To understand control strategies employed by the central nervous system (CNS) control movement or force generation in a limb, a seven degree of freedom cat hindlimb was modeled. In this study, the biomechanical constraints affecting force generation for balance and postural control were investigated. Due to the redundancies at the muscular and joint levels in the musculoskeletal system, even the muscle coordination pattern to statically produce a certain amount of force/torque at the ground is not straightforward. A 3D musculoskeletal model of the cat hindlimb was created from cat cadaver measurements using Software for Interactive Musculoskeletal Systems (SIMM, Musculographics, Inc.). Six kinematic degrees of freedom and 31 individual hindlimb muscles were modeled. The moment arms of the muscles were extracted from the software model to be used in a linear transformation between muscle activation, and end effector force and moment. The Jacobian matrix that establishes the relationship between joint torques and end effector wrench was calculated. Maximal muscle forces were estimated from the literature. A feasible set of forces that can be generated at the toe was constructed using combination of maximally activated muscle excitations. Because the endpoint torque is typically small in a cat, an optimization algorithm was also performed to maximize the force generation at the end effector while constraining the magnitude of the endpoint torque. The results are compared with the measured force magnitude and direction data from an acute cat hindlimb preparation for different postures. This static model is applicable for understanding muscle coordination during postural responses to small balance perturbations.

We study the Cohen-Macaulay property of Rees algebras of modules of Kähler differentials. When the module of differentials has projective dimension one, it is known that condition $F_1$ is sufficient for the Rees algebra to be Cohen-Macaulay. The converse was proved if the module of differentials is already $F_0$. We weaken the condition $F_0$ globally by assuming some homogeneity condition.<br> <br> We are also interested in the defining ideal of the Rees algebra of a Jacobian module. If the Jacobian module is an ideal, we prove a formula for computing the defining ideal. Using the formula, we give an explicit description of the defining ideal in the monomial case. From there, we characterize the Cohen-Macaulay property of the Rees algebra.<br> <br> In the last chapter, we study Gorenstein linkage mostly in the graded case. In particular, we give an explicit example of a class of monomial ideals that are in the homogeneous Gorenstein linkage class of a complete intersection. To do so, we prove a Gorenstein double linkage construction that is analogous to Gorenstein biliaison.

We establish consistent definitions for divisors, principal divisors, and Jacobians of a tropical elliptic curve and show that for a tropical elliptic cubic C , the associated Jacobian (or zero divisor class group) is the group S^1(Q).

Distortion tolerant fans represent the enabling technology for the successful implementation of highly integrated airframe propulsion system vehicles. This investigation extends the study of fan-distortion interactions to an actual turbofan engine with a total pressure distortion profile representative of a boundary-layer ingesting (BLI) embedded engine. The goal was to make a series of flow measurements that contribute to the overall physical understanding of this complex flow situation. Proper uncertainty analysis is critical to extracting meaning from the data measured in this study. The important information in the measurements is contained in small differences that lead to large impacts on the fan performance. In some cases, these differences were measured to a useful degree of accuracy, while in others they were not. One important application of the uncertainty analysis techniques developed in this work is the identification of the dominant error sources that resulted in unacceptable uncertainties. This dissertation presents an experimental study of transonic fan response to inlet total pressure distortion. A Pratt and Whitney JT15D-1 turbofan engine was subjected to a total pressure distortion representative of a boundary layer ingesting serpentine inlet. A 5-hole probe measured the aerodynamic response of the fan rotor in terms of flow angles, total pressure, and static pressure. A thermocouple embedded in the probe measured the rotor outlet total temperature. These measurements enabled the full characterization of the flow condition at each measurement point. The results indicate that a trailing edge separation and reattachment cycle experienced by the blades caused variations in the work input to the flow and resulted in a non-uniform rotor outlet flow profile. The details of the aerodynamic process and several means for improving distortion response are presented in this context. As a second theme, the modern measurement and uncertainty analysis techniques required to obtain useful information in this situation are developed and explored. Uncertainty analysis is often treated as a less glamorous afterthought in experimental research. However, as technology develops along lines of ever increasing system-level integration, simply suggesting the solution to a single flow situation does not repre- sent closure to the larger problem. In addition to frameworks for developing distortion tolerant fans, frameworks for developing frameworks are required. Uncertainty-drivenexperimental techniques represent the enabling methodology for the discovery and un- derstanding of the subtle phenomena associated with such coupled performance. These considerations are required to extend the usefulness of the results to the overarching issue of integrating the complex performance of individual components into an overall superior system. The experimental methods and uncertainty analysis developed in this study are presented in this context. / Ph. D.

No description available.

No description available.

No description available.

