4" Wooden Mecanum Wheel

[TheOtherGuy]

This is my second year in college, and I've been looking for something to keep me busy (robots?). I decided to create a mecanum robot roughly half the size of an FRC 'bot as a testbed for a variety of mechanisms and control schemes. I figured making low-cost, easy construction 4" mecanum wheels would be a neat sub-project. Not being particularly mechanically inclined (which is partially why I'm doing this), I enlisted the help of my dad (squirrel).

The design went through a series of iterations, but stayed mostly the same. I planned on 6 rollers per wheel to keep costs as low as possible. At first, the center plate and "fingers" were made of 1/8" steel, because that's what we have laying around. The idea was to cut slots at 45 degrees on a chop saw and weld 1/2" strap into those slots. After a short time, it became apparent that 1/2" plywood could be used for the center plate and 1/4" for the fingers. This eliminated the need for welding (wood glue now) and made cutting out pieces much simpler (table saw).

I didn't have many ideas in the way of roller construction, but the robot we made a few years ago used wooden dowels trimmed down on a lathe, so that's what we're using for this. We also found that rubber stoppers are available in a variety of sizes at McMaster, so buying two sizes with slopes that approximate the curvature of the rollers might work too (and then we wouldn't have to wrap them with anything!).

The rollers are held on by tightening two 7/32" aluminum tubes of 1/4" length over a 3" #10 threaded steel rod that passes through each finger. Washers are placed between the tube and the finger, and nuts at each end are tightened to provide a very rigid, low-friction axle for the wooden rollers (see attachment).

The current issue I'm having is the nuts are just a little too big (or the rollers too small). I would love to hear other ideas for attaching the rollers, unless making them slightly larger is the best solution.

My dad says they'll take forever to make. He's planning on teaching me how to use the lathe so I can make the other forty-seven rollers.

[Alan Anderson]

Originally Posted by TheOtherGuy

The current issue I'm having is the nuts are just a little too big (or the rollers too small). I would love to hear other ideas for attaching the rollers, unless making them slightly larger is the best solution.

Perhaps you could recess the nuts inside the end of the roller.

[WileyB-J]

maybe try lathing them with a machinable nylon polymer? it would seem a touch easier and more consistent. in my opinion wood will not stand the test of time. (meaning the hub and spokes seem brittle and weak) but the idea seems mint!

[MrForbes]

If you play with the plywood parts some you might change you're mind, they seem pretty strong.

But setting up the saw and jigs to make all the parts the same size seems to be a chore. I'll look into what it would take to make them out of welded steel, too.

I like the idea of redesigning it to use the rubber stoppers that already have a hole in them.
The wheels might have to be a bit smaller than this design's 4" diamter to work well though, as most stoppers seem to be 1" tall, and the current design requires the rollers to be about 1.25" tall

[TheOtherGuy]

Originally Posted by Alan Anderson

Perhaps you could recess the nuts inside the end of the roller.

That thought had crossed my mind, but it didn't seem like much material would be left surrounding the nut. Maybe just recessing it half the width of the nut would work, along with a slightly larger radius for the roller. Time to draw!

Originally Posted by WileyB-J

maybe try lathing them with a machinable nylon polymer? it would seem a touch easier and more consistent. in my opinion wood will not stand the test of time. (meaning the hub and spokes seem brittle and weak) but the idea seems mint!

The hub and spokes seem strong enough, but you might be right about the rollers. After time the center of the rollers might wear down, so maybe getting some of these and press fitting another aluminum tube inside would work?

[Ether]

Originally Posted by TheOtherGuy

I didn't have many ideas in the way of roller construction, but the robot we made a few years ago used wooden dowels trimmed down on a lathe

How did you determine the contour for the rollers?

[TheOtherGuy]

Originally Posted by Ether

How did you determine the contour for the rollers?

I found the cross section of two ellipses of vertical radius equal to the radius of the wheel and a horizontal radius of the wheel radius * sqrt(2). The ones in the vex picture were just estimated, I believe.

[Ether]

Originally Posted by TheOtherGuy

I found the cross section of two ellipses of vertical radius equal to the radius of the wheel and a horizontal radius of the wheel radius * sqrt(2).

