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This article was published in the April 2012 (#36)  edition of  Woodturning Design.

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Matching Tapers as 10 page pdf    Watch Matching Tapers Video

Introduction

In May of 1996 I got a newsletter from One-Way with an interesting article on making wooden Morse Tapers for the lathe (usually I can't be so precise in my attributions, but I happened to find the newsletter stuffed in a folder with One-Way's catalog).  In the article they used three blocks of wood so that the entire taper could be matched.  I tried it out, and it was easier and more accurate than using a parting tool at maximum and minimum diameters.  Making your own wooden drives isn't the only thing tapers are good for.  The can also be used to make removable caps and assemblies--almost anything you want to join together temporarily.  Matching tapered tenon/mortise joints have several nice attributes.  They're easy to make and tolerant of wood movement.  Unless the wood goes seriously oval, all that will happen is the tenon will stick out a little more or a little less.  It will still fit.  When used to drive the wooden surface won’t mar already finished work.

 

To form a tapered mortise, one generally drills a hole the minimum size of the taper, and then uses a reamer to taper the mortise.   Morse isn't the only system of tapers available--in particular there are tapered dowel pin reamers in a wide range of sizes to make tapered mortises.  Dowel Pin Reamers, also called Taper Pin Reamers are available from any Industrial Supplier.  They come in three flute styles—straight, spiral, and helical.  Straight seems best for this application, as they are easier to use to make a taper gauge than the spiral fluted ones.  Helical flutes are easy to use to make a taper gauge but are difficult to use by hand or even with a hand drill if a tapered mortise needs tweaking to size.  “Import Quality” is good enough for reaming wood and roughly half the price.  While you’re on the Industrial Supplier web site o buy a reamer, you might have a look at taper length parabolic flute drills.  They really do a better job clearing chips and are really nice for long holes.  While you wouldn’t need them to drill only 1” for a mortise, they’re great if you want to extend the hole to hold something.

 

I bought a few dowel pin reamers and started using them along with homemade taper gauges.  I quickly discovered wood wasn't the best choice for the gauge.  Wood is okay for occasional use (like Morse taper drives) but quickly wears out with continued use as the wood will compress and start yielding over size tenons.  So I tried metal, which worked better.  My own opinion is that any semi-serious tinker should have a wire fed welder--but I've tried methods that don't require one because that's not a universal opinion.

 

I discovered having a gauge preset to the largest diameter also made things go more quickly.  Then I figured out that if I attached the gauge to the handle of the taper gauge I'd find it a lot more quickly.  The taper gauge can be a bit "grabby" in use.  I found two solutions for that, the first being a little top-coat or other wax, and the second relieving all but the top edge of the gauge with a file.  In the original configuration the gauge has to be tilted in use to engage only the widest part to start, which limits how close the taper can be to a larger element.  I found that tapering the sides of the taper gauge minimized this problem and also made the gauge a bit easier to use.  Fig01 shows some of the gauges I've made over the years.  Starting at the left is a wooden gauge as in the original newsletter.  Next to it is what I think is the first metal gauge I made.  In the middle is a metal gauge with a built in maximum gauge.  To the right of that is a gauge milled from drill rod, and furthest to the right is the wood/metal gauge of this article.

 Fig01

Fig01:  Various ways of making taper gauges I've tried.

 

This article describes a weld-free way of making a taper gauge to match a #8 dowel pin reamer from wood with non-compressible metal sides.  The procedure for any other type reamer would be much the same, only with different proportions.  First the metal sides are made, then attached to wooden sides with CA glue and screws.  The gauge is assembled with wood glue to fit the taper.  A maximum diameter gauge is made of metal and attached to the handle.  Making tapered mortises with drill and reamer and tapered tenons with the gauge are shown.  Then a few examples of projects are shown to give you some ideas for applications.

