Studies in vortex motion

This thesis covers four different problems in the understanding of vortex sheets, and these are presented in four chapters.

In Chapter 1, free streamline theory is used to determine the steady solutions of an array of identical, hollow or stagnant core vortices in an inviscid, incompressible fluid. Assuming the array is symmetric to rotation through π radians about an axis through any vortex centre, there are two solutions or no solutions depending on whether A^(1/2)/L is less than or greater than 0.38 where A is the area of the vortex and L is the separation distance. Stability analysis shows that the more deformed shape is unstable to infinitesimal symmetric disturbances which leave the centres of the vortices undisplaced.

Chapter 2 is concerned with the roll-up of vortex sheets in homogeneous fluid. The flow over conventional and ring wings is used to test the method of Fink and Soh (1974). Despite modifications which improve the accuracy of the method, unphysical results occur. A possible explanation for this is that small scales are important and an alternate method based on "Cloud-in-Cell" techniques is introduced. The results show small scale growth and amalgamation into larger structures.

The motion of a buoyant pair of line vortices of opposite circulation is considered in Chapter 3. The density difference between the fluid carried by the vortices and the fluid outside is considered small, so that the Boussinesq approximation may be used. A macroscopic model is developed which shows the formation of a detrainment filament and this is included as a modification to the model. The results agree well with the numerical solution as developed by Hill (1975b) and show that after an initial slowdown, the vortices begin to accelerate downwards.

Chapter 4 reproduces completely a paper that has already been published (Baker, Barker, Bofah and Saffman (1974)) on the effect of "vortex wandering" on the measurement of velocity profiles of the trailing vortices behind a wing.

Experimental measurement of polyethylene chain modulus by scanning force microscopy

Nanoindentation technique and scanning force microscopy have been used to measure directly the polyethylene modulus along the chain axis. Single crystals of polyethylene were employed in order to obtain well-aligned chain segments. To minimize effects of scanner creep, a Z scan rate of 3 Hz was employed. The "X Rotate" value of 25 degrees was selected to eliminate effects of lateral tip motion. The results were analyzed by the Oliver -Pharr method for which direct observation and measurement of the contact area are not required. Considering the influence of tip roundness on the projected contact area, the nanoindentation results were analyzed by the Sawa method. The chain modulus obtained from the thinner polyethylene single crystal sample was 204 +/- 21 GPa by the Oliver-Pharr method and 168 +/- 17 GPa by the Sawa method. The lower values than expected were due to substrate effects and anisotropy of chain deformation during nanoindentation. An extrapolation of the chain modulus obtained by various strains to zero nanoindentation eliminated the effect of substrate and anisotropy of chain deformation. The corresponding chain modulus obtained from the thicker sample was 278 GPa by the Oliver-Pharr method and 267 GPa by the Sawa method, respectively, in better agreement with the value of 340 Cpa determined theoretically. (C) 2001 Elsevier Science Ltd. All rights reserved.

Learning Fine Motion by Markov Mixtures of Experts

Compliant control is a standard method for performing fine manipulation tasks, like grasping and assembly, but it requires estimation of the state of contact between the robot arm and the objects involved. Here we present a method to learn a model of the movement from measured data. The method requires little or no prior knowledge and the resulting model explicitly estimates the state of contact. The current state of contact is viewed as the hidden state variable of a discrete HMM. The control dependent transition probabilities between states are modeled as parametrized functions of the measurement We show that their parameters can be estimated from measurements concurrently with the estimation of the parameters of the movement in each state of contact. The learning algorithm is a variant of the EM procedure. The E step is computed exactly; solving the M step exactly would require solving a set of coupled nonlinear algebraic equations in the parameters. Instead, gradient ascent is used to produce an increase in likelihood.

