Open Collections

Computer aided design of developable surfaces

University of British Columbia

The design of objects employing developable surfaces is of engineering importance because of the relative ease with which developable surfaces can be manufactured. The problem of designing developable surfaces is not new. Two space curves, defining the edges of the surface, are first created, then a set of rulings are constructed between the space curves under the constraint of developability. A problem with existing algorithms for designing developable surfaces is the tendency to introduce non developable portions of the surface; areas of regression. A more reliable solution to the problem of creating a developable surface is proposed. The key to the method is to define the developable surface in terms of a normal direc trix. The shape of the normal directrix defines the shape of the developable surface. Algorithms are defined to compute the shape of a normal directrix from a pair of space curves. A non-linear optimization technique was implemented to further refine the shape of the developable surface, but failed to yield satisfactory results. Other algorithms were also created to intersect adjacent developable surfaces and to generate the flat plate lay outs. The algorithms were implemented using the C++ programming language and the AutoCAD CAD package. Recommendations for further work are given. The design of objects employing developable surfaces is of engineering importance because of the relative ease with which developable surfaces can be manufactured. The problem of designing developable surfaces is not new. Two space curves, defining the edges of the surface, are first created, then a set of rulings are constructed between the space curves under the constraint of developability. A problem with existing algorithms for designing developable surfaces is the tendency to introduce non developable portions of the surface; areas of regression. A more reliable solution to the problem of creating a developable surface is proposed. The key to the method is to define the developable surface in terms of a normal directrix. The shape of the normal directrix defines the shape of the developable surface. Algorithms are defined to compute the shape of a normal directrix from a pair of space curves. A non-linear optimization technique was implemented to further refine the shape of the developable surface, but failed to yield satisfactory results. Other algorithms were also created to intersect adjacent developable surfaces and to generate the flat plate lay outs. The algorithms were implemented using the C++ programming language and the AutoCAD CAD package. Recommendations for further work are given.

Thesis/Dissertation

application/pdf

2009-02-23

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http://hdl.handle.net/2429/4930

Mechanical Engineering

University of British Columbia

UBCV

DSpace