Making the Gauge

Metal Sides

Start with some 1" wide, 1/8" thick steel bar stock.  To make it easier to hold the metal for drilling, the drilling will be done before cutting the pieces from the bar.  Measure 1" from one end of the bar and make a mark (I used a thin line marker).  Draw a line across the bar angled 15 degrees towards the end.  Then mark for mounting hole locations, about 1/4” in and up from the corners.  I didn’t actually measure as it’s not critical.  Fig02 shows the bar after marking, along with a #4 combined drill and countersink, a very convenient way to drill and countersink the holes, as well as a box of #4 x 1/2" screws that will be used for mounting.

 Fig02

Fig02:  The steel bar after marking for drilling and cutting of the first metal side.

 

Clamp the bar securely to your drill press and mount a #4 combined drill and countersink in the drill press chuck.  You could use a separate drill and then countersink but the combined tool is easier and assures concentricity.  Drill the holes as in Fig03.  Fig04 shows the bar after drilling.

 Fig03

Fig03:  Using a #4 combined drill and countersink to drill mounting holes.

 Fig04

Fig04:  After drilling the mounting holes.

 

Now clamp the bar in a vise, angled so the 15 degree line is perpendicular which will make sawing along the line more natural.  Then use a hacksaw to cut along the line as in Fig05.

Fig05 

Fig05:  Cutting off the first metal side with a hack saw.

 

Lay out the second side.  Measure down 1" from the peak of the angle and draw a right angle line across the bar.  Then locate the two screw holes ?? in from each corner.  Remember that this side should be a mirror image of the other side (which is easy to forget when you're busy taking photographs).  Fig06 shows the second side laid out.  Clamp the bar to your drill press and drill the mounting holes as in Fig07.

Fig06 

Fig06:  The layout for the second metal side.  Be sure it's a mirror image of the first side.

 Fig07

Fig07:  Drilling mounting holes in the second metal side.

 

Clean up any burrs from cutting and drilling with a file as in Fig08.  Fig09 shows the difference between the two sides after filing one of them.  The success of the gauge depends upon having the sides at right angles to the base and it's pretty obvious that it would be more difficult with the un-filed piece on the right.  Fig10 shows the two finished side pieces.

 Fig08

Fig08:  Filing burrs and rough edges on a metal side.

Fig09 

Fig09:  Before and after filing.

Fig10 

Fig10:  The finished metal sides.

 

Wood Parts & Assembly

Now cut the wooden parts to size from a strong hardwood such as maple.  The parts should be glue-joint ready, so using a table saw is preferable.  The two side pieces are 5/8" x 3/4" x 1".  The bottom piece is 5/8" x 3/4" x 2".  The handle is 3/4" x 3/4" x 3-1/2" with a 1/8" wide slot cut 3/4" deep into one end.  Fig11 shows the wooden parts.

Fig11 

Fig11:  The wooden parts for the Taper Gauge.

 

Place waxed paper on a flat surface and use CA glue to fasten the metal sides to the 3/4" wide face of the wooden sides as in Fig12.  The waxed paper will prevent the glue from sticking to your working surface, letting you use the surface to align the straight end of the metal side with the 1" edge of the wooden side.  After the glue sets, check to make sure that the metal side is perpendicular to the bottom of the wooden side.  If not, make it so by sanding on a disc sander as in Fig13.

Fig12 

Fig12:  The set-up for gluing the metal sides to the wooden sides.

Fig13 

Fig13:  Sanding the bottom of the side perpendicular.

 

Now complete fastening the metal sides to the wooden sides with #4 x 1/2" wood screws.  As the screws will be close to the edge of the side it's necessary to drill pilot holes as shown in Fig14.  Then drive in the screws as in Fig15.

Fig14 

Fig14:  Drilling pilot holes for the mounting screws

Fig15 

Fig15:  Driving in mounting screws.

 

Use wood glue to fasten one of the sides to the 3/4" wide face of the bottom piece as in Fig16.  The metal side should face towards the middle.  Leave the assembly clamped until the glue is well cured.

Fig16 

Fig16:  Gluing the first side to the base.

