Une prothèse de genou est généralement, composée de deux parties fixées respectivement sur le fémur et sur le tibia et d’une troisième, dite intercalaire. Durant le processus de fabrication de ces composants des déformations apparaissent au niveau des bruts de fonderie. Les fabricants de prothèses choisissent d’assurer l’épaisseur nominale de la prothèse en enlevant une épaisseur constante sur le brut de fonderie. Cette opération est généralement réalisée manuellement. L’objectif de ces travaux de thèse est de contribuer à l’automatisation de ces opérations en proposant une méthode d’adaptation des trajectoires d’usinage aux variations géométriques de la surface cible. L’objectif de ce travail de recherche est d’adapter une trajectoire d’usinage sur un modèle nominal pour enlever une épaisseur constante sur une surface brute de fonderie mesurée. La méthode proposée commence par une étape d’alignement de la surface mesurée sur la trajectoire nominale en utilisant un algorithme d’ICP. Par la suite, la trajectoire nominale est déformée pour venir enlever l'épaisseur désirée sur la surface brute mesurée. Cette dernière est définie, dans ces travaux, suivant un modèle STL. Naturellement, les discontinuités de ce type de modèle induit une impression des motifs du STL sur la trajectoire adaptée et, donc, sur la pièce usinée. Par la suite, afin de d’atténuer ce problème et d’améliorer la qualité de fabrication, il est proposé de procéder à un lissage de la trajectoire.Afin de valider les développements théoriques de ces travaux, des essais ont été réalisés sur une machine cinq axes pour l’ébauche de composants fémoraux d’une prothèse uni-compartimentale de genou. / Commonly, knee prostheses are composed of two parts fixed respectively on femur and tibia, and a third one called intercalary. During the manufacturing process, of these components distortions appear on roughcast workpiece geometry. Thus, prosthesis manufacturers choose to ensure the nominal thickness of the prosthesis by removing a constant thickness on the roughcast workpiece. This operation is generally carried out realized manually.The aim of this thesis is to contribute to the automation of these manual operations by providing a method to adapt the machining toolpaths at geometrical variations of the target surface. The aim of this research work is to adapt a machining toolpath computed on a nominal model to remove a constant thickness on a roughcast measured surface. The proposed method starts with an alignment step of the measured surface on the nominal toolpath using an ICP algorithm. Subsequently, the nominal toolpath is deformed to remove the desired thickness of the measured rough surface defined in presented case by a STL model. Naturally, discontinuities of this type of model induce the apparition of pattern for the STL on the adapted toolpath and thus on the machined workpiece. Subsequently, to limit this problem and to improve the quality of realized surface, it is proposed a toolpath smoothing method. To validate theoretical developments of this work, tests were carried out on a five-axis machine for roughing of femoral components of a unicompartmental knee prosthesis.

Les surfaces complexes ont des applications dans divers domaines tels que ceux de la photonique, de l'énergie, du biomédical, du transport... Par contre, elles posent de véritables défis quant à leur spécification, fabrication et mesure ainsi que lors de l'évaluation de leur défaut de forme. Les processus de fabrication et de mesure de surfaces complexes sont fortement tributaires des dimensions, des tolérances et des formes spécifiées. Afin de rendre exploitable les informations données par le système de mesure, une étape importante de traitement s'impose. Il s'agit ici de la reconstruction de surfaces afin de reconstituer la géométrie et la topologie de la surface sous-jacente et d'en extraire les informations nécessaires pour des besoins de métrologie dimensionnelle (caractéristiques dimensionnelles et évaluation des défauts de forme). Dans la catégorie des surfaces asphériques pour lesquelles un modèle mathématique est associé, le processus de traitement de données géométriques, non nécessairement organisées, se fait par l'association du modèle aux données. Les résidus d'association recherchés en optique sont typiquement de l'ordre du nanomètre. Dans ce cadre, nous proposons l'utilisation de l'algorithme L-BFGS qui n'a encore jamais été utilisé en métrologie. Ce dernier permet de résoudre des problèmes d'optimisation non-linéaires, sans contraintes et d'une manière robuste, automatique et rapide. La méthode L-BFGS reste efficace pour des données contenant plusieurs millions de points. Dans la catégorie des surfaces gauches et notamment des aubes de turbines, la fabrication, la mesure et le traitement sont à une toute autre échelle, sub-micrométrique. Les surfaces gauches ne sont généralement pas définies par un modèle mathématique mais sont représentées par des modèles paramétriques de type B-Spline et/ou NURBS. Dans ce cadre, nous exposons un état de l'art détaillé et proposons une nouvelle approche itérative d'association B-Spline. L'algorithme s'affranchit de tous les problèmes liés à l'initialisation et au paramétrage initial. Par conséquent, un tel algorithme constitue une nouveauté dans ce domaine. Nous établissons une étude approfondie en évoquant les avantages et les limites actuelles de cette approche sur des exemples de courbes fermées en 2D. Nous complétons ensuite cette étude par des perspectives d'amélioration et de généralisation aux surfaces en 3D. / Complex surfaces exhibit real challenges in regard to their design specification, their manufacturing, their measurement and the evaluation of their manufacturing defects. They are classified according to their geometric/shape complexity as well as to their required tolerance. Thus, the manufacturing and measurement processes used are selected accordingly. In order to transcribe significant information from the measured data, a data processing scheme is essential. Here, processing involves surface reconstruction in the aim of reconstituting the underlying geometry and topology to the points and extracting the necessary metrological information (form and/or dimensional errors). For the category of aspherical surfaces, where a mathematical model is available, the processing of the data, which are not necessarily organized, is done by fitting/associating the aspherical model to the data. The sought precision in optics is typically nanometric. In this context, we propose the L-BFGS optimization algorithm, first time used in metrological applications and which allows solving unconstrained, non-linear optimization problems precisely, automatically and fast. The L-BFGS method remains efficient and performs well even in the presence of very large amounts of data.In the category of general freeform surfaces and particularly turbine blades, the manufacturing, measurement and data processing are all at a different scale and require sub-micrometric precision. Freeform surfaces are generally not defined by a mathematical formula but are rather represented using parametric models such as B-Splines and NURBS. We expose a detailed state-of-the-art review of existing reconstruction algorithms in this field and then propose a new active contour deformation of B-Splines approach. The algorithm is independent of problems related to initialization and initial parameterization. Consequently, it is a new algorithm with promising results. We then establish a thorough study and a series of tests to show the advantages and limitations of our approach on examples of closed curves in the plane. We conclude the study with perspectives regarding improvements of the method and its extension to surfaces in 3D.

