New Fence for a Marking Gauge

About 12-15 years ago, I met a man on a plane who noticed I was reading a woodworking magazine and we struck up a conversation.  Short story shorter, he ended up surprising me by sending a few tools that he was no longer using.  Among these was this marking gauge labelled "Worth", a name I didn't and still don't know anything about.  EDIT - an internet search came up with a thread on a "Garage Journal" forum where people identified Worth as being a brand from Bigelow and Douse Hardware of Boston, MA.  They further noted that the Worth tools were probably manufactured by Peck, Stow and Wilcox (Pexto) for the hardware store.

The Worth marking gauge

It had a wooden screw to clamp the beam in place, approx 3/8" x 10 tpi

Like many similar gauges, the wooden screw had become loose as the wood fibers were worn away.  Also, the mortise hole in the fence wasn't a great fit for the beam, so this gauge has been sitting in a drawer for a long time.

At first, I addressed the beam looseness problem by putting some blue masking tape on the beam to get a tighter fit in the fence.  Obviously not a long-term solution.  Then I thought about putting a threaded insert in the screw hole and using a metal thumb screw.

Brass threaded insert

It turned out that the brass insert was still a little loose in the hole, so I decided that I'd make a new fence.  If I was making a marking gauge from scratch, I'd mortise the fence first and then plane the beam to fit just right.  For this one, I wanted to use the Worth's beam, both for nostalgic reasons and because I like the scale printed on one side.  It was a little tricky to make the mortise just the right size to fit the existing beam.  I ended up using a caliper to measure the beam's width, locked the caliper at that measurement, then stabbed the inner diameter measuring fingers of the caliper on the new fence to mark for the mortise walls.

Mortise chopped and upper and lower facets shaped for the
curved top and bottom surfaces of the beam

At first, the fit seemed a little too loose, but after some shellac it fit very well.  Next, I bored a hole through the top, down to the mortise.  I had shaped and placed a stick in the mortise so that I wouldn't blow out the mortise's top wall.  The threaded insert went in that hole.

You can see the insert within the mortise

I used a leather punch to make this plastic "coin" (?) so that
the thumb screw would not damage the top of the beam

I get a good solid grip of the beam when the thumb screw is tightened

Then the screw was cut down to length.  To make the thumb screw more comfortable, I inset the "thumb hold" part of the screw into two small pieces of walnut that were carved out to fit the thumb hold and then glued together.  It was then shaped to make a much more comfortable grip and look a bit more like the original.

The new thumb screw next to the original

After shaping the fence for comfort, I gave the parts a few coats of shellac, then waxed all but the bottom of the beam - that's what gets pressed against the lower mortise wall when the screw is tightened and I don't want that to be slippery.

So I now have a nicely working marking gauge.  It looks a little funny being two-toned, but I got to preserve some of the gift I was given and give it new life.

Glamour shot #1

Glamour shot #2

BTW, I changed one thing in my fence from the original: there is more meat below the mortise in the walnut fence.  I like having that extra bearing surface when using a marking gauge.  The original had less than 5/8" of bearing surface to reference against a workpiece.

Spreadsheet for Determining Radius of a Curve

This post will be considered by some as an intellectual exercise only.  Maybe it's for math geeks, like myself.  There are simpler methods to do what I write about.  I'm all for simplicity, but I like the math.

When I want to put a curve on the underside of a chair rail or a table apron, a simple method is to place a clamp at either end of the intended curvature and bend a stick (or ruler) to the desired "bulge" of the curve.  While this method will give attractive results, the resulting curve will not be exactly circular.  The stick bends more at it's center than at its ends.  And it may not bend equally both sides of center.

Marked lines 1" from ends, and placed clamps near those marks

Centerline marked and 1 inch "bulge" marked from lower edge

Bend a stick to the "bulge" mark, and draw the curve

Here's the resulting curve

There are times when I want to end up with a curve that is part of a circle.  And when this is the case, I'd like to know the radius of the circle that will give the desired curve so that I can lay it out on the workpiece.

