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This thesis introduces a novel parametric beam model for describing the kinematics and elastic properties of ortho-planar compliant Micro-Electro-Mechanical Systems (MEMS) with straight beams subject to specific buckling loads. Ortho-planar MEMS have the ability to achieve motion out the plane on which they were fabricated, characteristic that can be used to integrate optical devices such as variable optical attenuators and micro-mirrors. In addition, ortho-planar MEMS with large output forces and long strokes could be used to develop new applications such as tactile displays, active Braille, and actuation of micro-mirrors. In order to analyze the kinematics and elasticity of a curved beam contained in a Micro Helico-Kinematic Platform (MHKP) device, this thesis offers an improved model of straight and curved flexures under compressive loads. This model uses an approach similar to the one applied to develop a regular Pseudo-Rigid -Body Model but it differs in the definition of a key parameter, the characteristic radius factor, γ, which is not a constant, but a function of the moment, γ*=γ(M) . This approach allows for the Pseudo-Rigid-Body Model (PRBM) to describe the motion taken by the deflected beam precisely over a large range of motion. In developing the model, this thesis describes kinematic and elastic parameters such as the angle coefficient, C9, the characteristic radius, γl, and the torque coefficient, Tθ. Furthermore, the torque coefficient is divided into two component functions, Tf, and, Tm, which can be used to find the working loads (force and moment) on the beam. The input displacement is the only needed state variable, object variables, which describe the beam, include the material modulus of elasticity, E, the moment of inertia, I, and its length, l.

The work in this thesis is concerned with the generation of Lumped Parameter Models (LPM) for two, slender, torpedo shaped, X-fin craft. This process involves the use of CFD to simulate captive maneuvers that are normally performed using test equipment in the field. These captive maneuvers are refereed to as planar motion mechanisms (PMM), and when simulated through CFD are refereed to as virtual planar motion mechanisms (VPMM). The results from VPMM are used to determine the hydrodynamic derivatives that inform the LPM. There was some inconsistency in the VPMM data based on the frequency and amplitude that the VPMM was run. A brief study was run to look at this effect. Afterwards, Open and closed loop, autopilot assisted, maneuvers are implemented and performed using the LPM model through Simulink. Results of these maneuvers are analyzed for craft stability. Additionally, comparisons of LPM maneuvers to field data are performed. Critiques of the craft stability and effect of the autopilot are made. / Master of Science / The work carried out in this thesis involves the creation of a physics based model of an underwater craft. This physics based model is informed through characteristics determined by running computational fluid dynamics (CFD) simulations. The benefit of such a model, is the simplification from CFD to a 6 degree of freedom (6-DOF) lumped parameter model (LPM). These physics models, LPM, are generated for two particular craft of interest. One craft is an existing design used by NUWC (named Tonnetto), while the other design is one generated to be similar in shape and size to the NUWC craft (named Hokie). Computer simulated maneuvers are carried out using these models to asses craft stability and performance. An autopilot is implemented into the models for some of these simulations to see its affects on the crafts performance. Additionally, these simulated maneuvers are compared to field data collected by NUWC.

Recent developments in autonomous underwater vehicles (AUV) have created the need for a low cost AUV that is comparable in class and payload capabilities to existing, commercially available, expensive and sub-optimal crafts. The Navy is active in research of autonomous, unmanned, highly efficient, high speed underwater craft. Small, low cost AUVs capable of swarm control are of special interest for military mine applications. No matter the nature of the application or class of craft, a common challenge is the accuracy of maneuvering predic- tions. Maneuvering predictions not only affect design, but also the real time understanding of mission capabilities and endurance. Thus the proliferation of AUVs in recent times for commercial and defense applications have led to the need of higher fidelity of physics based lumped parameter models. The sensor data, along with maneuvering model data can tie into a more accurate trajectory. Multiple such incremental advances in the literature for prediction of maneuvering shall lead to a more accuracy. This work hopes to bridge some important gaps that ensure the creation of such a non-linear LPM to predict the maneuver- ing characteristics of an AUV using non linear hydrodynamic derivatives obtained through static and dynamic CFD. This model shall be implemented for the craft designed for DIVE technologies, our industrial sponsor and an in-house craft, the 690. This model shall also be made generalized for most submerged craft with a torpedo or slender hull form, with cruciform or X configuration of fins. This dissertation looks to provide the framework to identify CFD informed high fidelity dynamic model for AUVs. The model thus created shall be spe- cialized to account for specific important effects such as flow interaction among appendages, effect of using steady and unsteady maneuvers as CFD information and kinematic charac- teristics of captive maneuvers. The specific, innovative contributions in this dissertation are listed below: 1. Definition of a new stability index to incorporate effects of gravity at low-moderate speeds 2. Novel method for identification of hydrodynamic derivatives 3. Systematic and comprehensive study on the parameters affecting VPMM / Doctor of Philosophy / The maneuvering model for an AUV is an indispensable tool that makes the autonomy part of AUVs possible and efficient. The maneuvering model that exists today is mostly linearized and of lower fidelity to increase efficiency. The use of a non linear, higher order hydrodynamic model facilitates better accuracy of maneuvering predictions, essential to mission completion of AUVs applied in research and defense sectors. This higher fidelity can be achieved through informing the model using CFD that is reasonably efficient in computation. This dissertation presents a non-linear, higher order hydrodynamic maneuvering model for the 690 and DIVE crafts, informed with steady and unsteady CFD.