This report is a Bachelor thesis and has been done within the area of mechanical engineering at Linköping university. The thesis has been performed as a project upon request from the company Bosch Thermoteknik AB in Tranås, Sweden. The company produces heat pumps, and in the process, brazing is used as a method to build the pipe modules the pumps contain. The brazing is currently made in terms of craftmanship in the production at the company. The purpose of this project was to investigate the possibilities to automate a brazing process and present a possible solution the company can use. The solution should mainly be based on the use of an industrial robot together with an equipment for induction heating.An iterative concept-generating process for production development was used as method to perform the project. Based on the method, a result consisting of two main areas were acquired. The first area was a study of the prerequisites for the project – the process demands and a review of the technique the resources used. The other area was the concept solution for how a brazing process can be automated.The concept itself was built by two areas. One physical part in the shape of a fixture to carry the pipe-modules during the process as well as tools and aids for the robot function. The other area was the program that forms the robot’s function. The program was based on solutions to enable identification of the modules, positioning of the robot arm with tool and a verification part to ensure the brazing has been done. The robot program was founded on a written program script to control the robot.

Im Rahmen des Forschungsprojektes ,,Entwicklung eines 3D Hochgeschwindigkeits-Rotationsdruckverfahren' an der Hochschule Mittweida, wird sich mit dem Erzeugen eines CAD-Modells eines Patientenschädels und der passgenauen Modellierung einer orthopädischen Helmschale für diesen beschäftigt. Ziel ist es die zeitintensive Modellherstellung mittels Gips einzusparen und die endgültige Helmschale im .stl-Format zu erzeugen. Weiter wird, mittels einer visuellen Programmierumgebung, ein Programm erzeugt um die Helmschale in einem polaren Koordinatensystem für den geplanten Hochgeschwindigkeits-Rotations-3D-Drucker auszurichten, zu slicen und die Koordinaten der einzelnen Punkte der Bahnkurven der Extruder auszugeben.

