Twisted Sheet Metal Transformers first created 30/01/07 - last modified 07/02/09 Page Author: Ty Harness
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Beta Version available to download from the members area Jan 2009.
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Preface

One of my favorite sheet metal developments is the hexagon-to-rotated hexagon with curved sides. I've never seen this particular development in a book although the triangulation technique is the same as Dickason's spiral finial [xx]. Mr Ward (who is still teaching at Grimsby College) usually sets this problem for all Part 3 Sheet Metal students. Unfortunately, these developments rarely crop up in industrial applications although, I hope, sheet metal workers who specialize in roofing still get the chance to 'knock up' some of the finer ornamental work.
The Twisted Transformers (TT) application is a light version of the Mould Loft software. TT allows you to design polygon to polygon transformers and define the side curves with a shape function. Figure 1 shows an elliptical function defining the side curves. There are 3 built in functions: Linear, quadratic and elliptical. There is also a fourth user definable function where you can use a 3rd party application to define any function you fancy. Defining functions is a powerful technique but a step away from keeping the software as simple as I first intended. There's more information on how to define functions at : TTfunctions.htm

By default it is possible to make up polygon to polygon transformers without any twist. Figure 1 shows such a case using 6 curved sides. An elliptical shape function is used to define the sides.

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Figure 1 - A hexagon to hexagon transformer with elliptical curved sides.


It's also then possible to twist the sides. The twist is entered as a percentage: For 3 sides 100% - 60 deg, 4 sides - 45 deg and 6 sides - 30 deg etc as shown in figure 2. Please note you can design the impossible with the software. Twists beyond 100% will soon become impossible to make in sheet metal.



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Figure 2 - Twisting the polygons is entered as a percentage


$R[(deg)/(percent)] = 1.8/N_s $

A further guide to the parameters describing the geometry can be found in the following PDF: tttest1.pdf

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Figure 2 - The same transformer as figure 1 but with a 30 deg rotation in the smaller hexagon relative to the larger hexagon.


Figure 3a shows two twisted transformers: 1) A square to square with an elliptical shape function only partially assembled and 2) a hexagon to hexagon with a quadratic shape function. After making the paper templates from the TT software it is preferable to transfer them to more durable templates (say thin steel) so that they can easily be scribed around. After all the segments are marked-out and cut. Pass the segments through the rollers to remove the cutting distortion. Roll each segment with no twist until it approximates the shape function. Starting from the small end, tack the segments to an end plate and work down and around the transformer by tacking every 1/2 inch. Use small increments between the tacks or you will get an unsightly 'bubble' in the segment which may not come out by 'dressing'.

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Figure 3a - Square to square partially tacked up and a hexagon to hexagon tacked up using TIG.
b) Square to square welded up and one made from brass sheet.


Figure 3b shows the same square to square made out of brass sheet. It always pays to make a trial piece out of steel before using expensive, exotic materials. Although the twisted job looks more complex the development still uses the triangulation method, and note the length of each side is equal to ensure the mitring will still work-out.

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Figure 4 - A 3D DXF export from the TT application and rendered in Right Hemisphere's Deep Exploration




Figure 3 shows a triangular, square, hexagon, octagon and a 12 sided polygons.

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Figure 5 - A selection of twisted finials created with TT,exported in the DXF format and finally rendered in TurboCAD 10.5 Pro.




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References {Please note I have no affiliation with any of the references below}
http://www.righthemisphere.com/
http://www.turbocad.com
ASCII to MathML used in this page: ASCIItoMathML homepage