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I have a small four-wheeled platform weighing 1.3kg with a height of 30cm. Its center-of-mass is located at 75% of the height, making it a little top-heavy.

I empirically measured the angle at which the platform topples over when not moving to be 20 degrees. However, when it encounters a small ledge or depression of 1cm while moving at 4cm/sec, the platform topples over, even though the depression only represents a tilt of about 10 degrees.

Is this is happening because the platform's momentum is applying an extra amount of force during the fall into the depression, causing it to topple forward even though its center-of-mass hasn't moved beyond the footprint of the wheels?

I'm trying to compensate for this by using a servo, attached to the top of the platform, to swing a counterweight backwards when a sudden acceleration forwards is detected. How would I calculate the mass of the counterweight and acceleration of the swing needed to keep the platform upright?

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closed as off-topic by CuriousOne, ACuriousMind, John Rennie, JamalS, user36790 Mar 29 '16 at 10:15

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  • $\begingroup$ Why not move the center of mass down and make the wheelbase larger? That sounds infinitely better than this idea of "rescuing" an unstable object by adding an extra degree of freedom. $\endgroup$ – CuriousOne Mar 28 '16 at 8:45
  • $\begingroup$ @CuriousOne, I agree, but significantly lowering the base's COG isn't really an option, because it's very compact leaving not much room to place extra mass. $\endgroup$ – Cerin Mar 28 '16 at 13:46
  • $\begingroup$ Did you make the bottom out of depleted uranium, already? If you haven't, then you have not explored the most obvious options. $\endgroup$ – CuriousOne Mar 28 '16 at 18:05
  • $\begingroup$ @CuriousOne, Please don't troll StackExchange. If you have no helpful comments, then please do not comment. $\endgroup$ – Cerin Mar 28 '16 at 23:04
  • $\begingroup$ That is a viable physical option and I have seen it used. You may substitute lead for depleted uranium, mostly because of the regulatory headache that the latter substance poses, and it's easier to come by to boot. I can guarantee you that if you brought this matter to me and any number of engineers that I worked with in the past for an engineering review, this would have been one of the first questions... and the words "Rube Goldberg machine" would surely have been used in jest over your suggestion of using an active mechanism instead of designing it as a stable platform. $\endgroup$ – CuriousOne Mar 28 '16 at 23:13
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When your platform is moving it has a kinetic energy which cannot just entirely vanish by encountering a small ledge in front of one of the wheels. The ledge causes the front wheel to stop but the kinetic energy go into a rotational energy. This rotation is eventually stopped by the gravitational force which is acting down. So the platform might or might not topple over according to the initial kinetic energy.

It would be easier to move the center of mass down instead of any fancy ways to compensate the torque.

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  • $\begingroup$ To clarify, it's a ledge, not a bump, so the front wheel isn't stopping. The front of the platform falls 10mm. But this doesn't answer my question. How would I calculate the necessary mass to add (to the top or the bottom), so that it doesn't topple? $\endgroup$ – Cerin Mar 28 '16 at 13:59
  • $\begingroup$ @Cerin: The plumb line of the COG can never fall outside of the supporting base. You should know that. $\endgroup$ – CuriousOne Mar 28 '16 at 18:08
  • $\begingroup$ @CuriousOne. Yes, I know that...how do I stop that from happening? $\endgroup$ – Cerin Mar 28 '16 at 23:04
  • $\begingroup$ @Cerin: You make the base wider and you lower the COG. Making the base wider doesn't necessarily mean that you need to extend the actual wheel base. How about adding "training wheels" or booms to prevent the "rollover"? Those are perfectly valid engineering solutions to your problem. $\endgroup$ – CuriousOne Mar 28 '16 at 23:54
  • $\begingroup$ You were right. A simple ballast on the bottom of about 150g was all it needed. $\endgroup$ – Cerin Mar 30 '16 at 15:41

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