Many mechanical systems exhibit nonlinear movement and are subject to perturbations from a desired equilibrium state. These perturbations can greatly reduce the efficiency of the systems. It is therefore desirous to analyze the asymptotic stabilizability of an equilibrium solution of nonlinear systems; an excellent method of performing these analyses is through study of Jacobian linearization's and their properties. Two enlightening examples of nonlinear mechanical systems are the Simple Inverted Pendulum and the Inverted Pendulum on a Cart (PoC). These examples provide insight into both the feasibility and usability of Jacobian linearizations of nonlinear systems, as well as demonstrate the concepts of local stability, observability, controllability and detectability of linearized systems under varying parameters. Some examples of constant disturbances and effects are considered. The ultimate goal is to examine stabilizability, through both static and dynamic feedback controllers, of mechanical systems

This thesis mainly focuses on proposing a 4D (three spatial dimensions plus time) tissue-volume preserving non-rigid image registration algorithm for pulmonary 4D computed tomography (4DCT) data sets to provide relevant information for radiation therapy and to estimate pulmonary ventilation. The sum of squared tissue volume difference (SSTVD) similarity cost takes into account the CT intensity changes of spatially corresponding voxels, which is caused by variations of the fraction of tissue within voxels throughout the respiratory cycle. The proposed 4D SSTVD registration scheme considers the entire dynamic 4D data set simultaneously, using both spatial and temporal information. We employed a uniform 4D cubic B-spline parametrization of the transform and a temporally extended linear elasticity regularization of deformation field to ensure temporal smoothness and thus biological plausibility of estimated deformation. A multi-resolution multi-grid registration framework was used with a limited-memory Broyden Fletcher Goldfarb Shanno (LBFGS) optimizer for rapid convergence rate, robustness against local minima and limited memory consumption. The algorithm was prototyped in Matlab and then fully implemented in C++ in Elastix package based on the Insight Segmentation and Registration Toolkit (ITK). We conducted experiments on 2D+t synthetic images to demonstrate the effectiveness of the proposed method. The 4D SSTVD algorithm was also tested on clinical pulmonary 4DCT data sets in comparison with existing 3D pairwise SSTVD algorithm and 4D sum of squared difference (SSD) algorithm. The mean landmark error and mean landmark irregularity were calculated based on manually annotated landmarks on publicly available 4DCT data sets to evaluate the accuracy and temporal smoothness of the registration results. A 4D landmarking software tool was also designed and implemented in Java as an ImageJ plug-in to help facilitate the landmark labeling process in 4DCT data sets.

Parallel manipulators have been the subject of study of much robotic research during the past three decades. A parallel manipulator typically consists of a moving platform that is connected to a fixed base by at least two kinematic chains in parallel. Parallel manipulators can provide several attractive advantages over their serial counterpart in terms of high stiffness, high accuracy, and low inertia, which enable them to become viable alternatives for wide applications. But parallel manipulators also have some disadvantages, such as complex forward kinematics, small workspace, complicated structures, and a high cost. To overcome the above shortcomings, progress on the development of parallel manipulators with less than 6-DOF has been accelerated. However, most of presented parallel manipulators have coupled motion between the position and orientation of the end-effector. Therefore, the kinematic model is complex and the manipulator is difficult to control. Only recently, research on parallel manipulators with less than six degrees of freedom has been leaning toward the decoupling of the position and orientation of the end-effector, and this has really interested scientists in the area of parallel robotics. Kinematic decoupling for a parallel manipulator is that one motion of the up-platform only corresponds to input of one leg or one group of legs. And the input cannot produce other motions. Nevertheless, to date, the number of real applications of decoupled motion actuated parallel manipulators is still quite limited. This is partially because effective development strategies of such types of closed-loop structures are not so obvious. In addition, it is very difficult to design mechanisms with complete decoupling, but it is possible for fewer DOF parallel manipulators. To realize kinematic decoupling, the parallel manipulators are needed to possess special structures; therefore, investigating a parallel manipulator with decoupling motion remains a challenging task. This thesis deals with lower mobility parallel manipulator with decoupled motions. A novel parallel manipulator is proposed in this thesis. The manipulator consists of a moving platform that is connecting to a fixed base by three legs. Each leg is made of one C (cylinder), one R (revolute) and one U (universal) joints. The mobility of the manipulator and structure of the inactive joint are analyzed. Kinematics of the manipulator including inverse and forward kinematics, velocity equation, kinematic singularities, and stiffness are studied. The workspace of the parallel manipulator is examined. A design optimization is conducted with the prescribed workspace. It has been found that due to the special arrangement of the legs and joints, this parallel manipulator performs three translational degrees of freedom with decoupled motions, and is fully isotropic. This advantage has great potential for machine tools and Coordinate Measuring Machine (CMM). / UOIT