This thesis deals with the usefulness of the application of quaternions in representing robot kinematics. It begins by showing the relationship of quaternions to the more commonly-known complex numbers and how it can represent rotations in three-dimensions. Then, the dual quaternions are introduced to represent both the three-dimensional rotation and translation. It will then be used to derive the forward and inverse kinematics, particularly, for the Universal Robot UR3 which is a 6-DOF robotic arm. Lastly, an actual application of dual quaternions in robot programming will be demonstrated

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The purpose of this thesis is to provide a complete package for the synthesis and design of the RSSR spatial function generating mechanism. In addition to the introductory material this thesis is divided into three sections. The section on background kinematic theory includes synthesis, analysis, link rotatability, transmission quality, and branching analysis. The second division details the computer application of the kinematic theory. The program RSSRSD has been developed to incorporate the RSSR synthesis and design theory. An example is included to demonstrate the computer-implemented theory. The third part of this thesis includes miscellaneous mechanism considerations and recommendations for further research. The theoretical work in this project is a combination of original derivations and applications of the theory in the mechanism literature. / Master of Science

Chapter One justified the need for research into methodology which can examine the upper limb stroke patients and older adults using portable kinematic recording software on the basis of the prevalence of stroke and aging and the potential importance of upper limb impairment as a predictor of recovery from stroke. Chapter Two reviewed the literature on methodologies which measured tracking in stroke patients and found that a wide range of methodologies were available but measurement metrics tended to focus on a small number of indices, mostly root mean square error, suggesting that measuring tracking using other indices might be informative. Chapter Three examined differences in tracking performance between stroke patients and older adults at a range of tracking speeds using a novel kinematic recording technology. The equipment appeared to be feasible for use in a community setting and found that older adults were less accurate, consistent and smooth compared to younger adults, and that accuracy was particularly affected by speed of trial. It was suggested that this interaction between speed and age may have been due to poorer feedback control mechanisms in older adults. Chapter Four looked at stroke patients compared to age-matched controls in tracking performance and found, contrary to the hypothesis, that stroke patients were more accurate, consistent and smooth with both the contralesional and ipsilesional hand; while there was no difference between the hands within stroke patients. Stroke patients may have outperformed controls due to qualitative differences in neural strategies for tracking control or the differences found may have related to methodological differences in collecting data. Chapter Five used the same stroke data to examine the relationship between tracking impairment, activity limitations and participation restrictions within the framework of the International Classification of Functioning, Disability and Health (ICF) (WHO, 2001). It was found that impairment of tracking consistency in the ipsilesional limb predicted participation restriction partially mediated by activity - 5 - limitation. It was argued that tracking in the “unimpaired limb” may be important for predicting participation restriction due to a potential mediating relationship with cognition. The study also suggested that the ipsilesional limb might have potential for rehabilitation of the contralesional limb. Chapter Six discussed the main findings of the thesis. Despite lack of sensitivity of tracking task to stroke impairment, the results of the thesis showed that measuring tracking in older adults and stroke patients provided important information about contralesional and ipsilesional hand function compared to age-matched controls and in relation to activity and participation after stroke. The methodology used may have the potential to examine other research questions which involve the measurement of upper limb kinematics after stroke.

Introduction: The incidence of anterior cruciate ligament (ACL) injuries in female floorball is relativley high, and the risk for sustaining a second ACL injury is greater compared to previously uninjured. Existing evaluation tests in rehabilition may not be discriminative enough to guide decisions on return to sport Aim: To evaluate the withinAsession and testAretest reliability of knee kinematics in floorball athletes and controls during a hop encompassing a sudden unanticipated change of direction. A second aim was to investigate the discriminative validity by comparing the test outcomes between the athletes and a control group of nonAathletes. Method: 11 elite floorball athletes and 8 controls were tested on two occassions separated by one to three weeks. Knee kinematics, ground contact time and number of succesfull hops were analyzed. Relative reliability was quantifyed by Intraclass correlation coefficient (ICC) and absolute reliability by standard error of measurement (SEM). Results: ICCs for knee kinematics withinAsession reliability were excellent (0.83A0.96) for athletes and poor to excellent (0.40A0.94) for the controls. For the testAretest reliability, the athletes had good to excellent (0.56A0.96) reliability and the controls had poor to excellent (0.26A0.93) reliability. Only two measured kinematic variables were significantly different between the groups. Conclusion: This pilot study indictate good to excellent reliability for the majority of the kinematic variables tested and, therefore, it could be assumed to be adequatley reliable. Discriminative validity needs to be further evaluated in a larger material.

