The following article appeared in the April, 1993, Bulletin. Antonio "Tony" Rizzo is a retired aerospace engineer from Torrance, California, and has been a SCAVM member since 1989. He is our president for the year 2001. He has a Web site at www.arviolins.com.
The objective is to develop a topographic map of a plate (top or back) from cross-sectional views of the arch, on the plan view of the plate. Once developed, each plateau of the topography can become a template for accurate replication without pantographic means.
I don't consider this a novel approach. I'm sure many variations of this scheme have been done before. For better or worse, here is the way I do it.
Let's review the arches from Sacconi's Secrets of Stradivari:
If we had a plate that we wanted to map, we could set up a height gauge to a specific height relative to the plate gluing surface and draw or establish a parallel plane on the plate which in a plan view will show as an outline for that particular elevation.
Incrementally raising or lowering the height gauge will establish parallel planes. An infinite number of planes could be established, however, from a practical sense, two millimeter increments will generate enough plateaus for reasonable accuracy.
Now lets take cross-sections at the five (quinte) locations as Sacconi did, and a cross-section of the longitudinal centerline. From the centerline in the plan view, at a quinte location, measure the distance to the topographic line for a particular plane, and transfer that point to the quinte cross-section on that corresponding plane. After all points are plotted from all planes, connect the points with a French curve and the arch for that cross-section is complete. Repeat this step for all quinte cross-sections.
It appears that this may have been the method used by Sacconi in copying the Stradivari G model violin in his book (along with a viola and cello).
So much for Sacconi.
Now let's assume the opposite which we often see in Strad magazine posters or purchased plans for instruments, where only the quinte templates and longitudinal template arches are shown along with the plate outline and with no topography. Establishing a topographic map could simplify an accurate reproduction of a particular instrument plate.
To begin with, we must have some confidence that the curves of the arches provided were reproduced accurately. Draw or trace the outline of the plate as a plan view, and the five transverse cross-sections and the longitudinal cross-section in views which can be projected on each other or superimposed. We can now begin to establish corresponding planes on each cross-section. Where these planes intersect the arch is the point that will be projected or transferred to the plan view. Accuracy here is important in determining the exact point of intersect when the slope of the curve and the intersecting plane form a shallow angle.
The lowest plane could be (on a violin) five millimeters up from the plate gluing surface. This would provide material for the four corners. Each plane above this plane could be set at two millimeters apart up to the highest arch dimension.
Project all points from each cross-section
arch to their corresponding line in the plan view. We now have
points located on each quinte line is where some guesswork comes
in, interpolating the topographical profile between points with
a French curve, and on the longitudinal centerline.
Here which when compared with the adjacent profile will produce a contiguous smooth flowing curve at any given cross-section. Connect all the points on each plane to form the outline of each plateau. The map is now complete.
Have a plate ready to be arched, with a thickness close to the dimension of the arch height.
Using the topographic layout of the plate, make a template for each elevation. Templates can be made from aluminum or plastic sheet stock, 1/16" or 1/8" thick. Drill a 1/8" diameter tooling hole at the center of the upper and lower bouts on each template. To assure that the hole center distance is alike with each template, stack all the templates aligned with each other and drill through the stack. Templates that are longitudinally shorter than the tooling hole center distance should be pinned with a separate set of holes.
Make a rectangular platen from 3/4" plywood, a few inches larger in size than the plate. From a template, transfer the two tooling holes on the centerline of the plate to be arched and to the platen. The holes in the plate should not be deeper than five millimeters (which can later be gouged out when graduating). The holes in the platen should be drilled through. Install 1/8" diameter dowel pins (steel or brass) into the platen with 1/16" projecting through the bottom side.
Bond or screw in place four feet to the bottom side of the platen at each corner. The feet should be the same thickness as the templates. In fact, the same material can be used. The feet will prevent the platen from tilting when a small template is being used.
Set up a drill press with a large plywood table extension fastened to the drill press table. Drill for, and install a 1/2" diameter guide pin centered with the drill press spindle. The pin should protrude no more than the thickness of the templates. Chuck a 1/2" diameter router bit in line with the guide pin. A router could be used instead of the drill press. It would require a fixture to support it directly over the guide pin.
Place the plate to be arched over the tooling pins on top of the platen. Fasten the plate to the platen with two #8 flat head wood screws from the underside of the platen and located inboard of the two dowel pins. Do not go too deep into the plate with the screws. Place a template over the tooling pins on the bottom of the plate. The templates could be held in place with flat head screws if desired. Now rest this assembly on the plywood drill press table.
Set the cutting edge/face of the router bit to the highest elevation using the top of the platen as a datum surface. Make sure that the corresponding template is installed under the platen.
Drive the router bit at a high speed and (CAUTION)
slowly push the work into the cutter, removing material, until
the template bears against the guide pin, the cutter is milling
away the corresponding plateau on the plate. Keeping the template
against the guide pin, guiding the platen around the pin as though
you are using a pin router setup. Change template as each plateau
is completed. Start with the highest elevation (smallest template)
and work down. Change the depth of cut of the router bit to correspond
with the appropriate template (say two millimeters between each
plane or whatever is established). If desired, mill the elevations
one half millimeter higher to allow material for hand finishing
and slight discrepancies in the setup.
With all of the plateaus milled, we now have established a series of steps where the internal corner or root of each step is the location of that topographic line of the layout. By planing away the corners of each step down to the root and blending the contours we will have an arch which will be dimensionally close to the copied instrument.
All Bulletin articles are copyrighted ©1997 by the Southern California Association of Violin Makers. Contact Bulletin editor John Gilson, at the address given on our home page, for permission to reproduce Bulletin material.
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