Wearable wireless inertial measurement for sports applications

A wearable WIMU (Wireless Inertial Measurement Unit) [1] system for sports applications based on Tyndall's 25mm mote technology [2] has been developed to identify tennis performance determining factors, giving coaches & players improved feedback [3, 4]. Multiple WIMUs transmit player motion data to a PC/laptop via a receiver unit. Internally the WIMUs consist of: an IMU layer with MEMS based sensors; a microcontroller/transceiver layer; and an interconnect layer with supplemental 70g accelerometers and a lithium-ion battery. Packaging consists of a robust ABS plastic case with internal padding, a power switch, battery charging port and status LED with Velcro-elastic straps that are used to attach the device to the player. This offers protection from impact, sweat, and movement of sensors which could cause degradation in device performance. In addition, an important requirement for this device is that it needs to be lightweight and comfortable to wear. Calibration ensures that misalignment of the accelerometer and magnetometer axes are accounted for, allowing more accurate measurements to be made.

A benchmark comparison between reconfigurable, intelligent and autonomous wireless inertial measurement and photonic technologies in rehabilitation

Advanced sensory systems address a number of major obstacles towards the provision for cost effective and proactive rehabilitation. Many of these systems employ technologies such as high-speed video or motion capture to generate quantitative measurements. However these solutions are accompanied by some major limitations including extensive set-up and calibration, restriction to indoor use, high cost and time consuming data analysis. Additionally many do not quantify improvement in a rigorous manner for example gait analysis for 5 minutes as opposed to 24 hour ambulatory monitoring. This work addresses these limitations using low cost, wearable wireless inertial measurement as a mobile and minimal infrastructure alternative. In cooperation with healthcare professionals the goal is to design and implement a reconfigurable and intelligent movement capture system. A key component of this work is an extensive benchmark comparison with the 'gold standard' VICON motion capture system.

Precision biomechanical motion tracking and throw characterisation in professional darts

In professional sports there are in general three steps required to improve performance namely task definition, training and performance assessment. This process is iteratively repeated and feedback generated from quantitative performance measurement is in turn used for task redefinition. Task definition can be achieved in a number of ways including via video streaming or indeed and as is more common, by listening to coaching staff. However non-subjective performance evaluation is difficult due to the complexity of the movements involved. When considering the subset of sports where precision accuracy and repeatability are a necessity this problem becomes inherently more difficult to solve. Until recently sports such as martial arts, fencing and darts, where the smallest deviation from a prescribed movement goal can result in large outcome error, were deemed too difficult to characterise fully. Advances in technology, as illustrated by this study, now make this type of physiometry possible.

An automated calibration tool for high performance wireless inertial measurement in professional sports

Traditional motion capture techniques, for instance, those employing optical technology, have long been used in the area of rehabilitation, sports medicine and performance analysis, where accurately capturing bio-mechanical data is of crucial importance. However their size, cost, complexity and lack of portability mean that their use is often impractical. Low cost MEMS inertial sensors when combined and assembled into a Wireless Inertial Measurement Unit (WIMU) present a possible solution for low cost and highly portable motion capture. However due to the large variability inherent to MEMS sensors, such a system would need extensive characterization to calibrate each sensor and ensure good quality data capture. A completely calibrated WIMU system would allow for motion capture in a wider range of real-world, non-laboratory based applications. Calibration can be a complex task, particularly for newer, multi-sensing range capable inertial sensors. As such we present an automated system for quickly and easily calibrating inertial sensors in a packaged WIMU, demonstrating some of the improvements in accuracy attainable.

Capturing the overarm throw in darts employing wireless inertial measurement

This work employs a custom built body area network of wireless inertial measurement technology to conduct a biomechanical analysis of precision targeted throwing in competitive and recreational darts. The solution is shown to be capable of measuring key biomechanical factors including speed, acceleration and timing. These parameters are subsequently correlated with scoring performance to determine the affect each variable has on outcome. For validation purposes an optical 3D motion capture system provides a complete kinematic model of the subject and enables concurrent benchmarking of the 'gold standard' optical inertial measurement system with the more affordable and proactive wireless inertial measurement solution developed as part of this work.

