Modelling mechanical systems using symbolic equations can provide many advantages over the more widely-used numerical methods of modelling these systems. The use of symbolic equations produces more efficient models, which can be used for many purposes such as real-time simulation and control. However, the number, complexity, and computational efficiency of these equations is highly dependent on which coordinate set was used to model the system. One method of modelling a mechanism's topology and formulating its symbolic equations is to model the system using a graph-theoretical approach. This approach models mechanisms using a linear graph, from which spanning trees can be used to define a mechanism's coordinate set. This report develops two tree selection algorithms capable of estimating the tree set, and hence coordinate set, that produces models having the fastest forward dynamic simulation times. The first tree selection algorithm is a heuristic-based algorithm that tries to find the coordinate set containing the minimal possible number of modelling variables. Most of this algorithm's heuristics are based on tree selection criteria found in the literature and on observations of a series of benchmark problems. It uses the topology information provided by a system's graph to find the coordinates set for the given system that produce very low simulation times of the system. The second tree selection algorithm developed in this report also uses graph theory. It bases most of its heuristics on observations of one of the methods developed to obtain a mechanical system's symbolic equations using graph theory. This second algorithm also makes use of, and improves upon, a few of the heuristics developed in the first tree selection algorithm. A series of examples for both algorithms will demonstrate the computational efficiency obtained by using the modelling variables found by the automated tree selection algorithms that are proposed in this report.

Modelling mechanical systems using symbolic equations can provide many advantages over the more widely-used numerical methods of modelling these systems. The use of symbolic equations produces more efficient models, which can be used for many purposes such as real-time simulation and control. However, the number, complexity, and computational efficiency of these equations is highly dependent on which coordinate set was used to model the system. One method of modelling a mechanism's topology and formulating its symbolic equations is to model the system using a graph-theoretical approach. This approach models mechanisms using a linear graph, from which spanning trees can be used to define a mechanism's coordinate set. This report develops two tree selection algorithms capable of estimating the tree set, and hence coordinate set, that produces models having the fastest forward dynamic simulation times. The first tree selection algorithm is a heuristic-based algorithm that tries to find the coordinate set containing the minimal possible number of modelling variables. Most of this algorithm's heuristics are based on tree selection criteria found in the literature and on observations of a series of benchmark problems. It uses the topology information provided by a system's graph to find the coordinates set for the given system that produce very low simulation times of the system. The second tree selection algorithm developed in this report also uses graph theory. It bases most of its heuristics on observations of one of the methods developed to obtain a mechanical system's symbolic equations using graph theory. This second algorithm also makes use of, and improves upon, a few of the heuristics developed in the first tree selection algorithm. A series of examples for both algorithms will demonstrate the computational efficiency obtained by using the modelling variables found by the automated tree selection algorithms that are proposed in this report.

In this study, the energy conservation equation in a cylindrical coordinate system and the moving heat source from the tool are used to establish a steady-state three-dimensional heat transfer model for the friction stir welding (FSW). Then, the simplified momentum conservation equation is employed to predict the material flow model for the FSW. Combining the effects of heat transfer and material flow, this numerical model successfully predicts the weld temperature field and the material flow for the FSW. Numerical results show that increasing the welding or translational speed of the tool has the effect of decreasing the magnitude of the temperature within the workpiece, while increasing the rotating speed has the opposite effect. During the feeding process, the material located on the back of the tool pin has higher temperature than that on the front. Moreover, the temperature profile are asymmetrical between the advancing and retreating sides due to the material flow stirred by the tool, and this temperature difference depends on the speed of material flow under the tool shoulder.

Coordinate measuring machines are widely used to generate data points from an actual surface. The generated measurement data must be analyzed to yield critical geometric deviations of the measured part according to the requirements specified by the designer. However, ANSI standards do not specify the methods that should be used to evaluate the tolerances. The coordinate measuring machines employ different verification algorithms which may yield different results. Functional requirements or assembly conditions on a manufactured part are normally translated into geometric constraints to which the part must conform. Minimum zone evaluation technique is used when the measured data is regarded as an exact copy of the actual surface and the tolerance zone is represented as geometric constraints on the data. In the present study, a new zone-fitting algorithm is proposed. The algorithm evaluates the minimum zone that encompasses the set of measured points from the actual surface. The search for the rigid body transformation that places the set of points in the zone is modeled as a nonlinear optimization problem. The algorithm is employed to find the form tolerance of 2-D (line, circle) as well as 3-D geometries (cylinder). It is also used to propose an inspection methodology for turbine blades. By constraining the transformation parameters, the proposed methodology determines whether the points measured at the 2-D cross-sections fit in the corresponding tolerance zones simultaneously.

