This thesis presents two unique micro-motion parallel kinematic manipulators (PKM): a three degrees of freedom (3-DOF) micro-motion manipulator and a 3-DOF micro-motion manipulator with actuation redundancy. The 3-DOF micro-motion manipulator has three linear-motion driving units, and the 3-DOF micro-motion manipulator with redundancy has four of these units. For both designs, the linear motion driving units are identical, and both machines have a passive link in the center of the structure. The purpose of this passive link is to restrain the movement of the manipulator and to improve the stiffness of the structure. As a result, both structures support 3-DOF, including one translation on the Z-axis and two rotations around the X and Y axes. The manipulator with redundancy is designed to prevent singularity and to improve stiffness. In this thesis, the inverse kinematic, Jacobian matrix and stiffness analyses have been conducted, followed by the design optimization for structures. Finally, the FEA (Finite Element Analysis) and dynamic analysis have also been performed. There are many practical applications for micro-motion parallel manipulators. The typical applications include micro-machine assembly, biological cell operation, and microsurgery . / UOIT

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.

In many problems involving the solution of a system of nonlinear equations, it is necessary to keep an approximation to the Jacobian matrix which is updated at each iteration. Computational experience indicates that the best updates are those that minimize some reasonable measure of the change to the current Jacobian approximation subject to the new approximation obeying a secant condition and perhaps some other approximation properties such as symmetry. All of the updates obtained thus far deal with updating an approximation to an nxn Jacobian matrix. In this thesis we consider extending most of the popular updates to the non-square case. Two applications are immediate: between-step updating of the approximate Jacobian of f(X,t) in a non-autonomous ODE system, and solving nonlinear systems of equations which depend on a parameter, such as occur in continuation methods. Both of these cases require extending the present updates to include the nx(n+l) Jacobian matrix, which is the issue we address here. Our approach is to stay with the least change secant formulation. Computational results for these new updates are also presented to illustrate their convergence behavior.

No description available.

In the adaptive finite element method, the solution of a p.d.e. is approximated from finer and finer meshes, which are controlled by error estimators. So, starting from a given coarse mesh, some elements are subdivided a couple of times. We investigate the question of avoiding instabilities which limit this process from the fact that nodal coordinates of one element coincide in more and more leading digits. In a previous paper the stable calculation of the Jacobian matrices of the element mapping was given for straight line triangles, quadrilaterals and hexahedrons. Here, we generalize this ideas to linear and quadratic triangles on curved boundaries.

Rhythmic motion is ubiquitous in nature and technology. Various motions of organisms like the heart beating and walking require stable periodic execution. The stability of the rhythmic execution of human movement can be altered by neurological or orthopedic impairment. In robotics, successful development of legged robots heavily depends on the stability of the controlled limit-cycle. An accurate measure of the stability of rhythmic execution is critical to the diagnosis of several performed tasks like walking in human locomotion. Floquet multipliers have been widely used to assess the stability of a periodic motion. The conventional approach to extract the Floquet multipliers from actual data depends on the least squares method. We devise a new way to measure the Floquet multipliers with reduced bias and estimate orbital stability more accurately. We show that the conventional measure of the orbital stability has bias in the presence of noise, which is inevitable in every experiment and observation. Compared with previous method, the new method substantially reduces the bias, providing acceptable estimate of the orbital stability with fewer cycles even with different noise distributions or higher or lower noise levels. The new method can provide an unbiased estimate of orbital stability within a reasonably small number of cycles. This is important for experiments with human subjects or clinical evaluation of patients that require effective assessment of locomotor stability in planning rehabilitation programs. / Graduate / 2018-11-22

In the adaptive finite element method, the solution of a p.d.e. is approximated from finer and finer meshes, which are controlled by error estimators. So, starting from a given coarse mesh, some elements are subdivided a couple of times. We investigate the question of avoiding instabilities which limit this process from the fact that nodal coordinates of one element coincide in more and more leading digits. In a previous paper the stable calculation of the Jacobian matrices of the element mapping was given for straight line triangles, quadrilaterals and hexahedrons. Here, we generalize this ideas to linear and quadratic triangles on curved boundaries.