Here's an example, same as in the above pics.  Suppose I have a 20" x 2 1/2" rail and I want to put a circular arc on the underside.  I want the arc to start 1" from each end of the rail and I want it to extend up into the rail's front face by 1".  So that's an arc 18" wide with a 1" bulge.

Using a little math, I can calculate that the radius of the circle that gives the appropriate arc is 41".  I can then use a stick (or piece of string) of that length and a pencil to lay out the curve.  I'll write more about the math below.

This stick will allow arcs up to approx. 48" radius

One end has a shallow slot to run a pencil in

You can put a screw anywhere on the stick for whatever radius you need.
The screw tip exits the bottom side, and it is used as a pivot point for drawing the arc.

Here, I'm using the radius jig to mark the arc on the workpiece.
Note that the screw has to be in line with the centerline of the workpiece.

The two methods give very similar results, so it really doesn't matter which you use.

You can see the slight difference in the two methods

But if you're doing a smaller piece, say an arc only 6" wide, then that bendy stick won't bend in that tight a space.  That's when it would be easier to use a radius stick.  For those smaller pieces, I can use my homemade trammel points to create the arc.  I'll show that below.

Another place where drawing a circular arc has come up is when laying out a camber on a scrub plane iron.  I recently made an iron that was 1 1/2" wide and I wanted a 1/16" bulge at the cutting edge.  For this iron, I simply filed a curve to get it close.  But if I wanted to be more precise, I could figure out what the radius of that curvature is and make a template.  Turns out it is about 4 1/2".

Cardboard template, 1 1/2" wide with centerline drawn

Homemade trammel points

Setting the distance to 4 1/2"

Drawing the appropriate arc on the template

Measuring the resulting bulge - it's about 1/16"

Comparing the template to the plane iron

OK, now here's the math part.  It has to do with right triangles and the Pythagorean theorem.  I'll start with the example of a table apron, which I want to put an arc on the bottom edge, starting some distance in from each end and rising up a certain amount.  In the picture below, points A and B are the ends of the arc, and C is a point centered between them.  The width of the arc I'll call "w", so the distance from C to B is 1/2 w.  The bulge of the arc is the distance from the lower edge of the board to the highest point on the arc.  I call it "b".

The workpiece with arc drawn.  The arc has width "w" and height "b".

Now I'm going to zoom out so you can see the rest of the picture.  The arc drawn on the workpiece is part of a large circle, whose center is at point O.  The radius of the circle, given by distance R, is the distance from point O to any point on the circle.  I'm using point B here.

Zoomed out pic shows the complete circle with radius drawn

Another radius is from the center, O, to the point at the top center of the arc, drawn straight up from the center.  That radius is made up of two distances, the distance from O to C, and the distance from C to the top of the arc.  The latter of those I've already called "b", the bulge.  So the distance from O to C is a radius minus the bulge, or R-b.  Triangle OCB is a right triangle, so from Pythagoras, the sum of the squares of the two legs (legs are the sides of the triangle making the right angle) equals the square of the hypotenuse.

R^2 = (R-b)^2 + (w/2)^2       (the symbol ^2 means squared)

R^2 = R^2 - 2Rb + b^2 + (w^2)/4

And simplifying, we get:

2Rb = b^2 + (w^2)/4, and then

R = (b^2 + (w^2)/4) / (2b)

So to draw an arc with a certain width and bulge, you can calculate the radius of the circle that describes the arc and use a stick to draw the arc.  I've put this formula into an Excel spreadsheet.  If you want to do the same, type the following in an Excel sheet:

=(C4^2 + (C3^2)/4)/(2*C4)

In this formula, C3 is the location in the spreadsheet where I entered the arc width (not half width, the whole width).  C4 is the location in the spreadsheet where I entered the bulge.

