This thesis presents a geometry design method to generate the surfaces of the globoidal cam with the conical roller follower. Based on the trace of the rigid body and the theory of differential geometry, the conjugate surfaces can be the offset surfaces of the ruled surface. With different roller¡¦s axial height, its radius and the meshing vector also be changed. For this reason, the contact points on the outward roller are hard to find. To overcome this problem, we propose the triangular graph with meshing angle, it can present the vector quantity caused from the motion angle. We replace it into the procedures of the rigid body transformation method to derive the cam surfaces with the conical roller follower. Furthermore, two models with modified sine and constant velocity motion curves are generated and analyzed.

The rigid body has been one of the most noteworthy applications of Newtonian mechanics. Applying the principles of classical mechanics to the rigid body is by no means routine. The equations of motion, though discovered two hundred and fifty years ago by Euler, have remained quite elusive since their introduction. Understanding the rigid body has required the applications of concepts from integrable systems, algebraic geometry, Lie groups, representation theory, and symplectic geometry to name a few. Moreover, several important developments in these fields have in fact originated with the study of the rigid body and subsequently have grown into general theories with much wider applications.In this work, we study the stability of equilibria of non-degenerate orbits of the generalized rigid body. The energy-Casimir method introduced by V.I. Arnold in 1966 allows us to prove stability of certain non-degenerate equilibria of systems on Lie groups. Applied to the three dimensional rigid body, it recovers the classical Euler stability theorem [12]: rotations around the longest and shortest principal moments of inertia are stable equilibria. This method has not been applied to the analysis of rigid body dynamics beyond dimension n = 3. Furthermore, no conditions for the stability of equilibria are known at all beyond n = 4, in which case the conditions are not of the elegant longest/shortest type [10].Utilizing the rich geometric structures of the symmetry group G = SO(2n), we obtain stability results for generic equilibria of the even dimensional free rigid body. After obtaining a general expression for the generic equilibria, we apply the energy-Casimir method and find that indeed the classical longest/shortest conditions on the entries of the inertia matrix are suffcient to prove stability of generic equilibria for the generalized rigid body in even dimensions.

The aims of the thesis were to study the response of temporary soil-filled walls both experimentally and numerically, and to develop an efficient and accurate analytical model to predict 2-D planar response from blast loading which could be used to efficiently calculate a pressure-impulse (P-I) curve. An explicit finite element (FE) formulation was constructed using LS-Dyna software, and two analytical models were also derived and presented: a Rigid-Body Rotation model as a preliminary model, and the Rigid-Body Hybrid model as the proposed model of this thesis. Seven full-scale experiments which consisted of blast loading simple free-standing soil-filled Hesco Bastion (HB) walls are presented. Apart from comparison of an experimental result where the soil-fill in the wall possessed sizable cohesion, the response of the Rigid-Body Hybrid model was in very good agreement with the experiments overall (within 10 %). A soil sensitivity study was conducted and overall very good agreement was reached between the Rigid-Body Hybrid model in comparison with the FE model in its ability to capture differences in displacement-time histories from differences in soil parameters. Comparison with the FE model for different height-to-width ratios of walls showed that the Rigid-Body Hybrid model was within 10 % for all rotation angles and predictions of critical overturning impulse for height-to-width ratios of walls . P-I curves were developed using the analytical and FE models for the three different wall configurations studied in the experiments. The results demonstrated that the proposed Rigid-Body Hybrid model is useful for calculating a P-I curve for a HB wall efficiently and yielded very accurate results (within 5 % for the impulse asymptotes).

