lay out a spiral

remember polar equations?

bill tindall, E. TN

>A formula that will enable you to graph hyperbolic spiral is r(theata) = a.

A way is to get some graph paper, ruler and protractor. Pick a spot. P, in the center of the paper and this will be the spot from which all measurements are made. " r" is the ruler distance from this spot. a is a constant. theata (which I am going to abbreviate T because I don't know how to make a greek theata is the angle on the protractor, which everyone has saved from their geometry class. I have 3 of them. Set the origin of the protractor on the point P of the graph. 90 degrees is straight up, 180 degrees is left, 270 down, etc. Now just plug in values of T, solve for r, and plot the r value on the graph paper.

for example:

to select a convenient value for "a" lets say it is 10 cm from our central spot on the graph paper. P, to half way to the top of the paper. For this 90 degree point our equations says ** rT = a** 10 times 90 = 900. So, our constant a will be 900.

To get the point on the spiral for 120 degrees we substutute

r (times) 120 = 900, and solving for r, r = 7.5 cm. At the protractor setting of 120 degrees measure out 7.5 cm from spot P and make a dot. At a protractor setting of 80 degrees, r (times) 80 = 900, so at 80 degrees the point on the spiral is 11.25 cm distance for point P. Repeat for as many values of T as you need to fill in the curve, using values. T can be made greater than 360 degrees to make successive loops of the spiral.

Another way is to draw a right triangle, with base b, height h and hypotenuse p. Now draw a second right triangle joining to (on top of) the first, using the first triangle's hypotenuse as the base of this second triangle and the same height h. Repeat making triangles each time using the previous hypotenuse and the next base, while keeping h the same.

You will soon seee that the outer points define a spiral.

A mechanical method

Dave Thompson

>Tether a pencil to a dowel with a thread. Place the dowel (preferably with a pointed tip) at the center of your spiral. As you rotate the pencil around the dowel, the radius shrinks as the thread wraps around the dowel.

The thickness of the dowel determines the distance between spirals. The distance between spirals will be (diameter of dowel)*3.14.

Probably easiest to do this on paper, and then transfer to wood with carbon paper.

Dave

Re: A mechanical method

Philip Duffy

>I think I like the mechanical way best! Phil

Re: lay out a spiral

Greg B�tit, Vergennes, VT.

>If you're laying out volutes for carving on ears, you should use the chisels to do the layout. The central circle of the ear is done with a #7/18mm, and the extension of the inner circle as it unwinds is done with a #5 20mm. (For an arm knuckle, the inner circle is traced with the #8/16mm, and the inner volute is finished with the #7/18mm.)

The outer circle is formed by scooping out a volute surface that starts at the top surface, and slopes to the depth of the inner volute (which is 3/8"-1/4" or so for the ear.)

Sorry for the rather ugly example carving...

greg

References

Tony - Memphis

>The method is shown in a couple of books. The Benjamin Asher books show it and the Chippendale book shows it (both from Dover online). I also wrote a program that draws them. I can try and find it and email it to you if you are interested. Or maybe I can send it to Ellis to make it available here. Nothing fancy, I'm a hacker, not a programmer! It was just something I fooled around with because I was interested.

Tony

Re: References

Philip Duffy

>Geee, you guys are so great to offer such explicit solutions to my problem. I am trying to carve volutes on my 2nd Windsor and it looks so simple but it is not. I would appreciate the s/w solution/pgm and will try everything to see how it works. ( I am a slow learner on these things!) Thanks to all, Phil