A Graphical Method of Computing Offset Curves

Computation of offset curves is an operation critical to many computer-aided design and manufacturing (CAD/CAM) applications. Though simple on the surface, differences between the straightforward mathematical definition and the demands of CAD/CAM environment in the formulation and expression of an offset curve create a problem for which only complicated, approximate solutions are presently available. This thesis explores one of the newest methods of offset curve computation, using graphics hardware to directly compute the offset curve for arbitrary input geometry. Linear segments of the input curve are represented as meshes in 3D space, and the rendering process is used to create a field of depth values from which the offset curve is extracted as an isoline. This results in significant performance enhancements over previous, similar methods. Combined with a quantification of the errors involved in a graphical approach, these advances bring the technique closer to industrial readiness. Algorithm performance is shown to be linear with respect to geometric complexity of the input curve

Coupled Experimentally-Driven Constraint Functions and Topology Optimization utilized in Design for Additive Manufacturing

Topology optimization (TO) is a structural optimization technique that searches for the proper material distribution inside a design space such that an objective function is maximized/ minimized. Rapid prototyping technologies such as additive manufacturing (AM) have allowed results from TO to be manufacturable. However, despite advancements in their ability to manufacture complex geometries, AM technologies still face certain constraints such as printing features at overhangs (unsupported features oriented at a certain angle from the axis normal to the build plate) and small feature sizes, amongst others. In the field of design for additive manufacturing (DfAM), it is common to only restrict one constraint to control the quality of the final parts. However, several studies have found that the final quality of a feature is heavily affected by at least two coupled constraints: the overhanging angle and the feature’s thickness. Modifying a structure’s layout while restricting only one constraint can uselessly increase the weight of a structure. To tackle this problem, the work done in this thesis considers the interplay between two geometrical constraints. The proposed research reviews some of the essential manufacturing constraints in topology optimization and emphasizes the need for coupling existing constraints. It first develops experiments to obtain a qualitative and a quantitative relationship between the design features’ surface qualities, orientation, and thickness. The relation between those parameters is used to update the layout of topologically optimized structures. The layout is changed by obtaining the medial axis of topologically optimized structures and then using implicit functions to conditionally thickening it. Throughout the analysis, it was observed that both the inclination and the thickness affect the surface quality. Furthermore, the effect of the parameters is more pronounced for low thicknesses and higher overhanging angles. The overhanging angle impacts the surface quality more than the thickness, which can be seen through ANOVA

Smooth path planning with Pythagorean-hodoghraph spline curves geometric design and motion control

This thesis addresses two significative problems regarding autonomous systems, namely path and trajectory planning. Path planning deals with finding a suitable path from a start to a goal position by exploiting a given representation of the environment. Trajectory planning schemes govern the motion along the path by generating appropriate reference (path) points. We propose a two-step approach for the construction of planar smooth collision-free navigation paths. Obstacle avoidance techniques that rely on classical data structures are initially considered for the identification of piecewise linear paths that do not intersect with the obstacles of a given scenario. In the second step of the scheme we rely on spline interpolation algorithms with tension parameters to provide a smooth planar control strategy. In particular, we consider Pythagorean–hodograph (PH) curves, since they provide an exact computation of fundamental geometric quantities. The vertices of the previously produced piecewise linear paths are interpolated by using a G1 or G2 interpolation scheme with tension based on PH splines. In both cases, a strategy based on the asymptotic analysis of the interpolation scheme is developed in order to get an automatic selection of the tension parameters. To completely describe the motion along the path we present a configurable trajectory planning strategy for the offline definition of time-dependent C2 piece-wise quintic feedrates. When PH spline curves are considered, the corresponding accurate and efficient CNC interpolator algorithms can be exploited

Smooth path planning with Pythagorean-hodoghraph spline curves geometric design and motion control

This thesis addresses two significative problems regarding autonomous systems, namely path and trajectory planning. Path planning deals with finding a suitable path from a start to a goal position by exploiting a given representation of the environment. Trajectory planning schemes govern the motion along the path by generating appropriate reference (path) points. We propose a two-step approach for the construction of planar smooth collision-free navigation paths. Obstacle avoidance techniques that rely on classical data structures are initially considered for the identification of piecewise linear paths that do not intersect with the obstacles of a given scenario. In the second step of the scheme we rely on spline interpolation algorithms with tension parameters to provide a smooth planar control strategy. In particular, we consider Pythagorean\u2013hodograph (PH) curves, since they provide an exact computation of fundamental geometric quantities. The vertices of the previously produced piecewise linear paths are interpolated by using a G1 or G2 interpolation scheme with tension based on PH splines. In both cases, a strategy based on the asymptotic analysis of the interpolation scheme is developed in order to get an automatic selection of the tension parameters. To completely describe the motion along the path we present a configurable trajectory planning strategy for the offline definition of time-dependent C2 piece-wise quintic feedrates. When PH spline curves are considered, the corresponding accurate and efficient CNC interpolator algorithms can be exploited

Specifying a hybrid, multiple material CAD system for next-generation prosthetic design