Here's a picture of what my Excel sheet looks like (replace the word "Iron" with "Arc")

The example shown above has an arc width of 18" and a bulge of 1".  The resulting radius is 41".

Here are the details for the other example of this - shaping a plane iron with camber to make a scrub plane.  It works exactly the same way.

The plane iron drawn in gray, with markings like the earlier example.

Here's the upper end shown closer up

Using the spreadsheet for an iron that is 1 1/2" wide and giving a 1/16" bulge, I get a radius of 4 1/2".

The cambered iron example

For anyone who is actually interested in this stuff, if you can't figure out how to get the formula I wrote above (shaded in yellow) to work in your own Excel spreadsheet, contact me using the "contact me" gadget somewhere on this blog page.  Specify that you want the radius spreadsheet, because I've got another spreadsheet for a different application and don't want to send the wrong one.

New Iron for a Scrub Plane

A few years ago I made this scrub plane.  See here and here for details.  For the iron, I used what appeared to be a homemade plane blade I had found at a garage sale.  

Scrub plane from 2022

Body, wedge and blade

The iron, as found

I had no idea what type of steel that iron was made from, and really didn't know if it was any good at all. It was thick - about 7/32" thick. When I made the plane, I hardened and tempered the iron.  I've used it a bit, though not a huge amount, and it seemed to be cutting well for a short time, but needed sharpening quickly.  Last year after using it a while I noticed some chips in the cutting edge.  Apparently the steel wasn't a type one should use for edge tools.  Either that or I messed up the heat treatment.

If you look closely, you can see the chips in the edge

Another view from bevel side

The plane has been sitting on the "rehab shelf" for several months now and finally I'm getting the chance to do something about it.  I tried reheat-treating the iron and got it to cherry red and nonmagnetic, but after quenching in oil, a file still was able to bite into it, so the heat treatment clearly didn't do the job I intended.  Time to punt on that iron.  I had a chunk of 1/8" thick O-1 steel of the same width as the old iron, and I shaped it, hardened it and tempered it.

Old iron and new one ready to be shaped

I drew a 1/16" bulge on the end and filed the shape

Then mounted it in a vise at about 25 deg and filed the bevel.
I followed that with the hand-cranked grinder.

Shaped the back end similar to some other irons I've got

Here's my heat-treating setup

The iron warped a little from heat treating.  The front 1" of the back side was hollow and it took a long time to get it flat.  The bevel side had a belly at the front 1".  The rest (not hardened) stayed flat.

The old iron had a more severe camber on the blade - about 1/8" bulge over the 1 1/2" width.  In practice, I never used the entire width of that iron because it was just too much wood removal.  The new iron I shaped to about 1/16" bulge over the 1 1/2" width.  That's about a 4 1/2" radius for anyone counting.

But because the new iron is thinner, I needed a thicker wedge.  Instead of making a new wedge, I glued a piece of wood to the underside of the existing wedge and planed it down so that the wedge would sit in the throat at the right location.  I thought I used the same wood, but apparently it's not because it looks much different.

Gluing a piece of wood onto the underside of the wedge

It looks a little funky, but it'll be functional

Here's the thing about the wedge.  It needs to be fairly precisely shaped to provide a good fit of the wedge/iron to the plane body.  But almost as important as that (and probably equally as important for other types of planes) is the fit and final location of the wedge's fingers.

Here's a pic of the unfinished wedge from a few years ago.
Note the angled shape of the end of the fingers (left).

Inside the plane's throat, at the bottom of the wedge abutments, the abutments angle toward the plane's sides.  This provides a ramp for the shavings coming off the iron.  It's very tough to get a good photograph of the wedge fingers and the plane body's lower abutments, but hopefully you'll see what I'm getting at.

Looking through the mouth, you can see the wedge and lower abutment.
A close-up image is next.

The red arrow points to the lower abutment that angles toward the plane's side.
The yellow arrow points to the wedge finger (note it is two-tone - both light
and dark colors are the finger).  The finger's angle should line up with the abutment's angle.