The aims of the thesis were to study the response of temporary soil-filled walls both experimentally and numerically, and to develop an efficient and accurate analytical model to predict 2-D planar response from blast loading which could be used to efficiently calculate a pressure-impulse (P-I) curve. An explicit finite element (FE) formulation was constructed using LS-Dyna software, and two analytical models were also derived and presented: a Rigid-Body Rotation model as a preliminary model, and the Rigid-Body Hybrid model as the proposed model of this thesis. Seven full-scale experiments which consisted of blast loading simple free-standing soil-filled Hesco Bastion (HB) walls are presented. Apart from comparison of an experimental result where the soil-fill in the wall possessed sizable cohesion, the response of the Rigid-Body Hybrid model was in very good agreement with the experiments overall (within 10 %). A soil sensitivity study was conducted and overall very good agreement was reached between the Rigid-Body Hybrid model in comparison with the FE model in its ability to capture differences in displacement-time histories from differences in soil parameters. Comparison with the FE model for different height-to-width ratios of walls showed that the Rigid-Body Hybrid model was within 10 % for all rotation angles and predictions of critical overturning impulse for height-to-width ratios of walls . P-I curves were developed using the analytical and FE models for the three different wall configurations studied in the experiments. The results demonstrated that the proposed Rigid-Body Hybrid model is useful for calculating a P-I curve for a HB wall efficiently and yielded very accurate results (within 5 % for the impulse asymptotes).

Injury, instrumentation, or surgery may change the functional biomechanics of the spine. Spinal fusion, the current surgical treatment of choice, stabilizes the spine by rigid fixation, reducing spinal mobility at the cost of increased stress at adjacent levels. Recently, alternatives to spinal fusion have been investigated. One such alternative is total disc replacements. The current generation of total disc replacements (TDRs) focuses on restoring the quantity of motion. Recent studies indicate that the moment-rotation response and axis of rotation, or quality of motion (QOM), may have important implications in the health of adjacent segments as well as the health of the surrounding tissue of the operative level. This dissertation examines the use of compliant mechanism design theory in the design and analysis of spinal arthroplasty devices. Particularly, compliant mechanism design techniques were used to develop a total disc replacement capable of replicating the normal moment-rotation response and location and path of the helical axis of motion. Closed-form solutions for the device's performance are proposed and a physical prototype was created and evaluated under a modified F1717 and a single-level cadaveric experiment. The results show that the prototype's QOMclosely matched the selected force-deflection response of the specified QOM profile. The use of pseudo-rigid-body modeling to evaluate the effects of various changes on motion at adjacent segments is also investigated. The ability to model biomechanical changes in the spine has traditionally been based on animal models, in vitro testing, and finite element analysis. These techniques, although effective, are costly. As a result, their use is often limited to late in the design process. The pseudo-rigid-body model (PRBM) developed accurately predicted the moment-rotation response of the entire specimen and the relative contribution of each level. Additionally, the PRBM was able to predict changes in relative motion patterns of the specimen due to instrumentation.

We introduce to computer graphics the Pseudo-Rigid-Body Mechanism (PRBM) and the chain algorithm from mechanical engineering, with a unified tutorial from disparate source materials. The PRBM has been used successfully to simplify the simulation of non-linearly elastic beams, using deflections of an analogous spring and rigid-body linkage. It offers computational efficiency as well as an automatic parameterization in terms of physically measurable, intuitive inputs which fit naturally into existing animation work flows for character articulation. The chain algorithm is a technique for simulating the deflection of complicated elastic bodies in terms of straight elastic elements, which has recently been extended to incorporate PRBM beam-elements in three dimensions. We present a new, mathematically equivalent optimization of the 3D PRBM chain algorithm, from its former asymptotic complexity of O(n^2) in the number of elements n, to O(n). We also extend an existing PRBM for combined moment-force loads to 3D, where the existing 3D PRBM chain algorithm was limited to 3D PRBM elements for a moment-only load. This optimization and extension are validated by duplicating prior experimental results, but substituting the new optimization and combined-load elements. Finally, a loose road-map is provided with several key considerations for future extension of the techniques to dynamic simulations.

This research provides realistic techniques to visualize the process of damage to residential building caused by hurricane force winds. Three methods are implemented to make the visualization useful for educating the public about mitigation measures for their homes. First, the underline physics uses Quick Collision Response Calculation. This is an iterative method, which can tune the accuracy and the performance to calculate collision response between building components. Secondly, the damage process is designed as a Time-scalable Process. By attaching a damage time tag for each building component, the visualization process is treated as a geometry animation allowing users to navigate in the visualization. The detached building components move in response to the wind force that is calculated using qualitative rather than quantitative techniques. The results are acceptable for instructional systems but not for engineering analysis. Quick Damage Prediction is achieved by using a database query instead of using a Monte-Carlo simulation. The database is based on HAZUS® engineering analysis data which gives it validity. A reasoning mechanism based on the definition of the overall building damage in HAZUS® is used to determine the damage state of selected building components including roof cover, roof sheathing, wall, openings and roof-wall connections. Exposure settings of environmental aspects of the simulated environment, such as ocean, trees, cloud and rain are integrated into a scene-graph based graphics engine. Based on the graphics engine and the physics engine, a procedural modeling method is used to efficiently render residential buildings. The resulting program, Hurricane!, is an instructional program for public education useful in schools and museum exhibits.

