Analysis, design, optimisation and testing of a gyroscopically stabilized platform
Thesis DisciplineMechanical Engineering
Degree GrantorUniversity of Canterbury
Degree NameDoctor of Philosophy
Gyroscopic stabilization can be used to maintain an otherwise unstable body in an upright position. Devices equipped with gyroscopes can balance upon a small area or point without falling over when the gyroscopic stabilizing force is greater than a rotational force or moment from an out-of-balance load that causes the device to tip.
A new concept for a gyroscopically stabilized platform has been proposed in the form of a schematic diagram. The proposed system comprises of four interconnected gyroscopes that react to the tipping of an inherently unstable external body. The purpose of this research is to evolve a design for, and establish the feasibility of building the proposed stable platform using available materials and technology. If feasible, the gyroscopically stabilized platform will be made at the most practical and economic size.
Louis Brennan developed a 37 tonne monorail that was maintained in the upright position with two 3 tonne counter rotating gyroscopes. The Brennan monorail is analysed to better understand the behaviour of a similar coupled gyroscopic stabilization system. The reactions between the components that maintain the monorail in the stable position are studied and comparisons are made between the proposed stable platform and the Brennan system.
A mathematical analysis of the proposed system is presented. The equations of motion for the system are derived using the Lagrangian Formalism. The characteristic equation of the system is then determined and from this a set of stability conditions imposed on the design of the physical parameters of the stable platform. The general solutions to the equations of motion are then derived. Expressions that model the behaviour of two of the variables that describe the motion of the stable platform are determined.
A systematic approach is adopted for establishing a new concept for the proposed system. Testing of the initial stable platform prototype (Prototype A) showed the system did not behave as intended. The platform was optimised further and this resulted in a second prototype, Prototype B. Prototype B exhibiting the desired oscillatory motion about the vertical of the platform.
Predictions made using the mathematical model are compared with empirical results. The mathematical model was found to be an accurate method for predicting the response of the stable platform.