4" Wooden Mecanum Wheel
 

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. :)

Re: 4" Wooden Mecanum Wheel
 

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

Re: 4" Wooden Mecanum Wheel
 

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!

Re: 4" Wooden Mecanum Wheel
 

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

Re: 4" Wooden Mecanum Wheel
 

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!
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?

Re: 4" Wooden Mecanum Wheel
 

How did you determine the contour for the rollers?

Re: 4" Wooden Mecanum Wheel
 

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.

Re: 4" Wooden Mecanum Wheel
 

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

Re: 4" Wooden Mecanum Wheel
 

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

Re: 4" Wooden Mecanum Wheel
 

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

Re: 4" Wooden Mecanum Wheel
 

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.

Re: 4" Wooden Mecanum Wheel
 

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.

Re: 4" Wooden Mecanum Wheel
 

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.

Re: 4" Wooden Mecanum Wheel
 

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

Re: 4" Wooden Mecanum Wheel
 

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.

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.

Re: 4" Wooden Mecanum Wheel
 

I don't follow you. What are you plotting and what are you comparing it to?

Re: 4" Wooden Mecanum Wheel
 

Squirrel,

This is how we turn the rollers for our mecanum wheels: http://www.youtube.com/watch?v=1-Zvib5nZVw&hd=1

Re: 4" Wooden Mecanum Wheel
 

Sorry, should have elaborated. The blue line is the ellipse I'm currently using for the roller contour, and the purple is the equation found on the last page of the third link. Specifically, the length of the roller L is 2sqrt(7/2)" (from ellipse equation), R is 4", and r is .5". The equations are then:
D = R – r = 4-.5 = 3.5
F = (sqrt(2*3.5^2+(1/2*sqrt(7/2))^2))
G = (sqrt(4*3.5^2+(1/2*sqrt(7/2))^2))
T = (4sqrt(2)/ sqrt(2*3.5^2+(1/2*sqrt(7/2))^2))
A = 32*(2*r-G*(T-1)) / (L^2*(T+1)^2)

But when I plot it, the roots aren't +/- sqrt(7/2). Oh well, maybe I'm just no good at copy-pasting.

Re: 4" Wooden Mecanum Wheel
 

Thank you for posting a link to the video! I thought about using a coarse abrasive if we used rubber rollers, but that would work well with wood too. It makes a mess, but it's an easy way to make the parts.

Re: 4" Wooden Mecanum Wheel
 

MIT is challenging, but also fun.

Working from http://www.engineersedge.com/screw_threads_chart.htm, tapping the threaded rods seems as though it will present its own set of difficulties.

Your 10-24 threaded rod has a 0.138" minor diameter (total diameter minus the depth of the threads). This means you will need to use 4-48 or small fasteners to have any material between the inner screw and the outer threaded rod.
Tapping #4 machine screw holes in steel by hand is a pain and repeating the process 48 (or is it 96?) times would likely result in several broken taps/drill bits.

Also, I believe you get into issues with loading on the screws and threaded rod. Speaking qualitatively #4 screws are at risk of breaking during shock loading.

Re: 4" Wooden Mecanum Wheel
 

Kevin and I talked on the phone about it, we came up with a few other solutions...like using round, internally threaded, 1/4" od spacers. And a few other ideas.

Good to hear you're keeping challenged, that was always your problem :cool:

Re: 4" Wooden Mecanum Wheel
 

Your parabola plot is correct.

The equation simplifies to y= 0.5-0.066683598*x^2

The roots are not supposed to be +/-sqrt(7/2). Why do you think they should be?

If you want the radius to go to zero, you need a longer roller.

Re: 4" Wooden Mecanum Wheel
 

I found the problem: the ellipse you plotted was not correct.

The ellipse you plotted was y=sqrt(4-x^2/2)-1.5 (see attachment 1).

The ellipse should be (sqrt(64-2x^2)-7)/2 (see equations #1 and #4 of attachment 2).

The ellipse in attachment 2 is plotted in attachment 3. It is a close (but not exact) fit for the parabola you plotted.

If your rollers are indeed contoured per the ellipse in attachment 1, then they are quite a bit off.


[edit]The good news is, this means a larger radius for your end fastener[/edit]

Re: 4" Wooden Mecanum Wheel
 

From eq.#1, it looks like you used the diameter of the mecanum wheel as the radius instead of the radius. The equation for the ellipse without translation should be y^2/4 + x^2/8 = 1. The second ellipse needs to be translated up 3 units in order to give the roller a diameter of 1 in the middle, so the second equation is (y-3)^2/4 + x^2/8 = 1. Solving for y, you should get 3/2, and plugging that back into the first equation gives roots of x as +/- sqrt(7/2).

Intersection of two ellipses

Ellipse shifted down 1.5

Roots of ellipse shifted down

I did a quick check on the wheel I CADed, and the rollers do indeed follow these ellipses (and have the correct side profile on the wheel itself).

Heh, just checked back on the parabola equation, seems I made a small error in setting the radius of the wheel R equal to 4" instead of 2"! That would do it. Here is the fixed parabolic equation with the ellipse above. Sorry about the confusion.

Re: 4" Wooden Mecanum Wheel
 

I used the radius that you gave me:


Not to worry. The difference between the ellipse and parabola is probably negligible for these size rollers anyway.

I did the analysis mostly to satisfy my own curiousity. However, for larger rollers requiring expensive tooling to be commercially produced, it might be worth using the parabola instead of the ellipse.

Re: 4" Wooden Mecanum Wheel
 

it gives me a warm fuzzy feeling to see my son arguing about (I mean discussing) equations

Re: 4" Wooden Mecanum Wheel
 

only in FRC....
wood=fragile, carve them from solid plexi

Re: 4" Wooden Mecanum Wheel
 

We try not to solve problems by throwing technology at them...we like to think of ways to make stuff using supplies/equipment that we have already, or can find easily. Big chunks of plastic and the machines needed to machine them to complex shapes, are not stuff we have or can get locally.

Re: 4" Wooden Mecanum Wheel
 

good point, then i suggest metal