Subject:
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Re: Competitive MINDSTORMS: Now in a store near you!
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Newsgroups:
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lugnet.robotics
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Date:
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Fri, 20 Aug 2004 18:28:06 GMT
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Viewed:
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1128 times
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In lugnet.robotics, Brian Davis wrote:
> In lugnet.robotics, David Perdue wrote:
>
> > 1:15 and 1:75 are, in fact, the gear ratios... there are
> > actually only two motors applying torque into the
> > drivetrain... wheel radius is 81.6 x 15
>
> Hmm. The way I see it, pushing power is limited (in an ideal world!) by one
> of two factors: applied torque (a function of motors and gearing), and the
> frictional force between the wheels and the surface (controled by the weight of
> the 'bot and the coefficient of friction). There's little point maximizing
> applied torque beyond the point where frictional contact of the wheels fails, so
> ideally (there's that word again) you'd like them to be equal. In mathmatical
> terms (forgive me):
> F_push = Torque_applied / r <-- applied torque limit
> F_push = mu m g <-- frictional limit
> Setting these two equal should give us the minimum torque needed to just match
> the frictional force that actually provides a forward "push":
> Torque_applied = mu m g r
> where mu = coefficient of friction
> m = mass of 'bot
> g = acceleration of gravity
> r = tire radius
> So, for instance, for a 3 lb (1.36 kg) sumo bot, assuming *all* that weight is
> carried on the driving wheels, you can get an idea of the minimum torque
> required to break the wheels free; assume mu = 1 (high friction, although under
> some circumstances there are LEGO wheels for which mu > 1. Honest.) and r = 4.1
> cm, and you need at least (1)(1.36)(9.81)(4.1) = 54.7 N cm (see, there's a
> reason I stayed in SI units the whole time... besides allowing certain
> rtlToronto folk to follow, that is ;-), these are the same units I know the
> motor torques in). That's the bare minimum that needs to be applied. I usually
> aim at this point or above, as there are a number of things that can reduce the
> delivered torque: due to low batteries, frictional losses in the geartrain,
> friction in the wheel axles (this can be minimized with good axle support, but
> there's a lot of weight riding on them), variations in motors.
> Also note that in terms of maximizing pushing power, skid plates (or
> non-driven wheels) should carry the minimum of weight possible: any weight not
> carried by the driven wheels reduces the maximum frictional force they can
> exert.
>
> > I'm not sure about the 900 Ncm wheel axle torque...
>
> The way I got that was to consider that when stalled, the standard gear motor
> delivers about 6 N cm of torque (less, about 4.5 N cm, if two are connected to
> one current-limited output port). Take 6 N cm and gear it up by a factor of 75,
> and each drive axle is at 450 N cm delivered, or a sum total of 900 N cm for the
> 'bot as a whole. Even at 15-to-1, delivered torque (again, assuming no losses)
> should be 180 N cm, enough to break the Mindstorms motorcycle tires free even if
> the 'bot weighed in at 3.3 kg (over 7 pounds).
Wow! That's a lot of math. I see now where the 900 N cm comes into the picture.
> > I'd love to bring Gargantuan-Bot Version BL58 with me to the
> > event, but I think that one might be too big under the rule
> > set. :)
>
> What's it weigh? Sumo 6 is a 2 lb limit (rtlToronto folks, that's 909 grams)
> and must fit upon start-up inside a 12" by 12" square (30 cm, guys). Come on
> down!
Unfortunately, BL58 does weigh over 2 lbs, but as Brian suggested, I could bring
it anyway and we could have several rounds with it just for fun.
Thanks,
David J. Perdue
www.davidjperdue.com
www.davidjperdue.com/competitivemindstorms
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Message is in Reply To:
 | | Re: Competitive MINDSTORMS: Now in a store near you!
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| (...) Hmm. The way I see it, pushing power is limited (in an ideal world!) by one of two factors: applied torque (a function of motors and gearing), and the frictional force between the wheels and the surface (controled by the weight of the 'bot and (...) (20 years ago, 20-Aug-04, to lugnet.robotics)
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