Thesis (PhD)--Stellenbosch University, 2001. / ENGLISH ABSTRACT: In this dissertation we set out to develop the first relativistic model for calculating complete sets of (p, 2p) spin transfer observables. In addition to this a new technique has been developed which allows us to evaluate the transition amplitude, which is used to calculate the scattering observables for the reaction directly. The influence of various modiuin-modificd parameters ()1I the scattered wave functions anr] NN interact ion lH-IVC' })('('11 invest igatcd DlIC t,C) (I,llIlJigllitic's surrounding the nNN coupling we have included both pseudosoalar and pseudovector coupling into the nucleon-nucleon interaction model. Furthermore we have included two different kinematic prescriptions to obtain the effective NN laboratory kinetic energy and center of mass scattering angle, which are used to obtain the NN scattering amplitudes. The aim of this study is to investigate the effects of the various model parameters on complete sets of scattering observables. Our investigation has shown that although the analyzing power is not very sensitive to nuclear medium effects, and the various other spin transfer observables such as Dnn should provide valuable insight. Further refinements of the model would be to include nuclear distortions as well as the IA2 model of the NN interaction. / AFRIKAANSE OPSOMMING: In hierdie tesis ontwikkel ons die eerste relatiwistiese model vir die berekening van 'n volledige stel (p, 2p) spin waarneembares. Verder word 'n nuwe tegniek ingevoer wat ons toelaat om die oorgangsamplitude, wat gebruik word in berekening van die verstrooings waarneembares vir die reaksie, direk te evalueer. Die invloed van verskeie medium-gemodifiseerde parameters op die verstrooide golffunksies en die NN wisselwerking word bestudeer. As gevolg van onsekerhede betreffende die лNN koppeling word beide die pseudoskalaar en pseudovektor koppeling in die nukleon-nukleon interaksie model ingesluit. Ons sluit ook twee verskillende kinematiese preskripsies in om die effektiewe NN laboratorium kinetiese energie en die massa middelpunt verstrooiings hoek, wat gebruik word vir die berekening van die NN verstrooiings amplitude, te bereken. Die doel van hierdie studie is om die effek van verskeie model parameters op 'n volledige stel spin waarneembares te ondersoek. Die studie toon dat alhoewel die analiseervermoë nie baie sensitief is vir medium effekte nie, die ander spin waarneembares soos byvoorbeeld Dnn waardevolle insig lewer. Daar word voorgestel dat die model verfyn word deur kerndistorsies as ook die meer algemele IA2 model vir die NN interaksie in te sluit.

published_or_final_version / Sports Science / Master / Master of Science in Sports Science

It has been suggested that Patellofemoral Pain (PFP) may be the result of a coordinate state which exhibits less joint coordination variability. The ability to relate joint coordination variability to PFP pathology could have many clinical uses; however, evidence to support clinical application is lacking. Vector coding’s coupling angle variability (CAV) has been introduced as a possible analysis method to quantify joint coordination variability. The purpose of this study was to assess the clinical usefulness of CAV measures from a dynamical systems perspective. This involved establishing the precision limits of CAV measures when physiological conditions are held constant, altering control parameters of knee pain and population then determining if the observed changes in CAV were clinically meaningful. 20 female recreational runners with PFP and 21 healthy controls performed a treadmill acclimation protocol then ran at a self-selected pace for 15 minutes. 3-D kinematics, force plate kinetics, knee pain and perceived exertion were recorded each minute. CAV were calculated for six knee-ankle combinations for 2 sets of 5 non-consecutive stride cycles at each capture period. Data were selected for the PFP group at a high (=>3) and low (<=high-2) pain level in a non-exhausted state (<14). Healthy data were used from the 11th minute of the running. Levels of agreement were performed between the 2 sets of CAV measures for both populations, a paired t-test compared low to high pain CAV measures and independent t-tests compared populations at the high pain state. Several CAV measures showed a significant increase in value with an increase in pain and were significantly greater for the PFP group. None of the observed changes exceeded the precision limits of all CAV measures investigated. These results do not agree with previous claims that less variability is indicative of pathology but rather the opposite. This suggests that there might be an optimal amount of variability to maintain a healthy coordinate state with deviations in any direction being detrimental. However; due to the volatile nature of CAV measures, the clinical use of CAV is not recommended using current analysis methods since changes observed weren’t considered clinically meaningful.

The Milky Way (MW) and M31 both harbour massive satellite galaxies, the Large Magellanic Cloud (LMC) and M33, which may comprise up to 10 per cent of their host's total mass. Massive satellites can change the orbital barycentre of the host-satellite system by tens of kiloparsec and are cosmologically expected to harbour dwarf satellite galaxies of their own. Assessing the impact of these effects crucially depends on the orbital histories of the LMC and M33. Here, we revisit the dynamics of theMW-LMC system and present the first detailed analysis of the M31-M33 system utilizing high-precision proper motions and statistics from the dark-matter-only Illustris cosmological simulation. With the latest Hubble Space Telescope proper motion measurements of M31, we reliably constrain M33' s interaction history with its host. In particular, like the LMC, M33 is either on its first passage (t(inf) < 2 Gyr ago) or if M31 is massive (>= 2 x 10(12) M-circle dot), it is on a long-period orbit of about 6 Gyr. Cosmological analogues of the LMC and M33 identified in Illustris support this picture and provide further insight about their host masses. We conclude that, cosmologically, massive satellites such as the LMC and M33 are likely completing their first orbits about their hosts. We also find that the orbital energies of such analogues prefer an MW halo mass similar to 1.5 x 10(12) M-circle dot and an M31 halo mass >= 1.5 x 10(12)M(circle dot). Despite conventional wisdom, we conclude it is highly improbable that M33 made a close (< 100 kpc) approach to M31 recently (t(peri) < 3 Gyr ago). Such orbits are rare (< 1 per cent) within the 4s error space allowed by observations. This conclusion cannot be explained by perturbative effects through four-body encounters amongst the MW, M31, M33, and the LMC. This surprising result implies that we must search for a new explanation for M33' s strongly warped gas and stellar discs.