I took a couple shavings off the underside of the wedge until the fit was just right.

Well, that's it.  The new iron fits great and the wedge holds it securely.  I put a little BLO on the wedge's added-on bottom and the scrub plane is back in business.  I'll report back if this new iron is not performing as I expect it to.

Shaker Handled Step Stool

This is a project I've been thinking about for quite some time.  We have a little step stool in the kitchen that helps my wife reach some things on higher shelves.  But she has to reach to the floor to grab it and move it.  I don't know where I first saw a design like this, but having a tall handle seems like a great idea for a kitchen step stool.

It'll look something like this

I made this out of the red oak I got from a neighbor's kitchen remodel.  The handle is about 30" tall, the step is 8 1/2" wide and 12 1/2" long and is 9" off the floor.  The joint between the step and the low upright (front legs) used dovetails.  It's been a few months since I dovetailed anything, and I felt a little rusty.

Tails cut and waste chopped

Pins cut and waste chopped out

The fit wasn't perfect.  I filled a couple of small gaps after glue-up.  For the joint between the step and the tall handle, I used multiple (roughly) square mortises and tenons.  I left the tenons about 1/16" proud, because I like the look.

Handle board below, step above, marked and ready for cutting

Another view.  The left/right extents of the mortises and tenons were marked
with a panel gauge, referencing off the same side (edge)

Mortises in the handle piece were first bored, then chopped to the lines

Checking for square inside walls

Looking pretty clean

The tenons came out pretty good, still a little paring to do here

Got a good fit

Added a rail under the step.  Through tenons.  The tenons were offset from center
of the rail so that I could leave more meat on the handle piece between the mortises
for the step and the mortise for the rail.  A curve was added to the rail's underside later.

I wanted to add something for visual interest (and so my wife might like it), so I cut out a heart shape at the top of the handle.  The heart doubles as a hand hole.  I practiced with scrap first, and that was a good idea so that I'd get a good heart shape on the real thing.

Practicing on scrap of same width

Making a template: two overlapping circles of 1 3/8" diameter, from the bottom
of those circles, mark down 1 3/8" along the centerline.  Then join the outside of
the two circles with a slight curve to that point.  The larger heart is 1/2" offset from the smaller one.

The heart/handle came out pretty good

Next was shaping the handle piece and creating feet.  The handle had gentle curves starting 1" above the step and ending a couple inches below the heart.  The feet were made by cutting out a half-ellipse, 5 1/2" minor axis and 10" major axis (only half the major axis length was used because I'm using a half-ellipse).

Template used to mark out the shape on the handle

Handle sides shaped - awaiting the half-ellipse for creating feet (no pics)

Before gluing up, I did a few dry-runs to figure out my clamping strategy.  The glue-up went fine, but it always looks so silly with all those clamps in place.  There's a lot going on in the picture below.  They're not seen in the photo, but there are two pieces of scrap placed between the front feet and back feet.  They are the exact length as the distance between the step's two shoulder lines - the dovetail side and the tenon side.  These pieces were placed between the feet so that the joints would stay square when clamped up.

Those deep-reach clamps extending out left and right are clamping the rail to the underside of the seat.  I made these many years ago from plans in Wood magazine (I think), and they really come in handy at times.

The glue-up

These cauls were used for clamping the multiple tenons (top)
and the dovetails (bottom)

I'm happy with the result.  The dovetails look pretty good and the the through tenons fit well.  The following pics are after a first coat of shellac.

The dovetails and through tenon of the rail

The multiple mortise and tenon joint, with rail tenon on the handle side

And the final product:

First coat of shellac applied

I've got three coats of shellac on now, and I'll give it another coat or two tomorrow (but not on the underside).  Time will tell if it gets used in our kitchen.  It's intended to replace (or be in addition to) a step stool that has huge sentimental value to my wife.