Circular logic, part 3

At this point in the series around radius cutting, we have a very reliable way to cut a convex or concave part. But making an accurate cut in woodworking is usually dependent on accurate layout. And so this entry will cover some of the results of my head-scratching on the topic. Coming from a straight and square world, some things transfer, and some don't.

As with part 2, it bears mentioning up front that this is NOT the way I'd do things in a one-off environment, or in a typical production environment. I went off the reservation a little bit, away from the job at hand, and into the realm of obsessive curiosity and experiment, in the hopes that it would make this particular project roll more smoothly into limited production.

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The photo above is a simple beam compass made with some T-track and scraps, a screw, and a modified X-Acto knife: I ground the knife to something close to a 90 degree point, for durability.  This is the curved version of a marking gauge, for my purposes: Among other things, I wanted a mark that would positively engage with the brad point of my drill bits when I went to drill the holes for the locating pins.

Note that I set the beam compass up with the blade at the end, and the pivot point in the interior of the beam. I learned to do that years ago. It allows me to rest the weight of the assembly on the point, and I can teeter the thing as needed to put only the desired pressure on the marking end. This is something I learned with pencil beam compasses, to keep from breaking leads or digging into the paper. It helps a lot here, too, for controlling the cut.  (A look at vintage compasses will reveal a shoulder on the pivot point, to keep it from digging too far into the paper. This supports the weight while the compass pivots, so the point doesn't just gouge in.)

When I set the radius, I do so with a good Starrett machinist's scale, as the graduations are etched, and the points (point of the knife, pivot point) will both register.

"Why?" Is an obvious question. Why make such a fuss over precision? The arch on the clock is free-floating, as it were, and doesn't connect to or reference against anything. There are no reference edges. The answer, in part, is that the locating pins for the radius jig needed to be precisely placed, and I used the scribed arc to register my brad point bits when I set up to drill the holes. Another answer is that when it comes time to connect to the three-way miters, every advantage helps.

Back to work...

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At this point in the project, with the concave part of a bending form in hand, I needed a mating convex part to use in the laminating proces. (I'm not using a vacuum press here.) And, to make matters more complicated than they needed to be, I wanted to make that part using the scraps that I had from cutting the concave part.

It occurred to me that for a bending form, I just wanted to take a certain amount off of the edge of the scraps, to account for the thickness of the part being laminated. If I had access to the geometric center, I'd use a compass to find the radius of the blank, subtract the amount I wanted to cut off, and lay out that way. But I didn't have access to the center. On a straight and square board, you can measure from a straight edge, at any point along the edge, to make a parallel cut. But in this case, there's no straight edge to reference against. But eventually it occurred to me that a center finding head will allow you to measure in from the edge pretty reliably, to lay out a concentric curve without knowing what the radius is. The blade will point towards the geometric center of the arch, and allow you to measure from the outside in, perpendicularly to the tangent line... which isn't the way I was taught to work with circles, so it bent my head for a minute. That's just a way to measure, it's not the same thing as laying out with a real marking gauge. But I found I could use it to guide a marking knife concentrically around the curve, and lay out that way. This really only works accurately for circular curves, but it turned out to be a pretty neat trick.

In the picture, you'll also see an arch with a labeled radius. That's one of my radius gauges.

At some point, it became clear that gauging a perfectly concentric arch off of a radius of unknown dimension wouldn't give me the precise results I was after. I needed an arch with a known radius, (radius gauge) to at least make sure the line I'd drawn was at the desired radius. This was when I made the beam compass. With a gauged line, you can see when you've accurately hit your mark. With the jig on the router table, I could fine tune the adjustments well enough to split the mark. (You can see when the knife mark remains in the edge you've just cut.) It's probably not precise enough for a machinist, but it was good enough for me.

Another interesting bit: Without knowing the radius of the edge of this blank up front, using the radius gauge and a center finding head allows me to get a reasonable measurement of the radius anyway. Using the center finding head, I can check to make sure the radius gauge is positioned concentrically. From there, I can measure from the outer edge of the radius gauge, to the outer edge of the curved blank to find out the difference in radii, and go from there.

 

The outer radius on the arch above (R= 10 1/4") corresponds to a pair of holes on the scissor jig, where the mounting pins drop through. The inner curve corresponds to the next set of holes, (9 9/32" *)  which are the holes I used on the jig for this operation. (You can see this in the pictures.) Those holes are centered at a 9 9/32" radius from the center of the pivot pin on the jig. So this was a necessary dimension to gauge where to drill the new holes, for the convex part of the bending form. The arch was an aide to help me make sure that my layout was accurate.

From there, I could set up the drill press to drill symmetrically placed holes...

The holes let me make a concentric cut on the band saw...

...and make the finish pass on the router table. 

As Mark had observed, I'd wandered pretty far away from paying work while I was tinkering with this. But as I was tinkering, a lot of things jumped out at me, all at once, about navigating curves, and I dove head-first into the rabbit hole. It's one thing to understand the geometry of a circle on paper; radii, diameter, calculating chord lengths, etc.. It's something else entirely to be able to create those things in a physical object. It's not a matter of being able to calculate what the measurements should be, it's a matter of being able to cut to those dimensions, and be able to refine the cut to course-correct as needed. This all began to feel like I was learning to lay things out and plan the process in a whole new way, so I steamed straight on ahead.

