Making a mainspring Length Gauge
The following article is based on an e-mail to the Clocks mailing list from W. R. Smith
For those interested in a mainspring gauge that gives a mathematically correct answer for the length of an in-barrel mainspring, rather than a rule of thumb guess, here is one that can be made quite easily. The articles describing the making of this gauge were published: April 15, 1983 Model Engineer, and the NAWCC, August 1992, Bulletin.
How it works
First of all, we must establish the principal on which it works. A mainspring of the correct length will occupy the same area of the barrel end view when wound and unwound, i.e., the wound and unwound areas must each be 1/2 of the total available area. Our gauge must find the point where this division of the area occurs.
In all the math I have studied, I have never seen what is now to be described. If a large circle and a small circle have the same centre, as would be the case of the outside of a barrel arbor and the inside of a mainspring barrel, the following is true, and can be easily proven mathematically. Imagine a radial line from the centre of the two concentric circles to the outside circle, as shown in Fig. 1. Where this line crosses the small circle, call the point A. Where the line touches the large circle, call it point B. It follows that if A-B is the base of an equilateral right triangle, the apex, C, (containing the 90 deg angle) will lie in the area between the two circles. Astoundingly, the apex also lies on the circle that divides the total area between the two circles into two equal parts. If we imagine line A-B being vertical and the apex, C, lying to the right, then a similar apex, D, on the opposite side of the base A-B will also lie on the same circle. Thus, lines drawn through A, B, C, D will form a square. Since our barrels and arbor will be of different sizes, we must somehow create a square that, within its range, can be infinitely changed in size. The problem has now become a simple one.
Making the Gauge
Take a piece of brass, Fig. 2, that is 7" long and, say, 3" wide. Draw a centre line (A) down its entire length. From end to end of the stock, draw a line on each side of the centreline (B & C), parallel to it and 1/2" away.
Starting 1/2" in from the end of stock, draw a square (D) 1-1/4" x 1-1/4" that has its diagonal lying on the centre line. Do this geometry carefully and then saw away the centre of the square and file to the line. Now draw lines outside and parallel to the four walls of the square and 1/4" away from them (E).
Next, starting a each apex of the square furthest from the centreline, draw lines (F) that gently curve down to touch lines B and C on the handle side of the square. This should form wall for the square that starts 1/4" wide at the apex of the square and gradually widens as it goes to the handle.
Follow this curved line and saw away the metal. This will leave a 1" wide handle with a square on its end. Round the other end of the handle (G). Saw away the excess metal left on the outside walls of the square opposite the handle. Lay a nickel, or a small washer, centred of the centreline and over the furthermost end of the square (furthest away from the handle), and mark an arc (H) that is 1/16" away from the inside apex of the square. Saw away the stock along the line. This is relief so the gauge can be placed over the arbor, miss the pivot, and allow sighting down the inside apex of the square and directly down the O.D. of the barrel arbor. The final shape of the bottom plate is shown in Fig. 3.
Make two of these pieces, as shown in Fig. 3.
For the top plate, saw away the two endmost walls of one of these pieces to obtain a handle with a part of the square remaining, which looks like a V with the handle coming out of its bottom, as shown in Fig. 4.
Put two 1-3/8" long slots, 3/4" apart, in this plate, just wide enough for a 6-32 screw and centred on the centreline. Lay the top plate on the bottom plate and drill and tap two 6-32 screw holes positioned such that with the slot against the screw, one square will lie directly over the other, and the top plate can slide forward creating a smaller square. Install two binder head screws and solder their threads to the bottom plate allowing clearance for the top plate to slide forward freely, changing the size of the square with each movement. The assembled tool is shown in Fig. 5.
Using the Gauge
Use the gauge as follows: Place the inside apex of the square (the one furthest from the handle) over the O.D. of the arbor. Slide the top plate until the apex of the top square nearest the handle lies directly over the I.D. wall of the barrel. An unwound spring of correct length will pass under the two remaining apexes, as shown in Fig. 6. A spring that is too long will pass nearer the arbor, and a spring that is too short will pass nearer the barrel wall. You can make a judgement call regarding the short portion of the spring that circles in to the arbor.
Happy fabricating,
W. R. Smith, FBHI, FNAWCC, CMC, CMW.
Gateway Clocks
7936 Camberley Drive
Powell, Tennessee 37849, U.S.A.
Phone: 423-947-9671
WRSmith2@AOL.COM
Bill has also written three books: How To Make A Grasshopper Skeleton Clock, How To Make A Lyre Skeleton Clock, How To Make A Skeleton Wall Clock and Clockmaking & Modelmaking Tools And Techniques, all available in America from the above address or in England from John Wilding, Wheelwrights, Hillgrove, Lurgashall, Petworth, Sussex GU28 9EW.
