Using Multiple Moulding Widths In One Frame

Last updated on July 23rd, 2019 at 10:48 pm

In this article, the first of the “Weird Wood” seriesintro, we show how to build a picture frame using four strips of moulding that aren’t all the same width. In Figure 1 we have three different sizes (only because I couldn’t find four different sizes in the same moulding family).

Multiple Moulding Sizes
Figure 1: Building a picture frame with different moulding widths (drawn to scale)

First The Math

Warning: This discussion includes a little trigonometry.  Do Not Panic! It’s not as bad as it sounds.

Corner Close-up
Figure 2: Close-up of the lower right corner of Figure 1


Definition of “Tangent” (skip ahead To Next paragraph if you still remember this):

There are three sides to any right triangle (a triangle with a 90° corner), which I will call the height and the width, which both touch the right (90°) angle and the hypotenuse, which is opposite the right angle and is the triangle’s longest side. You can use the ratio of the lengths of any two of those sides to find the size of the other two angles. Each possible ratio has a name, but we are only interested in one of them today. Probably the most common ratio and the one we will be using is called the tangent. The tangent is defined as the ratio between the height (the length of the side opposite the angle you are interested in) and the width (the length of the shorter of the two sides that create that corner that you are interested in). If you want to know the angle of corner α in the above drawing (Figure 2), for instance, you would calculate its tangent by dividing the height (3 inches in this case) by the width (1¼ inches), which is 2.4 this time. Then you would use your calculator (or phone app – I use RealCalc Plus by Quartic Software (even though it cost $3.50)) to find the angle corresponding to that tangent. On your calculator, the tangent is abbreviated “tan”.   If you enter 45 (degrees are assumed) and hit the “tan” button, you will get 1 because for a 45° angle the height is the same as the width, so their ratio is 1.  To go the other way (to find the angle), like we are trying to do, we need the inverse of the tangent. Look for the “tan-1” button (it could be the same button, in which case you may need to hit a (yellow) shift or second-function key, and then hit the “tan” button).  In this case, once we have the tangent of 2.4, we hit the inverse tangent button(s) to get 67.380135…. (the calculator is obligated to give you 8 or more digits – that doesn’t mean they mean anything.  In Figure 2, I rounded that answer to 67.4 degrees and even that third digit is suspicious.)

The Process

All you have to do is take the ratio between the widths of your two moulding pieces and take the inverse or arc-tangent to get the angle.  Here are a few things you need to remember:

  1. Which angle – the tangent gives you the angle that was touching the side whose length was used for the denominator (the width, which would be the second number in the division). The simplest way (but certainly not the only way) to get the other non-90° angle is to just subtract the first from 90° (since the two angles are complementary). Also remember that if the tangent was greater than one, the angle will be larger than 45°; if it was supposed to be a smaller angle (less than 45°), then you may have divided the two lengths in the ratio backward. Don’t worry, you just found the complementary angle and all you have to do to get the right answer is subtract what you got from 90.
  2. It is up to you to keep track of whether that angle you are cutting should be to the left or the right.  Making a drawing of your frame design might help.  To be useful, the drawing doesn’t even need to be that good. This should also tell you if you calculated the complement (the other angle in that corner (for the other piece of moulding)).
  3. Your saw may be measuring angle backward.  My miter saw calls a cut perpendicular across the board 0°, not 90°.  If that’s the case, just subtract the angle you calculated from 90.

As an exercise, go ahead and check the rest of my calculations in Figure 1.     😁

Make The Cuts

There is more than one way to make these cuts and more than one set of tools to help you. Which set of tools you should use will depend on such factors as how much of this work you intend to do, your skill set, what your budget is, and what tools you already have on hand.

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Looking through the Framers’ Corner, the forum of the Professional Picture Framers Association, I found recommendations for the following tools for this application:

12-pc Precision Angle Block set (1/4, 1/2, 1 to 5, & 5 to 30 degree)

Incra MITER1000SE Miter Gauge Special Edition With Telescoping Fence and Dual Flip Shop Stop.