The dowel pin reamer will be used to set the opening of the gauge.  But it is very difficult to balance the reamer with only one cutting edge in contact with each side.  If two edges are in contact with each side the reamer will be in a stable position, but will result in an undersized gauge.  The solution is to find the spot up the reamer where the distance will be correct--the slope will be the same.  Set a dial caliper to the minimum diameter of the reamer.  You can carefully measure this directly or find the minimum diameter by looking it up on the web site of an industrial supplier (the minimum diameter of the #8 reamer is 0.3971”).  Gently slide the caliper down the reamer as in Fig17 with two cutting edges in contact with each side of the caliper.  Make a mark with a marker where the caliper stops.

Fig17 

Fig17:  Using a dial caliper to determine what part of the dowel pin reamer to use to set the location of the second side.

Place the reamer against the glued in side of the gauge, with the mark on the reamer at the shorter edge of the side.  Spread glue on the other side and bring it up against the reamer and clamp the side in place as in Fig18.  After checking to make sure both sides are snugly up against two cutting edges of the reamer set the assembly aside for the glue to cure.  After the glue is cured you can drill a 1/2" hole 1/2" deep in the middle of the bottom of the bottom piece as in Fig19, to mount the handle.

Fig18 

Fig18:  Gluing on the second side, using the dowel pin reamer as a spacer.

Fig19 

Fig19:  Drilling a mounting hole for the handle in the base.

 

Mount the handle between centers on the lathe with the slot at the headstock end as in Fig20.  Turn the handle to a simple cylinder, with a 1/2" x1/2" tenon on the un-slotted end.  You can gently round over the slotted end.  If you end up making several sizes of gauges as I have over the years, it will be easier to find the one you want if you mark it.  You could just write the size of the reamer on the handle, but I chose to make 8 light V-cuts (a group of five and a group of three) as in Fig21.  Glue the handle into the bottom piece with wood glue.

Fig20 

Fig20:  The handle blank mounted for turning.

 Fig21

Fig21:  The handle after turning.

Starting Gauge

To make a starting gauge for the maximum diameter of the tapered tenon, clamp the steel bar to the drill press table and drill a 1/2" hole 3/8" from the end as in Fig22.  Cut off the last 2" off of the metal bar.  Using dial calipers, measure the separation between the taper gauge sides at the widest end.  Mark slightly narrower than this distance on the drilled end of the starting gauge as in Fig23.

Fig22 

Fig22:  Drilling a hole in the metal bar for the starting gauge.

Fig23 

Fig23:  After marking the starting gauge for sawing. 

Clamp the starting gauge in a vise and use a hack saw to saw out between the lines as in Fig24.  Reclamp the gauge sideways in the vise and smooth out the sawn edges with a file as in Fig25.  Check the distance between the now filed edges as in Fig26 (at more than one spot to ensure they're parallel) and file until the correct distance is achieved.  You want the starting gauge to be ever so slightly wide than the widest end of the taper gauge.  Ideally, when you remove wood compressed by the gauge you'll be a the correct diameter.  Fasten the starting gauge in the slot of the handle by drilling a hole and countersink for a wood screw in one side of the handle and a corresponding through hole in the starting gauge.

Fig24 

Fig24:  Sawing the starting gauge with a hacksaw.

Fig25 

Fig25:  Filing the starting gauge to the correct dimension.

Fig26 

Fig26:  Checking the opening of the starting gauge with dial calipers.

 

You can make the gauge less "grabby" in use by relieving the sides of the gauge behind the leading edges.  Clamp the gauge in a vise and use a round pile to file a groove behind the edge as in Fig27.  Do this for both sides.  Be sure not to file the top edges of the sides where they first contact the tenon.  The relieved edge is shown if Fig28.  The completed taper gauge is shown in Fig29.

Fig27 

Fig27:  Relieving the inside of the taper gauge.

 Fig28

Fig28:  After relief filing the inside.

Fig28 

Fig29:  The completed taper gauge.