There's gold in those hills, if you look for it. But one of the things I've learned recently from Mark Twain, is that getting the ore out is one thing, but nobody tells you that refining and smelting the ore is a wholly separate process, and the finished product can sometimes be smaller than what you think you dug up. Between the beam compass, radius gauges, etc, I burned up a solid day or so in tinkering. The nuggets were pretty shiny, but the final take-away was maybe not as big as I'd hoped. I'm still digesting what it all means, but I have no doubt that it will turn up in future work, when I get there. 

Considering that the point of departure for all of this was my frustration with more primitive methods of cutting curves, I can say that I went a LONG way towards easing those frustrations, and cutting curves is a lot simpler and more precise for me now than it used to be.

You can see by the shadows above that the sun was getting low on the horizon by the time I had this worked out. 

But the bending form came out cleanly...

And the finished part did, too.

Again, a lot of this is tantamount to driving From Boston to Connecticut, by way of Tokyo. (Which is clearly accomplished by driving a very over-thought car, with re-invented wheels.) Making a bending form is NOT a complicated task, and certainly doesn't call for this degree of caffeine-fueled head scratching. But then again, there are jigs that will come up later on that wouldn't have worked without some of the groundwork laid here.

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Side note, I wanted to add in here that the MFT was a really remarkable layout aide. Using dogs in the hole grid gave me a way to register parts against each other, or to hold and clamp them at a reliable 90 degrees to each other. I don't think that's enough of a reason to buy an MFT, but if you have one, it's reason enough to invest in some qwas dogs.

* 10 1/4", 9 9/32"... the radii on the jig seem bizarre, I know. I drilled the holes at 1" intervals along the beam, but the geometry of the dog-leg feature meant that the angles to the mounting holes were constantly changing, and the radii didn't end up working out to be 'regular' intervals. I'm sure it's possible to design and build a jig to have more 'even' sounding numbers, but at some point, it really becomes academic... or, more academic than this already is. Laying out a part to be cut with this system, means laying out the final radius with a compass, and laying out the concentric radius along which the locating pins would be placed, to make the jig work the way it's designed to. So, I had to measure the actual radii, from the center to the holes on the beams, to be able to lay them out... and the actual numbers ended up being weird ones. 

Auto-Regulator: Circular Logic, Part 2

So, this is where we were last time:

In the photo, we have sliding center point jigs for the band saw, and for the router table: A dog-leg scissors jig (foreground, on the right) mounts to a blank, using non-threaded pins, to guide the blank while cutting inside or outside radii. There's a center pin that forms the pivot for the scissor jig, that protrudes from the bottom of the jig, and drops into a hole in the mating part of the radius jig, of which there are two: one that mounts to the jigsaw, one to the router table.

The first test for the jig was to make a pile of MDF layers that would stack up into a bending form. And this is as good a place as any to point out that this particular jig isn't the standard, or smart way to accomplish the task. So I'll also confess here to being a little too cerebral. Mark wandered over, asked what I was up to, and pointedly remarked that I was doing things in 'long-hand.' And he was right. There are many ways to skin this particular cat, and almost all of them are much more efficient. His suggestion (based on much more experience than I have) was to cut one master curve, and pattern-rout the rest from that. But I wanted to see this experiment through, and see if the long-hand proof would result in something that would save me time down the road. I also figured that this particular exercise would test the system, to see how robust it was.

Center hole and center pin are at the bottom right.

Using the jig for cutting radii in either direction (inside or outside) is pretty simple.  Because the base jig slides, and the scissor jig has so many holes, it's easy to find a setting that will work for any radius. But for the purposes of identical parts, mounting pin placement in the blank was an X-factor. The holes for the pins are drilled at identical distances from the center, but the distance between pins is also relevant. Once the arc is laid out to locate the mounting pins, you can drill anywhere along that arc to locate the pins. But two identically shaped blanks with holes drilled at two different chord lengths will result in two differently shaped parts: The cuts made will have identical radii, but the cut will be placed differently in each blank. It was one of those details that's obvious in hindsight, but still made me scratch my head for a minute. Since the object is to create a bending form, all of the layers must be identical, so pin placement needs to be the same on all of them.

I laid out the first blank, and set up the pin holes to be exactly the same distance from each side, and from the front edge, and drilled them using a fence and a stop block. Drill, flip, drill, and the result is two holes with identical spacing from each end, and the edge.

To the band saw, and then to the router table...

 

Initially, I'd used a smooth pin, loosely installed in a hole to hold the center. I switched to a threaded bolt that ended in a smooth pin, because there was too much slop in the radius with just the loose pin. It made for a difference of maybe 1/64"- 1/32" from one radius to the next. But for a bending form, everything has to be exactly the same.

For the record, this was just about when Mark made the comment about doing things longhand, and flush trimming being faster for a bending form. Obviously, he was right. But I was being stubborn, and wanted to see just how accurate the jig was. Basically, I was reinventing the wheel, for the fun of it.

With the slop issue ironed out, the final stack was just about perfect. There were inconsistencies that I could feel, but they were small enough to fix with a plane. It felt a little bit like cheating, since I was trying so hard to make the the jig accurate enough to not need to smooth anything out.

All things considered, it's a very accurate system. The fact that I can re-adjust the center point and take a second pass on a radius cut sets this jig apart from other jigs that I've seen. And for production purposes, it means I can creep up on a very accurate radius for a master pattern, or on a wooden part. And with the incorporation of the router table in the process,  I can use this jig to make a finished curved surface that's ready for sanding, without any further work. 

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Part 3 will go into a little more theory on dealing with radii. The bending form is a 2 part form, so it will have a mating piece. But cutting that means taking the convex off-cuts from the concave form, with identical but unknown radii, and finding a way to locate the mounting pins to change the radius.