KINEMATIC JIG DESIGN
Understanding the science behind super-accurate tolerances.
SHOP OWNER: Steve Strickland
LOCATION: Quitman, TX
[EDITOR'S NOTE: In this article, Steve has given us an in-depth explanation of how he built his super-accurate tablesaw jig for making precision parts. But, the real purpose of the article is to illustrate a way of thinking about jig design in terms of controlling movement, to eliminate all sources of inaccuracy. There are no drawings here, nor dimensions given for the jig parts, but there's enough information here to build a similar jig if you're ambitious enough.]
The goal of this paper is to show you how to apply kinematic principles in your positioning devices. It's a system for analyzing the motion of any object in 3D Cartesian Space.
The first step is to break the problem of precision positioning into two parts. The first part is the idealized movement in a theoretically perfect space (called Cartesian Space) and the second part is the properties of materials in the real world, which I don't go into.
Types of Movement in Cartesian Space
In Cartesian Space there are three spatial dimensions which can be represented by axes, or directions. The X-axis is the left-right direction, the Y-axis is the top-bottom direction and the Z-axis is the front-back direction.
All objects are restricted by the laws of physics to only two types of motion. The first is linear movement along one axis and the second is rotational movement around one axis.
Linear and rotational movements can be added to each other to produce compound movements called vectors. For instance, we can move 6 in. in the X direction and then move 6 in. in the Y direction and end up 45 degrees from our starting direction. We can add the two moves together and simply state it as a single movement with a vector. The same thing is true for rotations. Compound rotations can be expressed as a series of simple rotations, all added together to form a rotational vector.
Accelerations and curved motions can be reduced to a series of tiny kinematic motions in Cartesian Space, so there's no need to worry about using calculus to analyze these types of complex motion. All possible motion can be expressed as a series of very simple steps.
Degrees of Freedom of Movement
There are six degrees of freedom of movement to consider when designing a positioning device. I suggest that you think about each one, in turn, when designing a jig for woodworking.
1. Free to move along the X axis
2. Free to move along the Y axis
3. Free to move along the Z axis
4. Free to rotate around the X axis
5. Free to rotate around the Y axis
6. Free to rotate around the Z axis
In the design of a jig our first goal is to restrict all possible motions to the six basic moves. This eliminates the need to deal with compound and complex motions. We can always make a tightly controlled compound move by making one basic motion at a time.
Applying the Theory
In my puzzle shop my goal is cut wood puzzle pieces on a table saw to precise tolerances. For instance, I make several puzzles that are composed of cubes. Making 10,000 very precise cubes is not a trivial task, it's pretty difficult. I can make a nice puzzle if my cubes are +/- 0.005". However, I don't care to be just another craftsman making "nice" puzzles; I want mine to be superb, so I'll aim for +/- 0.002" tolerance. So, let's build a table saw jig based on kinematic principles and see if we can cut a batch of cubes that are all the same size within tight tolerance.
We start off with a jig board made of 3/4" Baltic Birch plywood. We select the 13-ply because it has a higher degree of dimensional stability than the 7-ply does. Also, the 13-ply does not contain any voids in it like you'll find in 7-ply. Let's purchase the jig board from a dealer who stores the wood indoors in an environmentally controlled warehouse on good flat shelves. Our board must be very flat and smooth, not like the Baltic Birch found at lumber yards where the wood has been stored exposed to the weather on a warped shelf.
Since this jig board is going to slide along the surface of the table saw, the condition of the saw and it's top are important. The saw top must be flat and smooth. The saw must sit on the floor rock steady. It must not vibrate or shake. It's mechanical parts must be tight fitting and the bearings must be in excellent condition. If the saw is introducing any uncontrolled motions the work will not meet design tolerances. If the top is curved or damaged, this will transmit itself through the jig board and show up in the work as spoilage.
If you're lucky enough to have a table saw like the Delta Contractor, I want you to raise your right hand and swear this oath: "I will never use any metal scaper, sandpaper or file on my table top. I will never use anything more abrasive than steel wool to clean it. I'll keep it waxed and oiled at all times. I so swear." Keep that table top in excellent condition and it will give you excellent service. Abuse it and your work will suffer.
Before you begin, you need to fine-tune the saw using a machinist's stainless steel square as a gauge to square the blade and the miter. We're not going to use the fence so you can just remove it and store it somewhere. Using the miter gauge, cross cut a wood sample that's as thick as possible, then check it with the square. Hold it up against a very bright light (the sun works very well) and let the tiniest possible crack of light through. The smallest angle error will be very obvious. If you get the crack of light small enough you can see faint diffraction bands form. Adjust the saw accordingly and repeat this process until both the blade and the miter are set to perfect right angles. Once you get both angles set to square, prove it by making three more cuts and testing them. You may also adjust the blade parallel to one of the miter grooves. I use the right hand groove but you can use either one you wish.