Using

To make a matching tenon and mortise you need a drill with a diameter of the minimum of the reamer (13/32" for a #8 dowel pin reamer), the reamer, and the taper gauge.  Some spray Topcoat, or other wax, as shown in Fig30 makes the taper gauge a little more user friendly.  The drill shown is a taper length (nice if you drill and ream on the drill press as you won't have to raise and lower the table) parabolic bit.  The parabolic flutes clear chips better than standard drills so are very nice for drilling deep holes.

Fig30 

Fig30:  The "toolkit" for matching tapers of drill, reamer, taper gauge and topcoat.

 

For practice, before you try making an actual project, try making a few sets of sample matching tapers.  The photos will follow drilling and reaming the mortise on the lathe.  The steps are much the same if you use a drill press.  Begin by mounting a short practice piece in some kind of chuck so that you can drill and ream.   Create a starting dimple for the drill either with a turning tool, or with a combined drill and countersink as in Fig31.  Unlike the drill, the combined drill and countersink is too short and rigid to be deflected when engaging the work.  Now chuck up a drill.  You have to drill at least a little more than you plan to ream.  Tape makes a good depth gauge, as shown in Fig32.  Turn on the lathe at a moderately slow speed and advance the drill to the proper depth, pausing to clear chips necessary.  Mount the reamer in your drill chuck and again use tape to mark the depth.  Again using a slow speed, advance the reamer into the drilled hole to the proper depth as in Fig33.  This finishes a practice tapered mortise.

Fig31 

Fig31:  Using a combined drill and countersink to create a starting dimple.

Fig32 

Fig32:  Drilling the minimum diameter of the mortise.

 Fig33

Fig33:  Reaming the mortise with taper dowel pin reamer.

 

To practice a tapered tenon, mount a short piece of wood between centers and turn to round as in Fig34.  Mark off the length of the tenon at the tailstock end and cut to the starting diameter with a parting tool and the starting gauge on the handle of the taper gauge as in Fig35.  Reduce the rest of the tenon to the same diameter with your spindle roughing gouge or other tool as in Fig36.

Fig34 

Fig34:  Spindle blank mounted between centers:

Fig35 

Fig35:  Using a parting tool and starting gauge to establish the maximum diameter of the tenon.

Fig36 

Fig36:  After roughing the tenon to parallel.

 

Test the fit of the taper gauge at biggest end of the tenon, where the parting tool cut was.  If necessary reduce the diameter with a skew or other tool until the gauge starts to slip over the tenon as in Fig37.  Make a mental note how far the gauge fit and reduce the diameter a little below that point with the skew and then test again as in Fig38.  Again make a mental note (you can also watch for burnishing by the gauge) how far the gauge went and reduce below that point with the skew as in Fig39.  You may want to set the gauge down at first, rather than holding it with your left hand.  Continue in this fashion until the gauge fits over the entire tenon.  Fig37 thru Fig43 show the progression.  There will be a short video of this process embedded in this article on my web site.

 

Watch Matching Taper Video

 

 

 

Fig37 

Fig37:  The gauge is just starting to fit over the tenon.

Fig38 

Fig38:  The gauge now fits a little further over the tenon.

Fig39 

Fig39:  Trimming the tenon with a skew.  Put down the gauge if you're not skew comfortable.

Fig40 

Fig40:  The gauge now fits over about half of the tenon.

Fig40 

Fig41:  Almost all of the gauge now fits over the tenon.

Fig42 

Fig42:  The gauge now fits the entire tenon.

Fig43 

Fig43:  The progression of trimming and gauging the tenon until the tenon is cut to size. 

 

Test the fit of the mortise on the tenon as in Fig44.  It should push on easily and stay securely. 

Fig44 

Fig44:  Checking the fit of the sample mortise and tenon.

Drives

It is very handy to have both a mortise and tenon available to use as drives when making various parts.  Among other reasons you can maintain tailstock support until the majority of the heavier turning is done and then retract the tailstock to remove the nub and finish the entire article all at once.  You could use the sample pieces, together with a chuck, as drives, but why not stay on the same theme and make drives that go directly into you Morse taper?  The result will be much smaller and hand friendly when doing small work.  You can make a taper gauge for the Morse taper in the same way as the taper gauge for the dowel pin reamer.  It will just be a little bigger, and you can model the gauge directly off one of your existing drives. 

