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