forces due to the torque existing in the torsional spring and the damper between gyroscopes. The system is mounted on a vertical cantilever with the purpose of studying the horizontal and vertical vibrations. The equation of motion of the compound system (gyro-beam system) is introduced and solved to find the response measured on the primary system. This is fundamental to design, in some way, the dynamic absorber or neutralizer. On the other hand, the effect of the angular velocities of the gyroscopes are studied, and it is shown that the angular velocity (spin velocity) of a gyroscope has a significant effect on the behavior of the dynamic motion. Correctness of the analytical results is verified by numerical simulations. The comparison with the results from the derivation of the corresponding frequency equations shows that the optimized stiffness and damping values are very accurate.

In this article, gyroscopes and flywheels are used to prevent the rollover of a vehicle due to external forces. The rollover preventing performance of the flywheels for a heavy trailer (an inverted pendulum problem) is investigated at a high road bank angle risk. Two control moment gyroscopes (CMG) and a reaction wheel are controlled by proportional torques to keep the vehicle in a stable motion in the vertical position. The reaction wheel was used only to eliminate the dissipation energy of damper. By using the energy stored in the flywheels of gyroscopes, the sprung mass of a vehicle can make a stable oscillating motion of small amplitude, standing upright without tipping over. The optimum flywheel speed was derived from the frequency equations with the appropriate controller gain. Most importantly, the required angular momentum to keep the vehicle upright without tipping over depends on the amplitude of the gimbal oscillation and the frequency. It has also been observed that Matlab simulations of Lagrangian equations and simulations modeled in RecurDyn software are in perfect harmony.