No description available.

A multidisciplinary approach for the modeling and analysis of the performance of Olympic rowing boats is presented. The goal is to establish methodologies and tools that would determine the effects of variations in applied forces and rowers motions and weights on mean surge speed and oscillatory boat motions. The coupling between the rowers motions with the hull and water forces is modeled with a system of equations. The water forces are computed using several fluid dynamic models that have different levels of accuracy and computational cost. These models include a solution of the Reynolds Averaged Navier--Stokes equations complemented by a Volume of Fluid method, a linearized 3D potential flow simulation and a 2D potential flow simulation that is based on the strip theory approximation. These results show that due to the elongated shape of the boat, the use of Sommerfeld truncation boundary condition does not yield the correct frequency dependence of the radiative coefficients. Thus, the radiative forces are not computed in the time-domain problem by means of a convolution integral, accounting for flow memory effects, but were computed assuming constant damping and added mass matrices. The results also show that accounting for memory effects significantly improves the agreement between the strip theory and the RANS predictions. Further improvements could be obtained by introducing corrections to account for longitudinal radiative forces, which are completely neglected in the strip theory. The coupled dynamical system and the multi-fidelity fluid models of the water forces were then used to perform a sensitivity analysis of boat motions to variations in rowers weights, exerted forces and cadence of motion. The sensitivity analysis is based on the polynomial chaos expansion. The coefficients of each random basis in the polynomial chaos expansion are computed using a non-intrusive strategy. Sampling, quadrature, and linear regression methods have been used to obtain the these coefficients from the outputs generated by the system at each sampling point. The results show that the linear regression method provides a very good approximation of the PCE coefficients. In addition, the number of samples needed for the expansion, does not grow exponentially with the number of varying input parameters. For this reason, this method has been selected for performing the sensitivity analysis. The sensitivity of output parameters to variations in selected input parameters of the system are obtained by taking the derivatives of the expansion with respect to each input parameter. Three test cases are considered: a light-weight female single scull, a male quad scull, and a male coxless four. For all of these cases, results that relate the effects of variations in rowers weights, amplitudes of exerted forces and cadence of rowing on mean boat speed and energy ratio, defined as the ratio of kinetic energy of the forward motion to that of the oscillatory motions, are presented. These results should be useful in the design of rowing boats as well as in the training of rowers. / Ph. D.

In flexible fitting, the high-resolution crystal structure of a molecule is deformed to optimize its position with respect to a low-resolution density map. Solving the flexible fitting problem entails answering the following questions: (A) How can the crystal structure be deformed? (B) How can the term "optimum" be defined? and (C) How can the optimization problem be solved? In this dissertation, we answer the above questions in reverse order. (C) We develop PFCorr, a non-uniform SO(3)-Fourier-based tool to efficiently conduct rigid-body correlations over arbitrary subsets of the space of rigid-body motions. (B) We develop PF2Fit, a rigid-body fitting tool that provides several useful definitions of the optimal fit between the crystal structure and the density map while using PFCorr to search over the space of rigid-body motions (A) We develop PF3Fit, a flexible fitting tool that deforms the crystal structure with a hierarchical domain-based flexibility model while using PF2Fit to optimize the fit with the density map. Our contributions help us solve the rigid-body and flexible fitting problems in unique and advantageous ways. They also allow us to develop a generalized framework that extends, breadth-wise, to other problems in computational structural biology, including rigid-body and flexible docking, and depth-wise, to the question of interpreting the motions inherent to the crystal structure. Publicly-available implementations of each of the above tools additionally provide a window into the technically diverse fields of applied mathematics, structural biology, and 3D image processing, fields that we attempt, in this dissertation, to span. / text