The first step in making the jig is to cut the jig board to size. The edges don't really need to be square but it helps. Now, slice off a 3/8" thick strip from the length of the board. We'll use this to make the runner. Mark the location of the runner on the bottom of the board and glue the runner. When glueing wood, you should use enough glue so that excess oozes out of all sides. Make certain that you clean all of the excess glue. You don't want anything to hold the jig board out of contact with the table top.
Next, cut the reinforcer and blade guard (see photos below). This is important as it keeps the jig board flat after it's been cut. It also serves as excellent protection from the running blade. Glue the reinforcer board to the end of the jig board, then screw it in place.
Mix up a batch of epoxy glue (Devcon 5-minute epoxy works fine). Set the jig on its side. Apply a blob of epoxy to two spots on the side of the runner, each spot about 3/4" long. The front blob goes right at the leading edge of the jig, the back blob goes just behind the location of the backstop, about 12" back in this case. Do not allow the epoxy to get on the bottom of the jig board, it should only be on the side of the runner.
Once the epoxy sets, turn the jig over to its other side and apply one blob of epoxy halfway between the first two blobs and let it set. Once the blobs have hardened, rough them up with sandpaper and repeat the procedure making the blobs thicker. Let the epoxy cure overnight before going to the next step.
Next, heavily oil the bottom and edges of the jig, and I mean totally saturate them. I use a cheap, thin vegetable oil. Now, try to set the runner in the miter groove. It's too big and won't go in. Lightly sand the epoxy blobs until you get a tight fit. Slide the jig board back and forth a dozen times. If the fit is too tight, sand just the middle blob a tad until you get a smooth fit. Try pushing the jig sideways and observe if there is any side play. There should be none. Adjust thetightness by adding more epoxy to the single blob and sanding it down until a perfect fit is achieved. You should get the fit just a tad tight to start with so that only a couple of pounds of pressure will move the jig.
Before we go on, let's think about what we've got so far. Gravity and the table top restrict movement along the Y-axis. The table top blocks rotation around the X-axis and Z-axis. The runner and miter groove blocks movement along the X-axis and also blocks rotations around the Y-axis. Five of the six degrees of freedom of movement have been restricted. The jig is left free to make only linear moves in the Z-axis--it can slide along the miter groove and make no other movement.
The side of the runner with two blobs of epoxy forms the two positioning points that define a straight line in geometry. The third blob on the opposite side of the runner keeps the two positioning blobs in contact with one edge of the miter groove. The positioning blobs will follow that one edge of the miter groove faithfully. If the edge is flawed or damaged in any way, that flaw will transmit itself to the work. The same kind of thing applies to the table top. The jig board will faithfully stay in contact with the table top unless some foreign object or outside force detours it's movement. The quality of the table top and the miter groove are therefore limiting factors in the accuracy of our positioning device.
Before moving on to the construction of the goodies on this jig board I want to review a couple of basics that every precision worker in every field must constantly keep in mind. The first is to never assume a damned thing. If you absolutely must make an assumption, be aware that it can be a source of unwanted variation. You must constantly measure, test and check everything. The second precision basic is use fine measuring tools. Use precision crafted stainless steel machinist's squares, straight edges, dial micrometer calipers, etc. You cannot measure and test better that your tools, so use the best.
Mark the location where the backstop goes and cut the jig to that mark. Now, using the saw kerf as a referrence, draw a line for the front of the backstop "B" using a good square. Next, lay out the two lines that represent the innermost and outermost positions of the sideguide "A".
Cut an extremely accurate guiderail "C" and glue it in position square to the kerf. While the glue is setting, cut the backstop "B" and the sideguide "A". Cut the notches for the clamps. The sideguide notch will limit the range of sizes you can cut with the jig. The backstop will get undercut by the sawblade so make it wider than that. Both the backstop and sideguide must be cut extremely square and straight.
Once you get the notches cut, locate and drill the holes for the clamp bolts. I used carriage bolts, countersunk from the bottom using a Forstner bit. Do not allow these bolts to touch the table top of the saw. The clamp bolts will use fender washers, so make sure the washers clear the path of the saw blade, or grind down the edge of the fender washers to make clearance.