PMM testing is a method used to identify the added mass and damping coefficients used in the equations of motion of a vehicle by attempting to decouple the forces on a body due to velocity and acceleration as a result of creating "hydrodynamically pure" velocities and accelerations. This makes it possible to use quasi-steady state models with terms independent of both velocity and acceleration. This paper explores the ability of simple damping models (solely a function of velocity) with added mass terms (solely a function of acceleration) to simulate the heave force of an 8:1 ellipsoid undergoing PMM testing. In order to help explain the complexity of the flow during PMM tests, a flow analysis of the 8:1 spheroid is provided, which discusses the flow topology of spheroids at steady angle of attack, validity of quasi-steady models, and some other basic flow features seen in PMM testing. In this paper, a simple proportionality relationship between a linear and quadratic damping model is revealed. It is also shown that variations in the heave force response during PMM tests are most heavily influenced by viscous effects, especially cross flow separation. Finally, it is shown where these models break down, owing to the increasing nonlinearity of the flow induced by the harsher motions of large amplitude and/or large frequency tests. / Master of Science

For a general J wheeled mobile platform capable of up to 3-Degrees-Of-Freedom (DOF) planar motion, there are up to 2J independent input parameters yet the output of the planar platform is specified with only three independent parameters. Currently, the motion synthesis for such platforms is done with a Jacobian based “pseudo” inverse that uses a rectangular matrix for Jacobian. However, a mobile platform is a parallel mechanism and has a more direct solution to the inverse kinematics problem. To this effect, we propose a physical methodology for kinematic modeling of multi-wheeled mobile platforms using Instant Centers (IC) to describe the kinematic state of all system points up to the kth order using a generalized algebraic formulation. This is achieved by using a series of ICs (velocity, acceleration, jerk, etc.) where each point in the system has a time state with its magnitude proportional to the radial distance of the point from the associated IC and at a constant angle relative to that radius. The use of IC’s for mobile platform kinematics is not new, however we present a completely generalized and extensive formulation that also treats the higher order kinematics. To the best of our knowledge, this is the first time the third and higher order ICs have been presented in the literature. The components of this research effort are: (i) extension of the theory of instantaneous invariants to the higher order motion by generalizing the theory to any order, (ii) studying some special case 1-DOF, 2-DOF motions to understand the physical nature of the higher order ICs, (iii) applying the results of (i) and (ii) to the motion synthesis of planar, wheeled mobile platforms by first categorizing them into four distinct categories, and (iv) studying the dynamic model of a representative mobile platform to emphasize the importance of wheel dynamics and traction parameters on the performance of the mobile platform. The IC based formulation presents a concise expression for a general order time state of a general point on the rigid body with the magnitude and direction separated and identified. We showed that the method based on instant centers provides a straightforward and yet physically intuitive way to synthesize a general kth order planar motion of mobile platforms. The study of special case 1-DOF/2-DOF motions emphasized the geometric nature of the higher order ICs and also helped understand the influence of instantaneous kinematic states (such as angular velocity _, angular acceleration, _, etc.) on the various ICs. The application of this theory to planar mobile platform allowed us to categorize the platforms based on their dexterity and to generalize the motion synthesis to some extent. The study of the dynamic model of a representative mobile platform showed us that the redundant inputs (2J inputs versus 3 outputs) in this case may be employed to sustain and manage the uncertainties and nonlinearities in the wheel ground interaction. / text