Building the Circular Segment

The crux of this particular design is the beveled circular segment which provides a horizontal bearing surface for the platform's bearings and drive.

I can take no credit for the design or construction technique of this element. Reiner's site has a link to a platform by Ed Jones in which he describes this method. As soon as I read Ed's description, I knew I had to try it. He describes it as follows: "This is so cool to do and it makes a really smooth perfect bearing surface! I love it." Now having done it myself, I agree 100%. Thank you Ed Jones!

What I might be able to contribute is a bit of elaboration over his brief (but wholly adequate) description of the process.

The tricky part is the layout. The surface is actually conical, so radius of the front (outside/north) edge is slightly larger than that of the back (inside/south) edge. You will make the rough cut with the front edge up, and the beveled cut on the table saw with the back edge up. So both sides need to be marked, although only the inside one needs to be precise.

Terminology: which face is which

Here's how I did it. There certainly may be other ways that could work equally well or better.

For the circular segment, I used 4/4 maple planed to about 20mm thick. The first step is to take the stock and cut a bevel on one edge. This is the top edge, that will go against the bottom of the platform. My platform is 40° so the bevel angle is 50°.

Blade is at 50° to table for my 40° platform

Bevel the top edge

(A time-saving shortcut: if you have already cut the platform base and the bearing base, described in the next post, now would be a good time to bevel their edges too while the saw is set up.) 

With the bevel cut, mark the front (outside/north) and back (inside/south) faces to help keep track. Measure the length of the stock and make a square line across it at the center on both sides. Start with the front face and mark the segment width (dimension (cs) from the spreadsheet) on the center line by measuring from the edge of the bevel. In my case this was 67mm.

Now mark the arc. These markings are not critical; on the front face the marking is used only for the initial rough cut. The actual arc will be precisely made by the pivot setup on the saw. I made a radius stick with a pivot nail at one end and small holes at the other to mark the arcs. My front face radius (dimension (c)) is 454mm.

Turn the stock over and mark (cs) again on the back face. This is the important mark; you will go exactly to this mark when sanding the bevel. Below I refer to this mark as "the (cs) mark".

Sharp edge of bevel is to the left; "(cs) mark" is the dot at 67mm

Turn the stock over again so the front side is up and rough-cut the arc. I used a bandsaw but a jigsaw would work. Cut a little outside the line.

From now on everything you do will be on the back (inside) face. Make two marks on the edge of the bevel, equidistant from the center line. These will be used momentarily to position the pivot arm square to the edge. The distance does not matter (I used 200mm). Make another line 30mm from the (cs) mark and parallel to the beveled edge.

Use the radius stick to mark the arc on the back. On my platform the inside radius is 438mm. 

Marking the arc

This photo shows the equidistant marks (at 200mm) and the 30mm line. The edge of the pivot arm board (at top) will align with the 30mm line. 

Cut a scrap piece with parallel edges and draw a line down the center. This is the pivot arm. Place it on the segment so that its edge is exactly on the 30mm line and the centers are aligned. Square it to the segment, drill a pilot hole on the center line, and drive a screw to attach it to the back of the segment.

Measure and mark the inside radius on the pivot arm from the (cs) mark on the segment. To make this measurement I put the tape measure on the edge of the pivot arm, which is 30mm from the (cs) mark, and subtracted 30mm. My inside radius is 438mm so I measured 408mm on the pivot arm.

Pivot point on pivot arm board. Center attachment screw is visible in top photo 

Measure diagonally from the pivot location to the equidistant marks you made earlier to square the pivot arm with the edge of the segment. With only the single screw in place you can nudge the pivot arm until the measurements are equal. When the pivot arm is square, add one or two more screws to secure it to the segment. (These are visible in some of the saw photos below.)

Squaring the pivot arm. Make both sides equal.

Drill a small hole at the pivot location and position another piece of scrap (the pivot base) the same thickness as the segment under the pivot. Drive a small nail though the hole and into the scrap. This piece will be clamped to the saw table.

Now the fun begins! With the table saw's bevel angle set the same as before (the complement of your platform's inclination) and the blade lowered to about 1/8" above the table, clamp the pivot base to the saw table so that the center of the arm is roughly perpendicular to the leading edge of the blade and the lower face of the segment is just barely engaging the blade.

Swing the segment through the blade to make a shallow curved, beveled cut (!). Always push the work into the blade; don't pull it back while the saw is running. Raise the blade in 1/8" increments until the cut goes all the way through. At this point, you will likely still be some distance away from the arc marked on the back face.

After the blade is high enough to penetrate the top face, but still a bit away from the line. The pivot base (clamped to the table) can just be seen in the upper left corner

Now start nudging the pivot base closer to the blade and making additional passes until the top edge is within about 1/8" from the (cs) mark in the center. 

Almost at (cs); time to stop cutting and start sanding

Swap out the saw blade for the sanding disc (if you need to acquire a disc, it's called a "calibration plate", with an adhesive backed sanding disc affixed to it). I used an 80 grit disc, which, with additional sanding later, made a smooth-enough bearing surface.

Very close now

Keep making passes and nudging the pivot closer until you just skim that (cs) mark.

As a final step, with the sanding disc still mounted, rotate the saw's bevel setting back to 90 degrees. Then make a couple shallow passes to square off the delicate sharp edge at the bottom of the bevel.

That's it. If you've gotten this far, your platform is likely to be successful! The rest is run-of-the mill woodwork. (Oh, and those electronics.)