You would only need one of these (if any), not both.

(The Amazon.com descriptions are only used here as a reference. Although frequently competitive, Amazon isn’t always the only or the best place to buy something.)

Our workshop includes all of the tools listed in www.BeeHappyGraphics.com/about.html#BruceEquip, along with a number of other regular hand & power woodworking tools that Nancy has accumulated over the last several decades. For this project, I used our compound miter saw, but not without complications.

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The precision on this saw looked fine; you should be able to get within ¼° of your target. The first picture (Image A) shows me trying for 22.6° (which would be one of the angles between a 3″ and a 1¼” moulding).

Miter scale indicator for 22.6 (or 67.4) degree cut.
Image A: Peparing for a cut of 22.6°.

After cutting the 3″ piece, I ran into problems trying to cut the complementary angle (67.4°) on the 1¼” piece, as shown in Image B.

Miter scale limits
Image B: Trying to set up a cut of 67.4° exceeds the capabilities of the equipment.


I am not claiming that mine was the best path to reach our goal. In fact, I would love to see your ideas in the comment section about how to improve my techniques.

How I Did It

  1. Working with one corner at a time, I cut both pieces of moulding square just a tad longer than their overall/outside measurement according to your diagram (you will see why in Step 4). If you don’t already have one, this is also when you would put a perfectly square cut on the alignment block you’ll see in Figure 5 to the left of the moulding. I grabbed a 2″ by 4″, but the wider the better.
  2. I set the saw for the smaller of the two complementary angles, rechecking my diagram to confirm whether it should be to the left or right. In the setup shown below, the 3″ moulding would be clamped to the right of the blade.
Saw Setup For First Cut
Figure 3: Setting up for the first cut
  1. I made the cut.
sighting along saw blade
Figure 4: When you don’t have a reliable laser guide you might have to sight along the blade to line up the cut.
  1. Without adjusting the angle of the saw, I set up the second cut. I positioned my (newly cut) alignment block to the left (opposite the side we placed the moulding for the cut (in Step 2)) so that I could also place the 2″ moulding to the left of the blade and perpendicular (at a right (90°) angle) to the miter saw fence. After clamping down the alignment block, I added a support block to the right of the moulding to keep it in place. I could still move the moulding in or out to position the cut. You can see why I needed to precut this piece of moulding.
  2. I made the cut.
Saw Setup For Second Cut
Figure 5: Set up for the second cut
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For those who noticed that the color of the moulding in Figure 4 was different than in Figure 5, I had to make two different frames while doing research for this article 1) to confirm and refine my techniques and 2) because I didn’t get enough pictures the first time.

  1. Always check your work. If, when you put the two pieces of moulding together, the miter edge on one piece is longer than the other, that is the angle that should have been larger. The angle on the other piece of moulding should have been smaller (by the same amount).
If the angle is a little off
Figure 6: Example of cut with angle error ε.

Figure 7 shows the second setup from the right side. If you look close, you might notice that I didn’t cut enough to make a sharp corner and needed to recut.

Side View Of Second Setup
Figure 7: Side view of the second setup
  1. Moving to the next corner, I precut at least one more piece of moulding and repeated Steps 2 through 6.
  2. I repeated Step 7 two more times. The second time (when working on the last corner), I used the first two pieces of moulding I just finished cutting to mark the next cut by matching the inside edges, as shown in Figure 8.

Finishing

As with my normal (45° miter) frames, I would next need to make sure the inner lengths on opposite pieces of moulding matched, and the outer lengths as well. Figure 9 shows a way to check to see if the outside and inside corners of the opposite sides match using two carpenter squares (or equivalent).

Some of the tools we normally use next to finish putting the frame together, namely our Logan Precision Sander and Logan Pro Joiner, are worthless for this application. After gluing (and clamping the pieces together until dry) we had to pound the V-nails in by hand (interestingly, the simpler Logan Studio Joiner can be adapted).