The correct profile is actually closer to a parabola than an ellipse. If you're a purist, you might find these of interest:

roller profile parabola vs ellipse comparison:
http://www.chiefdelphi.com/media/papers/download/2750

parabolic profile roller projection to XY plane forms circular arc :
http://www.chiefdelphi.com/media/papers/download/2751

Equations for "bump-free" mecanum roller profile:
http://www.chiefdelphi.com/media/papers/download/2749

Win32 "bump-free" mecanum roller profile calculator:
http://www.chiefdelphi.com/media/papers/download/2770

bump-free mecanum roller equations (alternate derivation):
http://www.chiefdelphi.com/media/papers/download/2777

[MrForbes]

So I need to get the parabola attachment for my 1946 South Bend 9" lathe?

[Ether]

Originally Posted by squirrel

So I need to get the parabola attachment for my 1946 South Bend 9" lathe?

You can get it from the same place you got the ellipse attachment :-)

[MrForbes]

heh...I used the compound rest. I suggested that the error would be pretty low if we made the half roller as two cones. Kevin figured the angles at 6 and 16 degrees, I set the compound rest to those angles to turn it. then we sanded the lump in the middle to radius it.

[Ether]

Originally Posted by squirrel

heh...I used the compound rest. I suggested that the error would be pretty low if we made the half roller as two cones. Kevin figured the angles at 6 and 16 degrees, I set the compound rest to those angles to turn it. then we sanded the lump in the middle to radius it.

You could do a similar thing for the parabola.

Or if you had time to kill you could cut a series of steps.

Or not :-)

Anyway, I thought the math might be of interest.

[Fe_Will]

Have you considered a T nut driven into the end of each roller? You may need to modify the flange diameter but that can be accomplished with a grinder if needed.

[Matt H.]

They make products for this situation!

Undersized Machine Screw Hex Nuts are made slightly smaller than regular hex nuts:
http://www.mcmaster.com/#undersized-...x-nuts/=b192e8

Using the 10-24 undersized nut will reduce the corner to corner diameter by ~0.1 in.

If that's not enough you can use Allen nuts which would reduce the corner to corner diameter by ~0.12. However they are pricey ($0.90/nut).

http://www.mcmaster.com/#allen-nuts/=b18xlg
http://en.wikipedia.org/wiki/Internal_wrenching_nut

[TheOtherGuy]

Originally Posted by squirrel

heh...I used the compound rest. I suggested that the error would be pretty low if we made the half roller as two cones. Kevin figured the angles at 6 and 16 degrees, I set the compound rest to those angles to turn it. then we sanded the lump in the middle to radius it.

Looking back at it, the dowel comes slightly smaller than an inch at the largest, and our estimations cut it down on the inside by another fraction of an inch, which may have made the end of the roller near the nut too small a diameter. Then again, I haven't wrapped it yet... maybe I'll go buy some tape and try that out.

The whole parabola thing is very interesting, thanks for bringing that up! The difference is hardly noticeable in CAD, but there is a slight bulge near the ends of the rollers, despite the rollers meshing perfectly. The third link you provided gave a ghastly equation (well, a few relatively nice equations with lots of substitution ) on the last page for estimating the parabola, yet when I plot it, the length is off by quite a bit (should go to sqrt(7/2))... http://www.wolframalpha.com/input/?i=plot+y%3dsqrt(4-(x^2)/2)-1.5,+y%3d.5-(32(2*.5-(sqrt(4*3.5^2%2b(1/2*sqrt(7/2))^2))(+(4sqrt(2)/+sqrt(2*3.5^2%2b(1/2*sqrt(7/2))^2))-1))/(14*((4sqrt(2)/+sqrt(2*3.5^2%2b(1/2*sqrt(7/2))^2))%2b1)^2))x^2,+x%3d-2+to+2&incParTime=true

T-nuts are a possibility, although that would require changing the entire setup of the rollers so the axle is live. I'm not sure if that's a good idea with 3/16" plywood, but press fitting a small piece of the aluminum rod into the hole might give it enough strength.

Originally Posted by Matt H.

They make products for this situation!

Hey Matt! How's MIT?
Mr. Forbes mentioned those as a first solution, too. It may be worth looking into. I just had a crazy idea that may or may not work, but if it's possible to drill and tap into the end of a #10 threaded rod, maybe I can screw on a small washer onto the ends of the rod.