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Traditional methods in optical design like ray tracing suffer from slow convergence and are not constructive, i.e., each minimal perturbation of input parameters might lead to “chaotic” changes in the output. However, so-called inverse methods can be helpful in designing optical systems of reflectors and lenses. The equations in R2 become ordinary differential equations, while in R3 the equations become partial differential equations. These equations are then used to transform source distributions into target distributions, where the distributions are arbitrary, though assumed to be positive and integrable. In this project, we derive the governing equations and solve them numerically, for the systems presented by our instructor Martijn Anthonissen [Anthonissen et al. 2021]. Additionally, we show how point sources can be derived as a special case of a interval source with di- rected source interval, i.e., with each point in the source interval there is also an associated unit direction vector which could be derived from a system of two interval sources in R2. This way, it is shown that connecting source distributions with target distributions can be classified into two instead of three categories. The resulting description of point sources as a source along an interval with directed rays could potentially be extended to three dimensions, leading to interpretations of point sources as directed sources on convex or star-shaped sets.:1 Abstract 4 2 Notation And Conventions 4 3 Introduction 5 4 ECMI Modeling Week Challenges 5 4.1 Problem 1 - Parallel to Near-Field Target 5 4.1.1 Description 5 4.1.2 Deriving The Equations 5 4.2 Problem 2 - Parallel Source To Two Targets 8 4.3 Problem 3 - Point Source To Near-Field Target 9 4.3.1 Deriving The Equations 9 4.4 Problem 4 - Point Source To Two Targets 11 5 Validation - Ray tracing 13 5.1 Splines 13 5.1.1 Piece-Wise Affine Reflectors 13 5.1.2 Piece-Wise Cubic Reflectors 14 5.2 Error Estimates For Spline Reflectors 14 5.2.1 Lemma: A Priori Feasibility Of Starting Values For Near-Field Problems 15 5.2.2 Estimates for single reflector, near-field targets 16 5.3 Ray Tracing Errors - Illumination Errors 17 5.3.1 Definition: Axioms For Errors 18 5.3.2 Extrapolated Ray Tracing Error (ERTE) 18 5.3.3 Definition: Minimal Distance Ray Tracing Error (MIRTE) 19 5.3.4 Lemma: Continuity Of The Ray Traced Reflection Projection Of Smooth Reflectors 19 5.3.5 Theorem: Convergence Of The MIRTE 20 5.3.6 Convergence Of The ERTE 21 5.3.7 Application 21 6 Numerical Implementation 21 6.1 The DOPTICS Library 21 6.2 Pseudocode Of The Implementation 21 6.2.1 Solutions Of The Problems 22 6.2.2 Ray Tracing And Ray Tracing Error 22 6.3 ERTE Implementation 25 7 Results 26 7.1 Problem 1: Results 26 7.2 Problem 2: Results 26 7.3 Problem 3: Results 27 7.4 Problem 4: Results 27 8 Generalizations In Two Dimensions 29 8.1 Directed Densities 29 8.2 Generalized, Orthogonally Emitting Sources in R2 30 8.2.1 Point Light Sources As Orthogonally Emitting Sources 30 9 Conclusion and Future Research 32 10 Group Dynamic 32 References 32

This thesis focuses on applying one of the rapidly growing non-deterministic optimization algorithms, the ant colony algorithm, for simulating automatic hose/pipe routing with several conflicting objectives. Within the thesis, methods have been developed and applied to single objective hose routing, multi-objective hose routing and multi-hose routing. The use of simulation and optimization in engineering design has been widely applied in all fields of engineering as the computational capabilities of computers has increased and improved. As a result of this, the application of non-deterministic optimization techniques such as genetic algorithms, simulated annealing algorithms, ant colony algorithms, etc. has increased dramatically resulting in vast improvements in the design process. Initially, two versions of ant colony algorithms have been developed based on, respectively, a random network and a grid network for a single objective (minimizing the length of the hoses) and avoiding obstacles in the CAD model. While applying ant colony algorithms for the simulation of hose routing, two modifications have been proposed for reducing the size of the search space and avoiding the stagnation problem. Hose routing problems often consist of several conflicting or trade-off objectives. In classical approaches, in many cases, multiple objectives are aggregated into one single objective function and optimization is then treated as a single-objective optimization problem. In this thesis two versions of ant colony algorithms are presented for multihose routing with two conflicting objectives: minimizing the total length of the hoses and maximizing the total shared length (bundle length). In this case the two objectives are aggregated into a single objective. The current state-of-the-art approach for handling multi-objective design problems is to employ the concept of Pareto optimality. Within this thesis a new Pareto-based general purpose ant colony algorithm (PSACO) is proposed and applied to a multi-objective hose routing problem that consists of the following objectives: total length of the hoses between the start and the end locations, number of bends, and angles of bends. The proposed method is capable of handling any number of objectives and uses a single pheromone matrix for all the objectives. The domination concept is used for updating the pheromone matrix. Among the currently available multi-objective ant colony optimization (MOACO) algorithms, P-ACO generates very good solutions in the central part of the Pareto front and hence the proposed algorithm is compared with P-ACO. A new term is added to the random proportional rule of both of the algorithms (PSACO and P-ACO) to attract ants towards edges that make angles close to the pre-specified angles of bends. A refinement algorithm is also suggested for searching an acceptable solution after the completion of searching the entire search space. For all of the simulations, the STL format (tessellated format) for the obstacles is used in the algorithm instead of the original shapes of the obstacles. This STL format is passed to the C++ library RAPID for collision detection. As a result of using this format, the algorithms can handle freeform obstacles and the algorithms are not restricted to a particular software package.

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