minibot math - revisited clem mckown 1/31/2011. empirical learnings minibots can fall off the pole...
TRANSCRIPT
Minibot Math - revisited
Clem McKown1/31/2011
Empirical learnings
Minibots can fall off the pole when the motors startWe can’t drag stuff (especially magnets) up the pole – ideally only the wheels should contact the poleHeavy minibots are slow and can have traction problemsA minibot with a mass of 4-5 lb seems achievable
From mathematical analysis
The conditions that lead to a minibot falling off the pole when the motors start can be predicted……and avoidedWith 2 motors, a 2:1 step-up gear ratio with 4” diameter wheels is approx-imately right for the pole race. The 2:1 step-up can be achieved with 80T drive & 40T driven gears.
Drive-train model closer look
Modeling an 8 ft pole climb (not 9)Minibot mass from 4 to 5 lbNo wheel slippageNothing draggingUsing (2) Tetrix motors (have curves)Variables: Independent: Mass (lb), Wheel radius
(in) Dependent: time (s) to climb 8 ft
Results
MiniBot Mass (lbm)
4.0 4.2 4.4 4.6 4.8 5.01.5 3.491 3.584 3.683 3.786 3.896 4.0121.6 3.395 3.496 3.602 3.715 3.835 3.9631.7 3.320 3.428 3.544 3.667 3.799 3.9411.8 3.262 3.379 3.505 3.641 3.787 3.9451.9 3.220 3.348 3.485 3.635 3.787 3.9742.0 3.193 3.332 3.483 3.648 3.830 4.0302.1 3.180 3.332 3.498 3.682 3.886 4.1132.2 3.180 3.347 3.531 3.737 3.968 4.2292.3 3.193 3.377 3.582 3.814 4.074 4.380
Wheel R
adius (in)
Optimum wheel radius
Optimum Radius by Minibot MassMass r (in) t (s)4.0 2.15 3.1784.2 2.06 3.3304.4 1.97 3.4824.6 1.88 3.6344.8 1.81 3.7875.0 1.74 3.940
Chart Time to climb 8 ft
3.0
3.2
3.4
3.6
3.8
4.0
4.2
4.4
1.5 1.7 1.9 2.1 2.3
wheel radius (in)
tim
e, s
4.0
4.2
4.4
4.6
4.8
5.0
Opt
MiniBotMass(lb)
In conclusion
Avoid the “don’t do’s” Don’t fall off the pole Don’t drag stuff up pole Don’t let magnets touch the pole
Keep it light!Keep it simple! (including deployment)Use 2:1 step-up gearing w/ 2 motorsUse close-to-optimum wheel radius