Nancy pounding V-nails into frame.
Figure 10: Nancy pounding V-nails.

The Back Side

For completeness, the left figure below shows what the backside of the lower left corner would look like.  The gray section represents the rabbet, the equal-width (¼”) cut-out that holds the glass, mats, image, and backing of the picture inside the frame.  Some of you might be surprised to see that there is a triangular notch in this rabbet in the corner along the miter cut.  This notch has no effect on the functionality of the rabbet.  To solve this “problem”, however, you could make a compound cut 45° in from the inner edge to the edge of the rabbet and 79.7° in from the outer edge to the same point, as shown in the right figure below (as an exercise, you can check my math on these angles also).  But there is really no need to make these cuts. If the gray were to represent an equal-width feature on the front of the moulding, it might be worthwhile to take the extra trouble. Otherwise, don’t even think about it.

The End

Congratulations, you now have a fancy new picture frame. Of course, you still need to find a picture, cut mat(s) and backing, mount picture to same, cut glass, assemble the pieces without showing any annoying little specks, and apply a dust cover and hanging hardware, but all of that is beyond the scope of this article. Good luck!

As mentioned, this article is just the beginning of a series about “Weird Wood” that I announced months ago. Up next, we will look at handling moulding that is not of uniform width. You won’t find this moulding in any store; it is only an exercise to prepare you for our final project. But if it stimulates your creativity, that’s not always a bad thing. Stay tuned, and thanks for reading! Your comments are welcome and appreciated.

More About Adjusting A Logan Sander

Last updated on August 19th, 2018 at 10:54 pm

It occurred to me the other day that it might be good to be able to download the steps to adjust a Logan Sander, as I described in Another Method For Adjusting A Logan Precision Sander. While converting to the Acrobat .pdf format, I took the liberty of adding more information and, I hope, making it easier to follow. To download, click on the link below. Enjoy!

Get printable version(.pdf)

Another Method For Adjusting A Logan Sander

Last updated on September 15th, 2019 at 05:02 pm

To download a printable version of this article (AdjustingSander.pdf), click here.

We have a Logan Precision Sander Elite Model F200-2 disk sander for improving saw-cut miters for your picture frames to a “perfect 45°” after cutting the moulding to size on our miter saw. To maintain such perfection requires due diligence and occasional adjustment.

How Do You Know When It’s Time To Adjust Your Sander?

  1. You may notice that when you put your frames together, there is a small gap between the pieces of moulding either on the inside of all four corners or the outside of all four corners. If some corners have gaps on the inside and some have a gap on the outside, you have other problems.
picture frames showing that your sander needs adjusting
The sander used on the miters of these two frames needs to be adjusted. Note gaps in corners.

In the figures used in this article, the symptoms have been exaggerated for illustration purposes. If the condition of your sander gets this bad without you noticing, you may want to consider another profession or hobby.

  1. When you are comparing the lengths of opposite pieces, and you have them side by side with the miters face up and their back sides touching, you may notice by running your finger over the miter that they are the same length on one end of the miter but not the other, or that one piece of moulding is higher at one end of the miter and the other piece is higher at the other end.
Differences in the miter cuts of moulding
The differences (gaps) in the mitered ends of these pieces of moulding show that your sander needs adjusting

In either of these cases, it’s time to adjust your sander.

But What About The Miter Saw?

It may be true that the miter saw also needs adjustment, but that would have minimal impact on your frames because even if the angle of the cut was wrong, the sander should correct that problem. Of course, it would take more sanding to correct, which besides taking more time and effort could, in the worst case, result in your frame being too small, so it should periodically be checked and corrected according to the manufacturer’s instructions (I currently have no improvements or suggestions for that process). An indication that the miter saw needed adjustment would be if as you are sanding the miter, sawdust builds up on top of one side of the moulding faster than it accumulates on the other. If it takes too many revolutions of the sander to perfect the edge, that could also be a clue, or it could be time to change the sandpaper.

