Quote:
Originally Posted by GeeTwo
Today was the day (though I used a sheet of paper rather than a board). I'll follow up later (probably over the weekend) with a diagram, but the bottom line is that if the module has a short pendulum arm (vertical distance between the drive axle and the CoG), and ignoring bearing friction, wheel slippage can be avoided by ensuring that |
Quote:
Originally Posted by Greg Woelki
I'm having trouble trying to derive this so I'd love to see your analysis.
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I did make an error in my earlier analysis. I assumed that the force applied to the wheel by the module at the hub was horizontal, as it was there as a reaction force to the wheel pushing the robot. I reviewed this assumption, and figured out that it did not make sense. I now realize that (ignoring a couple of minor effects, such as bearing friction, pendulum effect, and wheel inertia as compared to the robot inertia), the force must be applied along the line between the drive axle and the wheel axle. This updates the answer to:
- tanθ >= r/( μ R (cos Ф + 1))
For a 4" Vex omni wheel and a Vex 60 tooth gear (I guessed), this comes out to a requirement that θ be no less than 19.1°. If the gear is larger relative to the wheel or the coefficient of friction is less or the pitch angle is larger, the angle will increase. Also, I did make a number of simplifying assumptions, but the bottom line appears to be that unless the module rotates to a nearly vertical orientation, the greater the rotation angle the less the likelihood of slippage.
I'm putting some finishing touches on a white paper (about four pages) that I'll post tonight or tomorrow.