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Point-based mathematics for computer-aided manufacture

Fisher, Matthew (2001)
Ph.D. thesis, University of Birmingham.

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This thesis demonstrates the feasibility of machining high quality sculptured surfaces directly from a point-based definition. The work is founded on the strategy of using a sparse set of points to characterise shape although it is assumed that an appropriately dense definition can be generated by the use of some unspecified high quality interpolation algorithm. This is in contrast to the conventional CAD/CAM approach where explicit parametric expressions are used to describe the part. The research is founded on the Inverse Offset Method (IOM) proposed by Kishinami; the algorithm is chosen because it possesses a number of desirable properties, most notably its versatility and robustness. The first fundamental contribution is an error analysis of the IOM that has not been published before, the analysis is dependent on the surface and cutter path point spacing, the tool radius and the local surface curvature. The accuracy of the error analysis is corroborated by the machining and measuring of a physical part. Furthermore it is established that the quality of the finished part produced by the IOM compares favourably with that produced by a commercial package for similar tolerances. The principal research achievement is the optimisation of the IOM to exploit the coherence of data ordered into sections. This results in the IOM generating cutter paths in a time period comparable to that of the commercial package without a reduction in the quality of the finished part. The last contribution made in this thesis is a report on the issues concerning the machining of point definitions derived from multi-surfaces. The work presented in this thesis offers an alternative strategy to the design and manufacture of free-form surfaces. The main benefits of adopting this strategy are gained because it removes the need to generate a parametric surface definition.

Type of Work:Ph.D. thesis.
Supervisor(s):Ball, Alan
School/Faculty:Schools (1998 to 2008) > School of Engineering
Department:Manufacturing and Mechanical Engineering
Keywords:Point-based, computer aided manufacture, inverse offset method
Subjects:TJ Mechanical engineering and machinery
QA Mathematics
Institution:University of Birmingham
Library Catalogue:Check for printed version of this thesis
ID Code:864
This unpublished thesis/dissertation is copyright of the author and/or third parties. The intellectual property rights of the author or third parties in respect of this work are as defined by The Copyright Designs and Patents Act 1988 or as modified by any successor legislation. Any use made of information contained in this thesis/dissertation must be in accordance with that legislation and must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the permission of the copyright holder.
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