The dissertation presents dynamic modeling and analysis of single rigid bodies, gyroscopic multi-body systems, and flexible robotics through the use of the moving frame method. Before analyzing the projects at hand, a brief introduction to the moving frame method will be presented. To properly model the gyroscopic systems and flexible robots, it is first necessary to establish the kinematical description of freely rotating bodies. To demonstrate the validity and efficacy of the method, it is applied to solve the mystery of the Dzhanibekov and tennis racket phenomena. It is known that a rotation about the intermediate principal moment of inertia axis becomes unstable, leading many to incorrectly conclude a violation of the conservation of angular momentum. Using the moving frame method, the torque-free Euler equations are clearly obtained and a complete explanation, including a geometric, analytic, and numerical solution is presented along with 3D animations to demonstrate that the conservation of angular momentum is truly preserved.
As an application of the moving frame method to rigid-multibody systems, analysis of two offshore gyroscopic structures will be performed. First, a gyroscopic ocean wave energy converter (GOWEC) is analyzed. The GOWEC is a fully enclosed ocean wave energy device that converts the rocking or pitching motion induced by the ocean waves into electricity. In this dissertation, the mathematical model of the energy converter is derived and the ideal conditions for maximum power output are identified. Second, as a natural extension of the GOWEC, the application of gyroscopes as a means of stabilization is examined. The active gyroscopic ship stabilizer uses the gyroscopic principles to cancel the rolling motion induced by the ocean waves. Of specific interest is the application of active gyroscopic roll stabilizers in ships to further aid in the safe transport of passengers and transfer of equipment onto platforms and offshore wind farm structures. The main parameters of the gyroscopic stabilizer are characterized and their effect on the ship is analyzed.
Lastly, modeling and analysis of flexible robots with internal actuation is presented. Two mechanical models for flexible or soft robots are derived: (i) a discrete multi-link model consisting of rigid links with elastic torsional springs at actuating joints. and (ii) a continuous beam model with distributed internal actuation. As an application of the continuous beam model, an inchworm with multiple actuation curvature fields is presented. With the flexible mechanical models, it is possible to know the internal actuation necessary for soft robots to reproduce desired shapes and resulting maneuvers. Furthermore, the nonlinear finite element equations along with active C^((1))-beam elements are developed and
used to create a finite element code