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Back in 2003 I first discovered a method for making these helix forms using a scroll saw with a spiral blade. The nesting helices are cut from the same dowel in a way that looks impossible. Mathematically the surfaces are classified as ruled surfaces because the shape of the surface is made by a line segment. Now you can find Youtube videos and information by others showing candlestick holders and ornaments made in a similar way. Those helix forms are made with the scroll saw table set square to the blade. Making the same thing with the table tilted causes some very interesting effects on the outcome. Here is a link to an article written by George Hart about my method.
I have an ebook available that shows you how to make the helix forms using a scroll saw with a table that can be tilted, and spiral blades. Along with the ebook, there is also an Excel spreadsheet that lets you design a helix form graphically by using sliders or scroll bars to adjust the parameters. As you change the parameters the cross-section of the helix form changes in real time. The price of the ebook is $24.99.
A pair of nesting helices in walnut. 2004 Sold.
In 2005 I manged to modify my band saw to make it capable of cutting with a homemade spiral blade and made a few larger helix forms that are too big to be made with a scroll saw. The one in this video slides together very easily. I ran into a lot of frustration with the homemade blade because it kept breaking and needed to be soldered back together. I suspect that the band saw wheels were too small causing the blade to fatigue.
"All Screwed Up" is the title of this helix sculpture that was made in 2005. A total of 7 helices were cut from a large block of black walnut. This video shows how the sculpture is assembled. There are 3 pairs of right-hand oriented nesting helices that are held in place by the ebonized and left-hand oriented helix that contains the center line of the cylinder. Makes me wish I had an abrasive waterjet to play with in my shop. :)