A smart wireless inertial measurement unit system: simplifying & encouraging usage of WIMU technology

Wireless Inertial Measurement Units (WIMUs) combine motion sensing, processing & communications functionsin a single device. Data gathered using these sensors has the potential to be converted into high quality motion data. By outfitting a subject with multiple WIMUs full motion data can begathered. With a potential cost of ownership several orders of magnitude less than traditional camera based motion capture, WIMU systems have potential to be crucially important in supplementing or replacing traditional motion capture and opening up entirely new application areas and potential markets particularly in the rehabilitative, sports & at-home healthcarespaces. Currently WIMUs are underutilized in these areas. A major barrier to adoption is perceived complexity. Sample rates, sensor types & dynamic sensor ranges may need to be adjusted on multiple axes for each device depending on the scenario. As such we present an advanced WIMU in conjunction with a Smart WIMU system to simplify this aspect with 3 usage modes: Manual, Intelligent and Autonomous. Attendees will be able to compare the 3 different modes and see the effects of good andbad set-ups on the quality of data gathered in real time.

Improved kinematic sensing for motion control applications

New compensation methods are presented that can greatly reduce the slit errors (i.e. transition location errors) and interval errors induced due to non-idealities in optical incremental encoders (square-wave). An M/T-type, constant sample-time digital tachometer (CSDT) is selected for measuring the velocity of the sensor drives. Using this data, three encoder compensation techniques (two pseudoinverse based methods and an iterative method) are presented that improve velocity measurement accuracy. The methods do not require precise knowledge of shaft velocity. During the initial learning stage of the compensation algorithm (possibly performed in-situ), slit errors/interval errors are calculated through pseudoinversebased solutions of simple approximate linear equations, which can provide fast solutions, or an iterative method that requires very little memory storage. Subsequent operation of the motion system utilizes adjusted slit positions for more accurate velocity calculation. In the theoretical analysis of the compensation of encoder errors, encoder error sources such as random electrical noise and error in estimated reference velocity are considered. Initially, the proposed learning compensation techniques are validated by implementing the algorithms in MATLAB software, showing a 95% to 99% improvement in velocity measurement. However, it is also observed that the efficiency of the algorithm decreases with the higher presence of non-repetitive random noise and/or with the errors in reference velocity calculations. The performance improvement in velocity measurement is also demonstrated experimentally using motor-drive systems, each of which includes a field-programmable gate array (FPGA) for CSDT counting/timing purposes, and a digital-signal-processor (DSP). Results from open-loop velocity measurement and closed-loop servocontrol applications, on three optical incremental square-wave encoders and two motor drives, are compiled. While implementing these algorithms experimentally on different drives (with and without a flywheel) and on encoders of different resolutions, slit error reductions of 60% to 86% are obtained (typically approximately 80%).

Improved APF strategies for dual-arm local motion planning

Manipulator motion planning is a classic problem in robotics, with a number of complete solutions available for their motion in controlled (industrial) environments. Owing to recent technological advances in the field of robotics, there has been a significant development of more complex robots with high-fidelity sensors and more computational power. One such example has been a rise in the production of humanoid robots equipped with dual-arm manipulators which require complex motion planning algorithms. Also, the technological advances have resulted in a shift from using manipulators in strictly controlled environments, to investigating the deployment of manipulators in dynamic or unknown environments. As a result, a greater emphasis has been put on the development of local motion planners, which can provide real-time solutions to these problems. Artificial Potential Fields (APFs) is one such popular local motion planning technique, which can be applied to manipulator motion planning, however, the basic algorithm is severely prone to local minima problems. Here, two modified APF-based strategies for solving the dual-arm motion planning task in unknown environments are proposed. Both techniques make use of configuration sampling and subgoal selection to assist the APFs in avoiding these local minima scenarios. Extensive simulation results are presented to validate the efficacy of the proposed methodology.