Now cut two guide blocks, straight and square (see photo, left). Their length should be as long as possible and still be able to move the entire range of adjustment for the sideguide. Position the sideguide to its innermost position, then position the guide blocks with about 1/16-in. clearance on both sides of the guiderail.
Next, cut two sticks "A" and "B" for the sideguide angle adjuster (see photo, right). Lay "B" on the sideguide and "A" on the guide blocks. Clamp "A" and "B" together and drill two pilot holes near each end. Use a drill press and get these holes in straight. Separate the sticks and countersink "B" for the clamp bolt in the center. Countersink "B" to accept the two angle adjuster bolts.
Set the clamp bolt and both angle adjuster bolts into "B". Thread two nuts with flat washers on the angle adjuster bolts, place "A" on the angle adjuster bolts, add the outside flat washers and lock nuts. Get everything in position and glue "B" to the sideguide and "A" to the guide blocks. The guide blocks should be positioned so that there is no play but not much pressure on the guiderail. The guide blocks need to slide along the guiderail.
Now set the clamp bolts for the backstop. Piece "C" has a bolt countersunk in it and is glued to the backstop. Piece "D" is glued to the jig board. A nut and flat washer hold the bolt tight to the backstop, and two nuts with flatwashers on either side of "D" furnish the micro-adjuster for setting the angle of the backstop. The backstop is positioned with the sideguide in its outermost position.
In this step, "A" is a stick glued to the guide blocks and "B" is a block screwed and glued to the edge of the jig board. The center bolt and two outer spring guides are drilled while the two pieces are clamped together. The outer spring guides are 1/8-in. dowel, glued "A". The spring guide holes in "B" are drilled oversize so that the dowels do not rub. The center bolt also has a spring on it. There is a nut to recieve the center bolt countrsunk into "A" from the other side. The knob on the centerbolt is plastic and features 62 straight ridges that run parallel to the bolt. The knob was drilled out and the center bolt is epoxied in.
The center bolt is a 1/4 - 20. One turn of the bolt will therefore move the sideguide 0.050". The knob has 62 ridges. Turning the knob one ridge will move the sideguide 0.0008" and turning the knob from a ridge to a groove will move the sideguide 0.0004". A sharpened paperclip furnishes the "pointer" to the knob.
Next, cut and assemble sideguide clamp "A" and backstop clamp "B". The tongue part that overhangs the guides need to be cut very straight. Coat the business side of the tongues with silicon adhesive applied about 1/16-in. thick. This will furnish outstanding friction to hold the work in place without applying pressure to it.
The clamp bolt for the backstop is assembly "C" in this picture. A block with a bolt in it is glued to the jig board. The clamp support block is taller than the clamp bolt block and is glued to the jig board.
To fine tune the jig, clamp a piece against the backstop and cut it. Test it for square, using the micro-adjusters to get it perfect. Repeat with the sideguide. Double check the blade tilt, it might not be exactly the same on the jig as it is on the table top. Once both guides are square you're in business.
You might take notice that the two angle adjusters control rotations in the Y-axis and the depth adjuster controls linear movement in the X-axis. All other kinematic motions have been restricted.
As a test, I cut 23 square sticks in mahagony, 0.655" x 7". I measured both dimensions of each end of the sticks for a total of 92 measurements with the dial micrometer calipers. One end ranged from 0.6500 to 0.6535. The other end ranged from 0.6530 to 0.6550. Judging from this, I need a tiny tweak on the angle adjuster of about 0.0015" and a move of about 1.5 ridges on the depth adjuster. Variation is 0.0025", well within my stated goal of 0.004". Total variation for the batch, including the slight angle error, is 0.005, twice as good as needed to make a "nice" puzzle.
I deliberately left out a lot of minutiae because the details of this particular jig are not important. For instance, there are many ways to construct a micro-adjuster, not just the opposing nuts method I employ. You could use pairs of push-pull bolts, you could use eccentric cam adjusters or moveable wedges or straight levers. The guide rail could have been a piece of ground round stainless with 3 ball bearing rolling on it or a shaft riding in bushings or a dovetail that machinist are so fond of.
The important thing is to use kinematic principles and careful shop technique to design and construct your positioning devices.
. . . Steve Strickland
CLICK HERE TO RETURN TO THE INDEX!
SEND US YOUR "SHOP SHOTS"
This is the place to share views of your shop, woodworking tips and methods,
mug shots, special tools or machines, finished work--you name it!
We prefer digital images via e-mail, but prints or transparencies will do. Include your name, address, phone number and a paragraph or two explaining the photo(s).
Not every entry will be used, we reserve the right to edit for length and clarity,
and we will not return photos.
P.O. Box 493
Springtown, PA 18081