How To Adjust The Sander

On the last page of the 4-page manual (available at www.logangraphic.com) are simple instructions for that adjustment that should work well if you are willing to follow Step 1 and remove the sandpaper.

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The full instructions are as follows:

Adjustment 45°

  1. Remove sand paper
  2. Place the 45˚ square flat against the wheel and up against bar (Fig. 7). Look for gaps against the bar.
  3. Adjust the bar using adjustment wrench until gap disappears.
Figure 7 of F200-2 Manual
Figure 7 of F200-2 Manual

When I don’t remove the sandpaper disk the technique doesn’t work as well, so I’ve come up with an alternate set of instructions:

  1. Put miter cuts on both ends of two long scrap pieces of your widest moulding.
  2. When you sand a piece of moulding, each end will use a different side of the sander. Call one side of the sander “A” and the other “B”. As you sand the two pieces of moulding, mark the back of each end of each piece with the side of the sander used (A or B).
  3. Find a good right angle, either in a reliable carpenter’s square or using other methods.
  4. Flip one of the pieces of scrap moulding upside down so you can join Corner “A” on both pieces to make a 90˚ (right) angle. Flipping is very important*.
  5. Put one piece of moulding along one edge of the reference angle (carpenter’s square) and slide the reference toward the second moulding until it just touches at one end or the other (if it touches at both ends, you are finished with Side A – skip ahead to Step 7). Measure the error gap (I like millimeters only because they are so small) at the end of the moulding that’s away from the reference line. Then measure the length of that piece of scrap moulding (using the same units of measurement).
  6. The adjustment screw on my sander had 32 threads per inch, and it was 109 millimeters from the pivot point. Based on that, your multiplier will be 25,000.
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    I’ll do the math just in case your sander has different measurements so that you can substitute the real numbers in for mine at the proper places. One complete turn of the adjustment screw is 360° or 1/32” and there are 25.4 millimeters per inch, so the constant multiplier would be 109 mm * 360° per turn of screw * 32 threads per inch ÷ 25.4 mm per inch ÷ 2 errors = 24,718.11. We’ll say 25,000.
    Divide the error you measured in the last step by the length of the moulding that you measured and multiply by 25,000. Your result will be the number of degrees you need to turn the adjustment screw. If the error gap was at the corner, then the angle is too large and you have to turn the screw counterclockwise to back it out. Conversely, if the error gap was at the end of the moulding, then the angle is too small and you have to turn the adjustment screw clockwise to push it out more. After making the adjustment, you may want to retest by repeating the process by starting at Step 2 and resanding the same two corners just used. Before sanding, I recommend drawing a line all the way across the end of the moulding with a pen or marker and then sanding until the line completely disappears.
  7. Repeat this whole process (starting at Step 4) for the other two miters, labeled “B”. Remember, for these two you will be playing with the adjustment screw on the other side of the sander.

That’s all there is to it. Congratulations.

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Math Warning: a quick note about trigonometry (OPTIONAL)!

This process was concerned with angles, not distances, but since angles are harder to measure with any precision we had to convert. When you take the ratio of the two perpendicular sides (the sides that are 90° apart) of a right triangle containing the angle you are interested in, that’s called the tangent of that angle, and you can have a good calculator app on your phone find it for you (for my Droid, I found RealCalc Plus by Quartic Software at the Play Store and was happy to pay $3.50. There are plenty of other options, though).

The error angle you measured (indirectly) was actually twice as large as the real error. One problem is that the tangent curve is not generally a straight line, which means that the tangent of twice some angle is not the same as twice the tangent of that angle. That’s why the normal procedure would be to convert to angles, do the adding, subtracting, or multiplying, and then convert back to distances we can measure again. We were able to use the small angle exception, however. It turns out that for angles less than say 10°, the tangent curve IS pretty straight and the error introduced by taking our shortcut isn’t worth worrying about. That’s what we did, and that’s why the problem was so easy. That’s your math lesson of the day week month. Let’s get back to work.