For many years, the biggest issue that causes discomfort and hygiene issues for patients with lower limb amputations have been the interface between body and prosthetic, the socket. Often made of an inflexible, solid polymer that does not allow the residual limb to breathe or perspire and with no consideration for the changes in size and shape of the human body caused by changes in temperature or environment, inflammation, irritation and discomfort often cause reduced usage or outright rejection of the prosthetic by the patient in their day to day lives. To address these issues and move towards a future of improved quality of life for patients who suffer amputations, Loughborough University formed the Next Generation Prosthetics research cluster. This work is one of four multidisciplinary research studies conducted by members of this research cluster, focusing on the area of Computer Aided Design (CAD) for improving the interface with Additive Manufacture (AM) to solve some of the challenges presented with improving prosthetic socket design, with an aim to improve and streamline the process to enable the involvement of clinicians and patients in the design process. The research presented in this thesis is based on three primary studies. The first study involved the conception of a CAD criteria, deciding what features are needed to represent the various properties the future socket outlined by the research cluster needs. These criteria were then used for testing three CAD systems, one each from the Parametric, Non Uniform Rational Basis Spline (NURBS) and Polygon archetypes respectively. The result of these tests led to the creation of a hybrid control workflow, used as the basis for finding improvements. The second study explored emerging CAD solutions, various new systems or plug-ins that had opportunities to improve the control model. These solutions were tested individually in areas where they could improve the workflow, and the successful solutions were added to the hybrid workflow to improve and reduce the workflow further. The final study involved taking the knowledge gained from the literature and the first two studies in order to theorise how an ideal CAD system for producing future prosthetic sockets would work, with considerations for user interface issues as well as background CAD applications. The third study was then used to inform the final deliverable of this research, a software design specification that defines how the system would work. This specification was written as a challenge to the CAD community, hoping to inform and aid future advancements in CAD software. As a final stage of research validation, a number of members of the CAD community were contacted and interviewed about their feelings of the work produced and their feedback was taken in order to inform future research in this area

CAD interface and framework for curve optimisation applications

Computer Aided Design is currently expanding its boundaries to include more design features in its processes. Design is identified as an iterative process converging to solutions satisfying a set of constraints. Its close relation with optimisation indicate that there is strong potential for the integration of optimisation and CAD. The problem addressed in this thesis lies in interfacing the geometric representation of design with other non-geometric aspects. The example of free-form curve modelling is taken to investigate such relationships. Assumptions are made that Optimisation is powered by Evolutionary Computing algorithms like Genetic Algorithms (GA). The geometric definition of curves is commonly supported by NURBS, whose construction constraints are defined locally at the data points. Here the NURBS formulation is used with GA in an attempt to provide complementary handles on the curves shape other than the usual data point coordinates and control points weights. Differential properties are used for optimising NURBS, Hermite interpolation allows for the definition of higher order constraints (tangent, normal, bi-normal) at data points. The assignment of parameter values at the data points, known as parameterisation also provides control of the curve’s shape. Curve optimisation is also performed at the geometric modelling level. Old mathematical theorems established by Frénet and further developed by other mathematicians provide means of defining a curve’s shape with it’s intrinsic equations. Such representation is possible by using Function Representation (F-rep) algebra available in the ACIS software. Frep allows more generic and exact means of interfacing with the curve’s geometry and new functionality for curve inspection and optimisation are proposed in this thesis. The integration of optimisation findings and CAD are documented in the definition of a framework. The framework architecture proposed reconstructs a new CAD environment from separate elements bolted together in a generic Application Programming Interface (API) named “Oli interface”. Functionality created to interface optimisation and CAD makes a requirement list of the work that both sides should undertake to achieve design optimisation in the CAD environment.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

The investigation of a method to generate conformal lattice structures for additive manufacturing

Additive manufacturing (AM) allows a geometric complexity in products not seen in conventional manufacturing. This geometric freedom facilitates the design and fabrication of conformal hierarchical structures. Entire parts or regions of a part can be populated with lattice structure, designed to exhibit properties that differ from the solid material used in fabrication. Current computer aided design (CAD) software used to design products is not suitable for the generation of lattice structure models. Although conceptually simple, the memory requirements to store a virtual CAD model of a lattice structure are prohibitively high. Conventional CAD software defines geometry through boundary representation (B-rep); shapes are described by the connectivity of faces, edges and vertices. While useful for representing accurate models of complex shape, the sheer quantity of individual surfaces required to represent each of the relatively simple individual struts that comprise a lattice structure ensure that memory limitations are soon reached. Additionally, the conventional data flow from CAD to manufactured part is arduous, involving several conversions between file formats. As well as a lengthy process, each conversion risks the generation of geometric errors that must be fixed before manufacture. A method was developed to specifically generate large arrays of lattice structures, based on a general voxel modelling method identified in the literature review. The method is much less sensitive to geometric complexity than conventional methods and thus facilitates the design of considerably more complex structures. The ability to grade structure designs across regions of a part (termed functional grading ) was also investigated, as well as a method to retain connectivity between boundary struts of a conformal structure. In addition, the method streamlines the data flow from design to manufacture: earlier steps of the data conversion process are bypassed entirely. The effect of the modelling method on surface roughness of parts produced was investigated, as voxel models define boundaries with discrete, stepped blocks. It was concluded that the effect of this stepping on surface roughness was minimal. This thesis concludes with suggestions for further work to improve the efficiency, capability and usability of the conformal structure method developed in this work

AutoGraff: towards a computational understanding of graffiti writing and related art forms.

The aim of this thesis is to develop a system that generates letters and pictures with a style that is immediately recognizable as graffiti art or calligraphy. The proposed system can be used similarly to, and in tight integration with, conventional computer-aided geometric design tools and can be used to generate synthetic graffiti content for urban environments in games and in movies, and to guide robotic or fabrication systems that can materialise the output of the system with physical drawing media. The thesis is divided into two main parts. The first part describes a set of stroke primitives, building blocks that can be combined to generate different designs that resemble graffiti or calligraphy. These primitives mimic the process typically used to design graffiti letters and exploit well known principles of motor control to model the way in which an artist moves when incrementally tracing stylised letter forms. The second part demonstrates how these stroke primitives can be automatically recovered from input geometry defined in vector form, such as the digitised traces of writing made by a user, or the glyph outlines in a font. This procedure converts the input geometry into a seed that can be transformed into a variety of calligraphic and graffiti stylisations, which depend on parametric variations of the strokes