 

To make a male (tapered tenon) drive start with a spindle blank 1" x 1"  4-1/2".  Turn the Morse taper drive between centers, then mount it in the lathe's Morse taper.  Then turn the taper matching the Dowel Pin Reamer. 

 

You could follow the same procedure for the female (mortise) drive, but it's better to put in a bit more work so that if the tenon gets stuck hard in the drive you don't have to whack it out, possibly marring your earlier work.  Start with a blank that's 1" x 1" x3-3/4".  Draw a line 1" from one end and saw a kerf down the middle of two adjacent sides from the other end to the line as in Fig45.  Compress the kerfs and turn the Morse taper, with the small end of the taper at the unsawn end.  Fig46 shows two ways of compressing the kerf while turning the tapers.  On the top #1 jaws in a 4-jaw chuck compress the kerfs.  On the bottom, strapping tape is used to maintain the compression achieved with clamps and then mounted between centers.  After turning the Morse taper, insert the drive in your lathe's Morse taper, being sure to compress the kerf.  Then drill and ream the drive to make the tapered mortise.  Now when you're finished turning an object placed in the female drive, just use a knock-out rod to eject the drive.  The kerfs will open, permitting the object to be removed easily.  Fig47 shows the finished male and female drives.

Fig45 

Fig45:  Female Drive blank.

Fig46 

Fig46:  Two ways of compressing the kerfs of the female drive to turn the Morse taper.

Fig47 

Fig47:  The completed Male and Female drives.

Tweaks

If your taper gauge, or the resulting matching tapers aren't quite what you want there are a lot of tweaks short of starting over that you can try. 

 

If your tenon seems undersized you can either file the metal sides of the taper gauge to make it larger or simply ream the mortise less deeply.  If the tenon seems over sized you can ream more deeply when making the mortise.

 

If your starting gauge is too small, then file it larger.  If it is too large you can compress the gap using a vise.    This will result in edges out of parallel which will need refiling.  You could also center punch vigorously along both edges on both sides.  This will result in a somewhat rippled edge which will need refiling.

Applications

There are any number of things you can make that take advantage of assembly and dis-assembly using matching tapers.  Here are a few examples to get you started thinking.

 

A niddy-noddy is a device used by hand-spinners to wind yarn into a skein and measure it at the same time.  While it is very handy for that use, it is remarkably ungainly to store unless it comes apart.  The niddy-noddy shown in Fig48, made of 5 pieces with matching tapers can be stored in a quart zip-lock bag.  It can be assembled to measure skeins 1, 1-1/2, and 2 yards in circumference.

Fig48 

Fig48:  The niddy-noddy assembled and disassembled.

 

Fig49 shows an all-wood pen...well, almost, as it has a standard refill.   The barrel of the pen has a tapered tenon on both ends, allowing the cap with a matching tapered mortise to fit on either end.

Fig49

Fig49:  The almost all-wood pen capped and uncapped.

 

Fig50 shows a similarly almost all wood purse sized pen.  The barrel of the pen has two tenons located next to one-another at the same end of the barrel.  This lets the barrel nest well into the cap for a compact length when closed, but measure almost normal pen length when open.

 Fig50

Fig50:  A purse pen open and closed.  Note the difference in length.

Tools

Taper Gauge

Drill Press

#4 combined drill and countersink

hacksaw

Vise

screwdriver

file

disc sander

drill bits

clamps

dial caliper

dowel pin reamer

 

Turning drives and projects

spindle roughing gouge

parting tool

skew or other tool of choice

Materials

1/8" x 1" steel bar stock

small pieces of maple or other hard wood

#4 x 1/2" wood screws

CA glue

wood glue

Topcoat or wax

Author

David Reed Smith is a tinker and basement woodturner living in Hampstead, Maryland.  He welcomes comments and questions via email at david@DavidReedSmith.com.  This article, with supplementary photos and video will be available along with more than 50 other articles on his web site at www.DavidReedSmith.com.