A novel hip exoskeleton with six degrees of freedom (DoF) was developed, and multiple prototypes of this product were created in this thesis. The device was an upper level of the 12-DoF lower-body exoskeleton project, which was known as the Orthotic Lower-body Locomotion Exoskeleton (OLL-E). The hip exoskeleton had three motions per leg, which were roll, yaw, and pitch. Currently, the sufferers of hemiplegia and paraplegia can be addressed by using a wheelchair or operating an exoskeleton with aids for balancing. The motivation of the exoskeleton project was to allow paraplegic patients to walk without using aids such as a walker or crutches. In mechanical design, the hip exoskeleton was developed to mimic the behavior of a healthy person closely. The hip exoskeleton will be fully powered by a custom linear actuator for each joint. To date, there are no exoskeleton products that are designed to have all of the hip joints powered. Thus, packaging of actuators was also involved in the mechanical design of the hip exoskeleton. As a result, the output torque and speed for the roll joint and yaw joint were calculated. Each hip joint was structurally designed with properly selected bearings, encoder, and hard stops. Their range of motions met desired requirements. In addition, a backpack assembly was designed for mounting the hardware, such as cooling pumps, radiators, and batteries. In the verification part, finite element analysis (FEA) was conducted to show the robustness of the structural design. For fit testing, three wearable prototypes were produced to verify design choices. As a result, the weight of the current hip exoskeleton was measured as 32.1 kg. / Master of Science / Currently, patients who suffer from paraplegia are commonly treated with wheelchairs. However, the drawbacks of using wheelchairs introduced new medical challenges. One of the medical issues is the decrease in bone density. To address these medical problems and increase the quality of life of patients, lower-body exoskeletons are produced to assist with walking. To date, most of the current exoskeleton products require aids for balancing patients’ walking, and they don’t have fully actuated joints at the hip. As for the hip exoskeleton introduced in this thesis, all of the hip joints will be powered. Also, this device was the upper design of the Orthotic Lower-body Locomotion Exoskeleton (OLL-E), which aimed to create a self-balancing exoskeleton with total 12 of lower-body joints powered. The final goal of OLL-E is to assist the patient to walk at normal human speed without using aids. This thesis discusses the process of designing a hip exoskeleton, which starts from requirements development to modeling and prototype tests. The conservative calculations and assumptions made in this paper guided the structural design of the hip exoskeleton. The robustness of the structures was ensured with rigorous finite element analysis. In the end, wearable prototypes were produced to examine the fitting tests. Overall, this design of the hip exoskeleton provided critical references for the future development of the OLL-E.

The experiment was an attempt to gain a more precise understanding of the temporal relation between the development of analytic units and equivalence relations. Two prompting procedures were used during training to pinpoint when eight subjects learned the conditional discriminations. Near simultaneous presentation of probe and training trials allowed for examination of the temporal relation between conditional discrimination acquisition and derived performances on stimulus equivalence probes. The data show that, for seven of eight subjects, a decreased reliance on prompts was coincident with the development of equivalence-consistent choices on either all or some probe trials, which suggests that the development of analytic units is sufficient to give rise to equivalence relations among stimuli.

The divisor theories on finite graphs and metric graphs were introduced systematically as analogues to the divisor theory on algebraic curves, and all these theories are deeply connected to each other via tropical geometry and non-archimedean geometry. In particular, rational functions, divisors and linear systems on algebraic curves can be specialized to those on finite graphs and metric graphs. Important results and interesting problems, including a graph-theoretic Riemann-Roch theorem, tropical proofs of conventional Brill-Noether theorem and Gieseker-Petri theorem, limit linear series on metrized complexes, and relations among moduli spaces of algebraic curves, non-archimedean analytic curves, and metric graphs are discovered or under intense investigations. The content in this thesis is divided into three main subjects, all of which are based on my research and are essentially related to the divisor theory of linear systems on metric graphs and its application to tropical geometry and non-archimedean geometry. Chapter 1 gives an overview of the background and a general introduction of the main results. Chapter 2 is on the theory of rank-determining sets, which are subsets of a metric graph that can be used for the computation of the rank function. A general criterion is provided for rank-determining sets and certain specific examples of finite rank-determining sets are presented. Chapter 3 is on the subject of a tropical convexity theory on linear systems on metric graphs. In particular, the notion of general reduced divisors is introduced as the main tool used to study this tropical convexity theory. Chapter 4 is on the subject of smoothing of limit linear series of rank one on re_ned metrized complexes. A general criterion for smoothable limit linear series of rank 1 is presented and the relations between limit linear series of rank 1 and possible harmonic morphisms to genus 0 metrized complexes are studied.

