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Ellipses, Upside down.

4DThinker's picture

I have a student that designed a coffee table with an elliptical table top.  The ellipse is 36" long and 14" wide.  The large length-to-width ratio proved to be impossible to create with the typical crossed slots and trammel type ellipse jig.  The student was able to use AutoCAD and plot out the full sized pattern.  But trying to cut it out accurately with a hand-held jig saw in 1" thick hard maple didn't yield useable results (the blade wouldn't track vertically).

I thought I could invert the typical jig strategy to make a guide I could clamp to the bandsaw table which would pass her board on an elliptical path through the blade. The guide worked fine, but the ellipse does not remain tangental to the blade kerf, and as such binds the blade within a few inches of the cut.  It became clear that I could use the guide on a router table to cut the ellipse, but in the student's case the router bit would remove too much of a path.  The student wants to use both the interior ellipse and the remainder of the rectangle in her design, fitting them back together with only a minor gap in one tranformation during use.  We've now found someone local with a high-pressure water pattern cutter that can use her ACAD drawing to cut the pattern from her 1" thick rectangular maple blank.

In experimenting with my new ellipse jig, though, I discovered it can be used to make very extreme ellipses.  I'm making an elliptical plant stand, for example.  The top is a golden-ratio ellipse approx. 14" x 22.5".  It is supported by crossing rectangular/tapered panels that have ellipses cut from the center, and half-ellipses cut from the bottom edge to create feet.  I was able to accurately cut 22.25" x 10" and  22.25" x 4.75" full ellipses from the center of the panels, and 11" x 6" and 4.125" x 6" half ellipses from the bottom edges.  With my jig all panels were passed on an elliptical path through a 1/2" straight bit on my router table.  The bit was raised in 1/4" increments for each pass, with the last pass cutting through and releasing the interior ellipse from the exterior panel.

If anyone is interested, I'd be happy to write a full article on the jig, and the process of creating this particular table with it.  When the table is done I'll try and post a picture in the gallery.  IF you've every needed an extreme elliptical part or hole, this is a sure way to create them.

If there are any clever jig makers/engineers out there, I'm still interested in a jig that will pass a board on an elliptical path tangentally through a bandsaw blade. Any ideas?

4DThinker  (Dave Brown, professor at Kansas State University, Interior Architecture Dept.)

Edited 10/16/2003 4:50:48 PM ET by 4DTHINKER

WayneL5's picture

(post #79210, reply #1 of 24)

Just when you think everything has been invented, pow!  The jig sounds like a great idea.  I hope it gets published somewhere.

Another way of doing shapes is to make a pattern of ¼" MDF.  Prepare the pattern, in this case it could be a little over one quarter of the ellipse, and use files and other tools to fair the edge.  Then, rough cut the blank 1/16" oversize.  Using the pattern and a bearing-guided flush cutting bit in a router, smooth up the stock.  David Marks uses this technique often on his TV show.

You're the first person I ever heard of using a waterjet on wood.  Certainly an unconventional solution that fits your situation of mating parts and small kerf well.

I think you'll have a lot of people thinking about an ellipse jig for bandsaws now.

4DThinker's picture

(post #79210, reply #3 of 24)

In 20+ years of teaching a furniture design class, I've done more pattern making/ pattern bit router trimming than anything else.  In fact they tend to call me the "Router King" due to my experience with it and the creative uses I've found for it.

The high pressured water cutting is done by a materials technology shop funded by my university's engineering department.  They also do CNC plasma cutting, CNC routing, and a few other things we haven't figured out how to take advantage of. Most of the water jet work so far has been cutting intricate and/or multiple repeated parts from baltic birch plywood.  It works amazingly well.  The students do have to pay for the work, but the cost is far below what it would be had they gone to a commercial for-profit shop.  The shop enjoys helping our students, since the stuff they challenge the shop with is usually far more interesting than what the engineering kids want done.

As for the bandsaw jig, I could probably figure it out myself.  But I think I've probably already made a few years worth of ellipses with my router jig, and won't be interested in making any more for awhile.  Having one would sure be nice, though.  Using a 1/2" router bit turns a great deal of hardwood into sawdust.  If I could have used the bandsaw and a 1/16th inch kerf, there would have been 1/8th the mess.


Steinmetz's picture

(post #79210, reply #5 of 24)

4D thinker, I believe you meant " If i used 1/16" kerf rather than a 1/2" router bit I could have saved 16 times the mess." 

 BTW, Nobody mentioned laser cutting. An aquaintence of mine, converted his Rule and Die business to laser cutting.