<p>This thesis has two aims. The first one is the investigation and analysis of the errors occurring in the measurements with pulsed time-of-flight (TOF) terrestrial laser scanners (TLS). A good understanding of the error sources and the relationships between them is necessary to secure the data accuracy. We subdivide these errors into four groups: instrumental, object-related, environmental and methodological. Based on our studies and the results obtained by other researchers, we have compiled an error model for TLS, which is used to estimate the single-point coordinate accuracy of a point in the point cloud, transformed to the specified coordinate system.</p><p>The second aim is to investigate systematic instrumental errors and performance of three pulsed TOF laser scanners – Callidus 1.1, Leica HDS 3000 and Leica HDS 2500 – and to develop calibration procedures that can be applied by the users to determine and correct the systematic errors in these instruments. The investigations have been performed at the indoor 3D calibration field established at KTH and outdoors. The systematic instrumental errors, or calibration parameters, have been estimated in a self-calibration according to the parametric least-squares adjustment in MATLAB®. The initial assumption was that the scanner instrumental errors are similar to those in a total station. The results have shown that the total station error model is applicable for TLS as a first approximation, but additional errors, specific to the scanner design, may appear. For example, we revealed a significant vertical scale error in the scanner Callidus 1.1, caused by the faults of the angular position sensor. The coordinate precision and accuracy of the scanners, estimated during the self-calibration, is at the level of several millimetres for Callidus 1.1 and Leica HDS 3000, and at the submillimetre level for Leica HDS 2500.</p><p>In other investigations, we revealed a range drift of up to 3 mm during the first few hours of scanning, presumably due to the changes in the temperature inside the scanners. The angular precision depends on the scanner design (“panoramic” or “camera-like”), and the angular accuracy depends on the significant calibration parameters in the scanner. Investigations of the influence of surface reflectance on the range measurements have shown that the indoor illumination and surface wetness have no tangible influence on the results. The type of the material does not affect, in general, the ranging precision for Callidus 1.1, but it affects the ranging precision and accuracy of the scanners Leica HDS 3000 and Leica HDS 2500. The reason may be different wavelength and, possibly, different design of the electronics in the laser rangefinders. Materials with high reflectance and those painted with bright “warning” colours may introduce significant offsets into the measured ranges (5 – 15 cm), when scanned from close ranges at normal incidence with the scanner Leica HDS 3000. “Mixed pixels” at the object edge may introduce a range error of several centimetres, on the average, depending on the type of the material. This phenomenon leads also to the distortions of the object size, which may be reduced by the removal of the “mixed pixels” based on their intensity. The laser beam intensity recorded by the scanner tends to decrease with an increased incidence angle, although not as assumed by the popular Lambertian reflectance model. Investigations of the scanner Leica HDS 2500 outdoors have revealed no significant influence of the “normal” atmospheric conditions on the range measurements at the ranges of up to 50 m.</p><p>Finally, we have developed and tested two simple procedures for the calibration of the vertical scale (and vertical index) error and zero error in laser scanners. We have also proposed an approach for the evaluation of the coordinate precision and accuracy in TLS based on the experiences from airborne laser scanning (ALS).</p>

Total Hip Replacement (THR) has become a common surgical procedure in recent years, due to the increase in the aging population with hip osteoarthritis. Identifying the proper orientation of the pelvis is a critical step in accurate placement of the femur prosthesis in the acetabulum in THR. The general approach to localize the orientation of the pelvic anatomical coordinate system (PaCS) is to use intra-operative X-ray fluoroscopy in a specialized interventional radiology facility to guide the procedure. Employing intra-operative ultrasound (US) imaging fused with pre-operative CT scan or fluoroscopy imaging was proposed to eliminate the ionizing radiation of intra-operative X-ray to the patient and the need for radiology facilities in the OR. However, the use of pre-operative imaging exposes patients to accumulative ionizing radiation which is desirable to be eliminated. In this thesis, I propose to replace pre-operative imaging with a statistical shape model (SSM) of the pelvis which is constructed from CT images of patients. An automatic deformable registration of a pelvis anatomical shape model to a sparse set of 2D ultrasound images of the pelvis is presented in order to localize the PaCS. In this registration technique, a set of 2D slices are extracted from the pelvic shape model, based on the approximate location and orientation of a corresponding 2D ultrasound image. The comparison of the shape model slices and ultrasound images is made possible by using an ultrasound simulation technique and a correlation-based similarity metric. During the registration, an instance of the shape model is generated that best matches the ultrasound data. I demonstrate the feasibility of our proposed approach in localizing the PaCS on four patient phantoms and on data from two male human cadavers. None of the test data sets were included in the SSM generation. / Thesis (Master, Electrical & Computer Engineering) -- Queen's University, 2010-08-23 17:57:24.708

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Eine in der Geoda¨sie bekannte Regel besagt, dass die Genauigkeit zu transformierender Neupunkte im Schwerpunkt der Anschlusspunkte am höchsten ist. Weniger bekannt ist, unter welchen Voraussetzungen dies generell gilt. Allgemein unbekannt ist bisher, auf welche Koordinatentransformationen man diese Regel ausdehnen kann. Wir zeigen dies auf und untersuchen einen Fall, in dem diese Regel nicht gilt. Es stellt sich heraus, dass der am genauesten transformierbare Neupunkt theoretisch sogar außerhalb der konvexen Hülle der Anschlusspunkte liegen kann. / A rule well-known in Geodesy states that the accuracy of points to be transformed is best in the centre of gravity of the control points. Less well- known is, under which conditions this rule gen- erally applies. The exact set of coordinate transforms, to which we can extend the validity of this rule, is widelyunknown. We demonstrate this and investigate a case, in which this rule does not apply. It turns out that the most accurately transformable point be even be located outside the convex hull of the control points.

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