As a valuable asset in human augmentation and medical rehabilitation, exoskeletons have become a major area for research and development. They have shown themselves to be effective tools for training and rehabilitation of individuals suffering from limited mobility. However, most exoskeletons are not capable of balancing without the assistance of crutches from the user. Leveraging technology and techniques developed for force controlled humanoid robots, a project was undertaken to develop a fully self-balancing, compliant lower-body robotic exoskeleton. Due to their many beneficial features, series elastic actuators were utilized to power the joints on the exoskeleton. This thesis details the development of four linear series elastic actuators (LSEA) as part of this project. All 12-degrees of freedom will be powered by one of these four LSEA's. Actuator requirements were developed by examining human gait data and three robot-walking simulations. These four walking scenarios were synthesized into one set of power requirements for actuator development. Using these requirements, analytical models were developed to perform component trade studies and predict the performance of the actuator. These actuators utilize high-efficacy components, parallel electric motors, and liquid cooling to attain high power-to-weight ratios, while maintaining a small lightweight design. These analyses and trade studies have resulted in the design of a dual-motor liquid-cooled actuator capable of producing a peak force 8500N with a maximum travel speed of 0.267m/s, and three different single-motor actuators capable of producing forces up to 2450N continuously, with a maximum travel speeds up to 0.767m/s. / Master of Science / Patients who suffer a severe back injury that results in paralysis from the waist down (paraplegia) commonly regain mobility in their daily lives by using a wheelchair. However, staying in a seated position for long periods can cause serious medical issues to arise. In order to address these issues, lower-body exoskeletons have been developed to help patients walk again. Exoskeletons are mechanical devices a person can wear to enhance their physical strength or endurance beyond their normal capability. These exoskeletons have shown themselves to be effective tools for training and rehabilitation of individuals suffering from limited mobility. However, most exoskeletons are not capable of balancing the user while they walk. In order to maintain balance, the user must hold themselves up with crutches. As with a wheelchair, heavy dependence on crutches can lead to new medical issues for the patient. To solve this problem, technology and techniques created for humanoid robots were used to develop a fully self-balancing exoskeleton. This exoskeleton is known as the Orthotic Lower-body Locomotion Exoskeleton. This thesis details the development of four actuators to power all twelve joints of the exoskeleton. These actuators utilize high-efficiency components, multiple electric motors, and liquid cooling to maintain a small lightweight design and while obtaining very high-power outputs.

Ziel dieser Arbeit ist die explizite Berechnung gewisser geometrischer Zykel in Modulräumen von Kurven. In den letzten Jahren wurden Divisoren auf $\Mbar_{g,n}$ ausgiebig untersucht. Durch die Berechnung von Klassen in Kodimension 1 konnten wichtige Ergebnisse in der birationalen Geometrie der Räume $\Mbar_{g,n}$ erzielt werden. In Kapitel 1 geben wir einen Überblick über dieses Thema. Im Gegensatz dazu sind Klassen in Kodimension 2 im Großen und Ganzen unerforscht. In Kapitel 2 betrachten wir den Ort, der im Modulraum der Kurven vom Geschlecht 2k durch die Kurven mit einem Büschel vom Grad k definiert wird. Da die Brill-Noether-Zahl hier -2 ist, hat ein solcher Ort die Kodimension 2. Mittels der Methode der Testflächen berechnen wir die Klasse seines Abschlusses im Modulraum der stabilen Kurven. Das Ziel von Kapitel 3 ist es, die Klasse des Abschlusses des effektiven Divisors in $\Mbar_{6,1}$ zu berechnen, der durch punktierte Kurven [C, p] gegeben ist, für die ein ebenes Modell vom Grad 6 existiert, bei dem p auf einen Doppelpunkt abgebildet wird. Wie Jensen gezeigt hat, erzeugt dieser Divisor einen extremalen Strahl im pseudoeffektiven Kegel von $\Mbar_{6,1}$. Ein allgemeines Ergebnis über gewisse Familien von Linearsystemen mit angepasster Brill-Noether-Zahl 0 oder -1 wird eingeführt, um die Berechnung zu vervollständigen. / The aim of this thesis is the explicit computation of certain geometric cycles in moduli spaces of curves. In recent years, divisors of $\Mbar_{g,n}$ have been extensively studied. Computing classes in codimension one has yielded important results on the birational geometry of the spaces $\Mbar_{g,n}$. We give an overview of the subject in Chapter 1. On the contrary, classes in codimension two are basically unexplored. In Chapter 2 we consider the locus in the moduli space of curves of genus 2k defined by curves with a pencil of degree k. Since the Brill-Noether number is equal to -2, such a locus has codimension two. Using the method of test surfaces, we compute the class of its closure in the moduli space of stable curves. The aim of Chapter 3 is to compute the class of the closure of the effective divisor in $\M_{6,1}$ given by pointed curves [C,p] with a sextic plane model mapping p to a double point. Such a divisor generates an extremal ray in the pseudoeffective cone of $\Mbar_{6,1}$ as shown by Jensen. A general result on some families of linear series with adjusted Brill-Noether number 0 or -1 is introduced to complete the computation.