 The plywood matrices are neatly incised with curvilinear grooves to acsept the cutting blades (Which are similar to the blade on a retracting. taperuler. Stein. 

Edited 10/17/2003 3:46:19 AM ET by steinmetz

4DThinker's picture

(post #79210, reply #7 of 24)

OK, Stein.  I could have meant that a 1/16th inch kerf would consume 1/16th of what a 1/2" router bit does, but I didn't.  There are 8, 1/16ths of an inch in a half inch.  I meant that if I'd been able to cut the ellipses with the band saw, the mess would have been 1/8th of what it was when cut with a 1/2" router bit.

At least I think that's what I meant.  Instead of math, maybe I should have just said there would have been much less mess.

As for laser cutting, that service I mentioned DOES also do laser cutting.  We've had several students get metal parts laser cut.  In fact I've got one former student who now works for a firm that designs furniture and fixtures entirely from laser-cut then powder-coated metal plate.  The service prefers water cutting wood, since it tend to start fewer fires.


Steinmetz's picture

(post #79210, reply #9 of 24)

4D, Thanx for the clarification.and the downside of laser cutting wood.

 I was under the impression those matrics I mentioned ,were only penetrated into  the ply about 5 1/6"and done using C N C in an inclosure surrounded (bathed?) in an atmosphere of Argon or whatever they call the gas used to snuff out fire in raised, flooring enclosures. ( Long winded sentence) 

Anyway, the discussion with the Rule and Die guy, took place 15 years ago.  WHO KNEW?  Regards, Stein.

Edited 10/17/2003 8:02:53 PM ET by steinmetz

Jamie_Buxton's picture

(post #79210, reply #2 of 24)

Is it really less expensive to get a shop to do water-jet cutting than it would be to buy more maple and make the inner and outer parts seperately?

And while I'm asking questions, what is the effect of a water jet on wood?   I'd be guessing that the high pressure would drive water a long way into the wood, so that it'd take long time to dry back out.  Heck, it might even get the wood wet enough, deep enough, that you might see end-checking as it dries out.

4DThinker's picture

(post #79210, reply #4 of 24)

Cost wasn't really a factor.  The table design could have been done as seperate inside/outside parts, but the grain across the top would not be continuous as it will be using the small kerf and water jet.  And the student's project was going to take several steps and stages had we not been able to utilize the water jet service. With it, she delivers one rectangular blank of maple and a ACAD drawing.  She gets three complicated and precisely cut parts with no burning, tearing, splitting or other potential process artifacts.

The effect on maple isn't known yet.  Previous students have had 3/4" baltic birch plywood cut using this process, and there appeared to be no consequence from the water exposure.  At extremely high pressure, and with a tightly focused jet, the water is simply a cutting tool.  And very little water is actually used.  She will probably have the work done next week.  I'll let you know how it turns out.


ianneuhaus's picture

(post #79210, reply #6 of 24)


a perfect elipse can be marked out with a pencil, a loop of string and two nails.  with a nail placed at each foci and the string sized appropriately a perfect elipse will result.  The maths goes like this:

a =  1/2 the long axis of the ellipse, in this case 36/2 = 18 in
b =  1/2 the short axis of the ellipse, in this case 14/2 = 7 in
e =  the eccentricity of the ellipse, where e^2 = 1 – b^2/a^2
f  =  1/2 the distance between the foci, where  f = e x a  (the foci lie along the long axis of the ellipse an equal distance either side of the centre point)
s  =  length string tied into a loop = 2 x (f + a)  (the loop itself is only f + a long)

now in this case:  
e^2 = 1 – 7^2/18^2  =  1 – 49/327 = 0.8501529, and e = 0.92204
f  = e x a = 0.92204 x 18 = 16.59667 in,  about 16 - 19/32 in, so
s  = 2 x (f + a) = 2 x (16.59667 + 18) = 69.1933 in, about 69 - 3/16 in

A jig could consist of a pin on the wasste side of the bandsaw blade, and a two pins 2 x f apart on a template.  Take a loop of packaging strap and stretch it arround all three pins.  cut the template keeping the loop tight.   use the template with a router and to cut the maple stock


4DThinker's picture

(post #79210, reply #8 of 24)


Thanks for the math.  I've explored at least four ways to create an ellipse, and yours is one of them.  It does work very well for drawing an ellipse, but is harder to adapt to a useful jig or guide. And assuming I could "upside down" the idea to let the bandsaw blade be the pencil, it suffers the same flaw my current jig does:  The path the part takes through the blade does not stay tangent to the blade kerf.  Thus the band saw blade has to twist to follow the ellipse, and it can't.  The reason all the available jigs work with a router is that the circular router bit is non-directional.  The "orientation" of the bit to the ellipse is irrelivent.  But cutting an ellipse with the band saw requires the ellipse to maintain a perpendicular orientation to the blade at all points along the path.  It's a very complicated path, and one that no current jig accomodates.  For example, you could not use a hand-held jig saw instead of a router on any commercial ellipse router jig, as the blade would twist in the kerf.

