How do you model the mecanum rollers?

Ok so this is somewhat of a puzzle I think…

Even though my team has never used mecanums, I’ve been thinking about them and the design challenge they pose.

So it got me thinking about making a CAD model, and while running the model through my head, the most obvious problem was the rollers.

so this is a puzzle for you: how would you model the rollers of a mecanum wheel?

to give everyone a chance, please post your method in a white font, requiring someone to highlight it in order to read it:


1)create a cylindrical roller, and a giant tube with an ID of the desired wheel OD. extrude cut with the tube (or use boolean subtraction: result=roller-tube). now the roller has a profile on it which can be used in order to revolve cut the rest of the roller.


this method is still somewhat convoluted in my opinion and I’d like to hear something easier and/or cleaner (or just any other creative idea!).

Ready? set. CAD! ::safety::


Draw a sectioned profile of the part, with a construction line where the center of the part should be. Revolve the mass around the central line. Done.

Step two: Insert a single roller into your mecanum wheel, and circular pattern it the appropriate number of times around the wheel’s axis.

Remember, CAD is supposed to do all the hard stuff for you. If you find yourself doing a repetitive task, there’s probably a tool that does it for you in a single step.

The first way to do it that comes to my mind is the way Craig would do it. I could think of some other ways but they would take more time to make the same part.

I’d love it if someone could find a simpler method. I’m always hunting down methods for shortening my workflow…

I know there’s a way to do it with Lofts, but I’m not so sure if it’s faster/more accurate…

Am I missing something obvious? I didn’t think the profile for the roller was a simple shape you could draw…

If it’s an ellipse, is there some easy to find relation between the wheel diameter and roller diameter that i’m missing?

We found that two radii with a “point” between them was the optimal shape for rollers. This was through experimentation only, and I’m not sure of the math behind it. Since the parts are patterned, it’s simple to adjust the effective diameter by tweaking a single roller. Your mileage may vary, of course.

If R is the radius of your wheel and assuming that he rollers are the 45 degrees,

Draw an ellipse with major radius of R*sqrt(2) and minor radius of R
the axis of the roller will be perpendicular to the minor radius of the ellipse and the profile of the roller is the top of the ellipse where the minor radius crosses the perimeter.

I’ll have to check this out, but are you sure this is the exact curve required, or is it a very good approximation?

This is the exact curve required.

If you look at that ellipse at a 45 degree angle it will look circular (sin(45)=1/sqrt(2))

thus with this profile for the roller if you look at the wheel from the side it will look like a perfect circle.

I have done this in inventor before.

An analysis which takes into account the 3 dimensional aspects of the rollers seems to indicate that the correct equation for the profile is parabolic rather than elliptical.

The analysis is given in the presentation titled “equations for bump-free mecanum roller profile” located here:

[edit] A one-page PDF titled “roller profile parabola vs ellipse comparison” at the same link compares how well a least-squares fit parabola vs ellipse matches a set of XY roller profile data.

Constructive criticism and questions welcomed.


Thanks for this! very interesting!