Development of a Bridge Weigh-in-Motion Sensor: Performance comparison using fibre optic and electric resistance strain sensor systems

This paper addresses the problems of effective in situ measurement of the real-time strain for bridge weigh in motion in reinforced concrete bridge structures through the use of optical fiber sensor systems. By undertaking a series of tests, coupled with dynamic loading, the performance of fiber Bragg grating-based sensor systems with various amplification techniques were investigated. In recent years, structural health monitoring (SHM) systems have been developed to monitor bridge deterioration, to assess load levels and hence extend bridge life and safety. Conventional SHM systems, based on measuring strain, can be used to improve knowledge of the bridge's capacity to resist loads but generally give no information on the causes of any increase in stresses. Therefore, it is necessary to find accurate sensors capable of capturing peak strains under dynamic load and suitable methods for attaching these strain sensors to existing and new bridge structures. Additionally, it is important to ensure accurate strain transfer between concrete and steel, adhesives layer, and strain sensor. The results show the benefits in the use of optical fiber networks under these circumstances and their ability to deliver data when conventional sensors cannot capture accurate strains and/or peak strains.

Quantifying Submerged Fluvial Topography Using Hyperspatial Resolution UAS Imagery and Structure From Motion Photogrammetry.

Quantifying the topography of rivers and their associated bedforms has been a fundamental concern of fluvial geomorphology for decades. Such data, acquired at high temporal and spatial resolutions, are increasingly in demand for process-oriented investigations of flow hydraulics, sediment dynamics and in-stream habitat. In these riverine environments, the most challenging region for topographic measurement is the wetted, submerged channel. Generally, dry bed topography and submerged bathymetry are measured using different methods and technology. This adds to the costs, logistical challenges and data processing requirements of comprehensive river surveys. However, some technologies are capable of measuring the submerged topography. Through-water photogrammetry and bathymetric LiDAR are capable of reasonably accurate measurements of channel beds in clear water. Whilst the cost of bathymetric LiDAR remains high and its resolution relatively coarse, the recent developments in photogrammetry using Structure from Motion (SfM) algorithms promise a fundamental shift in the accessibility of topographic data for a wide range of settings. Here we present results demonstrating the potential of so called SfM-photogrammetry for quantifying both exposed and submerged fluvial topography at the mesohabitat scale. We show that imagery acquired from a rotary-winged Unmanned Aerial System (UAS) can be processed in order to produce digital elevation models (DEMs) with hyperspatial resolutions (c. 0.02 m) for two different river systems over channel lengths of 50-100 m. Errors in submerged areas range from 0.016 m to 0.089 m, which can be reduced to between 0.008 m and 0.053 m with the application of a simple refraction correction. This work therefore demonstrates the potential of UAS platforms and SfM-photogrammetry as a single technique for surveying fluvial topography at the mesoscale (defined as lengths of channel from c.10 m to a few hundred metres). This article is protected by copyright. All rights reserved.

Automatic measurement of key ski jumping phases and temporal events with a wearable system.

We propose a new method, based on inertial sensors, to automatically measure at high frequency the durations of the main phases of ski jumping (i.e. take-off release, take-off, and early flight). The kinematics of the ski jumping movement were recorded by four inertial sensors, attached to the thigh and shank of junior athletes, for 40 jumps performed during indoor conditions and 36 jumps in field conditions. An algorithm was designed to detect temporal events from the recorded signals and to estimate the duration of each phase. These durations were evaluated against a reference camera-based motion capture system and by trainers conducting video observations. The precision for the take-off release and take-off durations (indoor < 39 ms, outdoor = 27 ms) can be considered technically valid for performance assessment. The errors for early flight duration (indoor = 22 ms, outdoor = 119 ms) were comparable to the trainers' variability and should be interpreted with caution. No significant changes in the error were noted between indoor and outdoor conditions, and individual jumping technique did not influence the error of take-off release and take-off. Therefore, the proposed system can provide valuable information for performance evaluation of ski jumpers during training sessions.