And the original point of cutting the maple on the band saw was to be able to use both the center ellipse and the outer rectangle.  The router bit still consumes too much of the maple.  This "perfect bandsaw ellipse jig" must be able to seperate the inner ellipse from it's surround with only a single blade kerf difference.


Clay's picture

(post #79210, reply #10 of 24)

I think it highly unlikely that you can get a bandsaw to cut with the kind of accuracy that would give you a really fine kerf.  I am quite certain that I could cut to a line with a hand held jig saw in one inch material and then clean up both sides of the cut with a belt sander and end up with about 5/32" kerf.  I know this because I have done many similar cuts and I am familiar with my expectable accuracy.  You need a good saw to do this with a variable speed and variable blade orbit (set the blade orbit at the lowest setting).  You also need a high quality blade.  The Bosch "progressor" blades are my favorite.  When making this type of cut use a new blade that has an aggressive tooth pattern (you may need 2 or 3 blades for a real long cut in maple).  You can smooth the cut as you belt sand to the scribe lines (you need three lines, cut line, inside scribe line, and outside scribe line).  A fine toothed blade will deflect excessively toward the far side of the cut.  You need to be patient, feed the blade into the cut gently, if you lose the line in the dust STOP and clean it up before you continue (my saw has a little blower to help keep the line clear but it isn't foolproof).  This is a skilled operation but not a real challenging one.

ianneuhaus's picture

(post #79210, reply #11 of 24)

my original off-the-cuff response to your first post was "get a better jig saw"  Without going into brand specifics, some jig saws are much better than others at cutting perpendicular to the machine's base plate.  If I were doing what you're trying to do, I'd modify my jig saw's base plate with a steel pin beside the blade to track the "string" and use a thin narrow blade (my saw will take a blade about 1 mm wide and 5 mm long that should easily turn the radii you're looking at)


Edited:  should have read to the end of the thread before posting.  Some one else beat me to the "better jigsaw response"

Edited 10/18/2003 10:57:42 AM ET by ian

4DThinker's picture

(post #79210, reply #12 of 24)

I'll agree a better jig saw might have helped, and that even using one still would have left us with more than 1/16th gap (after sanding to clean up the cut marks).

And I'll admit that in retrospect the ONLY technology that will make this student's table turn out as designed seems to be the hight-pressure water-jet cutting technique.   But such is often the case when teaching furniture design to students who rarely have any prior woodworking or machining experience.  I love the originality in design that this naivety leads to, though.  My experience in how the tools perform, what their tolerances are, and the degree of precision they will allow often stops or steers my creative process.   It's a very enjoyable class to teach, since I often steal inspirations from the students to expand my own design reach. 

Personally, having a bandsaw ellipse jig would still simplify the use of my table-router upside-down jig.  To "rough out" the ellipse accurately on the bandsaw to within 1/8 or less of the final shape would mean the router bit would then only have to finish off that 1/8 or less to leave me with a perfect and smooth ellipse.  In the process of hogging a 1/2" path through 3/4" or thicker cherry I end up with a few burns and plunge steps to sand off.  Yea, I could make the "rough" ellipse 1/16th larger, then cut it again to exact size.  But I'd much rather let my bandsaw do that original rough work.  It's just much more efficient.


ianneuhaus's picture

(post #79210, reply #13 of 24)

4D, I think there is a way.  But it turns a lot of fine timber into dust.  Starting with a plank much thicker than you want, rough out the shape and then trim both the piece and off-cut at a 45deg angle, then thickness both so that the kerf closes.  Look at the attachment



angled_kerf.wmf4.74 KB
4DThinker's picture

(post #79210, reply #14 of 24)

Thanks for the trick, Ian.  I've used that one a few times before for assorted student project problem solving.  But I don't think it will work in my student's coffee table ellipse case.  The design could use an angled cut at the tip of the ellipse, but the angle of the cut would have to get progressively more vertical as it approached the center of the long side.  Her project is flat for storage as a rectangle.  But in use the rectangular ends fold down to about 45 degrees from the ellipse center to become the legs.  A section of tambour then fills in the elliptical cut between the legs to lock the structure into a stable configuration.