Voltage stability is a challenging problem in the design and operation of terrestrial and shipboard power systems. DC links can be integrated in the AC systems to increase the transmission capacity or to enhance the distribution performance. However, DC links introduce voltage stability issues related to the reactive power shortage due to power converters. Multi-infeed DC systems make this existing phenomenon more complicated. In addition, shipboard power systems have unique characteristics, and some concepts and methodologies developed for terrestrial power systems need to be investigated and modified before they are extended for shipboard power systems. One goal of this work was to develop a systematic method for voltage stability assessment of hybrid AC/DC systems, independent of system configuration. The static and dynamic approaches have been used as complementary methods to address different aspects in voltage stability. The other goal was to develop or to apply voltage stability indicators for voltage stability assessment. Two classical indicators (the minimum eigenvalue and loading margin) and an improvement (the 2nd order performance indicator) have been jointly used for the prediction of voltage stability, providing information on the system state and proximity to and mechanism of instability. The eliminated variable method has been introduced to calculate the partial derivatives of AC/DC systems for modal analysis. The previously mentioned methodologies and the associated indicators have been implemented for the application of integrated shipboard power system including DC zonal arrangement. The procedure of voltage stability assessment has been performed for three test systems, the WSCC 3-machine 9-bus system, the benchmark integrated shipboard power system, and the modified I RTS-96. The static simulation results illustrate the critical location and the contributing factors to the voltage instability, and screen the critical contingencies for dynamic simulation. The results obtained from various static methods have been compared. The dynamic simulation results demonstrate the response of dynamic characteristics of system components, and benchmark the static simulation results.

This work focuses on efficient modelling and adaptive control of friction damping in bladed disks. To efficiently simulate the friction contact, a full-3D time-discrete contact model is reformulated and an analytical expression for the Jacobian matrix is derived that reduces the computation time drastically with respect to the classical finite difference method. The developed numerical solver is applied on bladed disks with shroud contact and the advantage of full-3D contact model compared to a quasi-3D contact model is presented. The developed numerical solver is also applied on bladed disks with strip damper and multiple friction contacts and obtained results are discussed. Furthermore, presence of higher harmonics in the nonlinear contact forces is analyzed and their effect on the excitation of the different nodal diameters of the bladed disk are systematically presented. The main parameters that influence the effectiveness of friction damping in bladed disks are engine excitation order,  contact stiffnesses,  friction coefficient, relative motion at the friction interface and the normal contact load. Due to variation in these parameters during operation, the obtained friction damping in practice may differ from the optimum value. Therefore, to control the normal load adaptively that will lead to an optimum damping in the system despite these variations, use of magnetostrictive actuator is proposed. The magnetostrictive material that develops an internal strain under the influence of an external magnetic field is employed to increase and decrease the normal contact load. A linearized model of the magnetostrictive actuator is used to characterize the magnetoelastic behavior of the actuator.  A nonlinear static contact analysis of the bladed disk reveals that a change of normal load more than 700 N can be achieved using a reasonable size of the actuator. This will give a very good control on friction damping once applied in practice. / <p>QC 20170310</p> / TurboPower

This study presents Computer-Aided Fixture Design Verification (CAFDV) - the methods and implementations to define, measure and optimize the quality of fixture designs. CAFDV verifies a fixture for its locating performance, machining surface accuracy, stability, and surface accessibility. CAFDV also optimizes a fixture for its locator layout design, initial clamping forces, and tolerance specification. The demand for CAFDV came from both fixture design engineers and today's supply chain managers. They need such a tool to inform them the quality of a fixture design, and to find potential problems before it is actually manufactured. For supply chain managers, they will also be able to quantitatively measure and control the product quality from vendors, with even little fixture design knowledge. CAFDV uses two models - one geometric and one kinetic - to represent, verify and optimize fixture designs. The geometric model uses the Jacobian Matrix to establish the relationship between workpiece-fixture displacements, and the kinetic model uses the Fixture Stiffness Matrix to link external forces with fixture deformation and workpiece displacement. Computer software for CAFDV has also been developed and integrated with CAD package I-DEAS TM. CAD integration and a friendly graphic user interface allows the user to have easy interactions with 3D models and visual feedback from analysis results.