gear-motors time to speed & location

Lynbrook Robotics Team, FIRST 846

Gear-MotorsTime to Speed & Location

David Giandomenico October 23, 2013

2013

Special Topics In Robotics

Lynbrook Robotics Team, FIRST 846

Distance vs time & gear reduction

Gear Reduction ✚

Time

✚

Dis

tanc

e ✚

Lynbrook Robotics Team, FIRST 846

Force vs Speed

Lynbrook Robotics Team, FIRST 846

Force vs Speed

Lynbrook Robotics Team, FIRST 846

Effect of Gear Reduction

Force

Lynbrook Robotics Team, FIRST 846

Newton’s 2nd Law

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Need 2nd relation

Lynbrook Robotics Team, FIRST 846

Need 2nd relation

m

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Do the math...

m

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Solve the Differential Equation

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2nd Solution

Choose A = -1 so that α(0)=0

A

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-1

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f(x) = e-x Slope of f(x) = -f(x)

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e-t/k Effect of Time constant, K

K = 1/2

K = 1

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K for our Robot

Lynbrook Robotics Team, FIRST 846

K for our Robot

A pound-force is the amount of force required to accelerate a slug at a rate of 1 ft/s2

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Add Gear RductionImprove Force at Wheel

Lynbrook Robotics Team, FIRST 846

Speed/Force diff.eq.with Gear Reduction

Lynbrook Robotics Team, FIRST 846

Speed/Force diff.eq.with Gear Reduction

Lynbrook Robotics Team, FIRST 846

K for our Robot

Lynbrook Robotics Team, FIRST 846

Effect on Alpha(t,g)

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Velocity as function of GearRedux

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Effect on Velocity(t,g)

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Optimize V – pick best ‘g’

Lynbrook Robotics Team, FIRST 846

Optimize V – pick best ‘g’

Quotient Rule for derivatives:

Lynbrook Robotics Team, FIRST 846

Optimize V – pick best ‘g’

Quotient Rule for derivatives:

Lynbrook Robotics Team, FIRST 846

Optimize V – pick best ‘g’

Lynbrook Robotics Team, FIRST 846

Optimize V – pick best ‘g’

Lynbrook Robotics Team, FIRST 846

0.63980 @ s=1.2564

Graphical check: Plot best V

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Optimum V

Optimum choice of g envelopes all other curvesThis validates the math...

Lynbrook Robotics Team, FIRST 846

Optimum g for Velocity

Ko = 20 seconds

Gea

r Rat

io

Target Time (sec)

Lynbrook Robotics Team, FIRST 846

K for our Robot w/GearRedux

Lynbrook Robotics Team, FIRST 846

Optimize for Distance

Lynbrook Robotics Team, FIRST 846

Optimize for Distance

Lynbrook Robotics Team, FIRST 846

Optimize for Distance

Lynbrook Robotics Team, FIRST 846

Optimum GearRedux for Distance

Lynbrook Robotics Team, FIRST 846

Optimum Ratio for Distance

Lynbrook Robotics Team, FIRST 846

Optimum Ratio for Distance

Lynbrook Robotics Team, FIRST 846

Distance vs Time and Gear Redux.

g=4g=8

g=10

Lynbrook Robotics Team, FIRST 846

Distance vs time & gear reduction

Gear Reduction ✚

Time

✚

Dis

tanc

e ✚