As for a tangential bandsaw ellipse cutting jig, I spent the weekend analyzing the path an ellipse would have to take to remain tangential to the saw blade.  It looks like a geared or linked translation would be required in addition to the normal crossed-slots and trammel path. Not an easy thing to contemplate.  But the seed  of an idea is now planted.  I just hope it's a quick growing one. 


4DThinker's picture

(post #79210, reply #15 of 24)

My student got back from the water-jet  source today with her ellipse table pieces cut.  Some observations:

The path the cutter took appears faceted instead of a constant curve.  The pattern was originated in AutoCad, and exported as a DXF file.  In AutoCAD I believe there is a variable for how smoothly arcs and circles (and ellipses) are rendered. By default the onscreen curves may LOOK smooth, but clearly when rendered full scale this faceting should have been refined.  She'll have useable pieces, but they aren't the smooth ellipse one would get with a crossed-slots and trammel type router jig.  It's possible that now knowing this the service could revise the pattern to a smooth ellipse, but I doubt the student wants to start over... again.

The cut has a few "bumps" along it.  I don't know if that was an effect of the varying grain encountered in the wood, someone bumping the machine, or what.  But this technique (high pressure water jet cutting) is certainly not going to work for producing very precise parts in hard woods.  It DID get her three fitted pieces (an ellipse and two end pieces) that could not have been made as easily any other way.  They just are not ideally smooth.

I may spend some time at that service to see if the flaws I noticed are expected and unaviodable in the process, or if they are something that can be tweaked out.


WayneL5's picture

(post #79210, reply #16 of 24)

If someone were to systematically develop a process for cutting wood with a waterjet, there are a number of parameters that could be altered.  I'm sure the process was designed for other materials and not the best possible process for wood.  Like trying to crosscut with a ripping blade.  The few parameters which come to mind are orifice diameter, grit size, grit concentration, grit material, jet speed, travel speed.  The process could certainly be made better with some research.  Only after research could one give up and say it can't be a good process for cutting wood.

ianneuhaus's picture

(post #79210, reply #17 of 24)


For what it's worth.  About 15 years ago I had to cut an opening in the 25mm thick steel plate of a bridge girder.  For a number of reasons, water jet cutting was the way to go – however the edge of the hole was no smoother than what would have resulted if the hole had been cut with a gas torch.  For the application this was OK as the primary purpose of using water was to avoid the slag spray generated by gas cutting. 


corners's picture

(post #79210, reply #18 of 24)

The problems with the cut not being a smooth curve comes from the software issue that most simple CNC machines only cut circular arcs not elipse or curves. The software has converted the CAD - DXF drawing into a series of circular curves for cutting. I have learned a lot of tricks to use these circular curves to cut some simulated curves but a pure elipse is an elusive thing on these machines.

4DThinker's picture

(post #79210, reply #20 of 24)

You're right, Corners. Except that the CNC machine didn't convert the ellipse to arcs... It converted it to short straight sections.  And I think we've deduced that by changing a variable in AutoCAD the length of each straight can be much smaller, leading to what would appear like a smooth ellipse.   But I'm going to have to wait for the next student who needs an ellipse cut by water to find out. 


4DThinker's picture

(post #79210, reply #19 of 24)


The edges certainly were not smooth, but at least they were very vertical (unlike the results from a jig saw cut).  It didn't take the student much time to get them smooth though.  The piece is sanded and ready for a finish.  The student has a little "figuring out" to do as to how it's all going to work, but in the end (of the semester) it should be a wonderful looking piece of furniture.


ianneuhaus's picture

(post #79210, reply #22 of 24)

Don't forget to have her post a picture

4DThinker's picture

(post #79210, reply #21 of 24)

Being the curious kind of guy I am, I've been playing with my ellipse jig.  The first thing I tried was to make the slots something other than 90 degrees to each other.  As it turns out, this still produces an ellipse.  But the ellipse will be oriented at an angle to the major axis. 

The second thing I tried was making one of the slots curved.  Anyone need an egg-shape jig?   By curving (arcing) one slot and using a curved slider in it, the jig will produce an ellipse that is fatter near the end closer to the center of the arc.  The tighter the arc, the greater the difference will be between the upper and lower halves of the ellipse.

I suppose both slots could be curved.  The result may still be an egg shape, but be a little distorted toward one side.  Might be nice if you need an asymmetric natural curving form for a table top.

Now I just need to find a way to make the curved slot variable.  I can imagine the slider being segmented to follow any reasonable curve.  But I have no idea what I could make a flexible C-channel out of, nor how I'd control it (fix it in any position).

So, Egg shapes can be made with a revised ellipse jig.  Now I just need some uses for egg shapes.  Ideas, anyone?

4DThinker  ;-)


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