gear-motors time to speed & location
DESCRIPTION
Special Topics In Robotics. Gear-Motors Time to Speed & Location. David Giandomenico October 23, 2013 2013. Distance vs time & gear reduction. Distance ✚. Time ✚. Gear Reduction ✚. Force vs Speed. Force vs Speed. Effect of Gear Reduction. Force. Newton’s 2 nd Law. - PowerPoint PPT PresentationTRANSCRIPT
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Gear-MotorsTime to Speed & Location
David Giandomenico October 23, 2013
2013
Special Topics In Robotics
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Distance vs time & gear reduction
Gear Reduction ✚
Time
✚
Dis
tanc
e ✚
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Force vs Speed
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Force vs Speed
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Effect of Gear Reduction
Force
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Newton’s 2nd Law
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Need 2nd relation
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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
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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
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Speed/Force diff.eq.with Gear Reduction
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Speed/Force diff.eq.with Gear Reduction
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K for our Robot
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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’
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Optimize V – pick best ‘g’
Quotient Rule for derivatives:
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Optimize V – pick best ‘g’
Quotient Rule for derivatives:
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Optimize V – pick best ‘g’
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Optimize V – pick best ‘g’
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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...
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Optimum g for Velocity
Ko = 20 seconds
Gea
r Rat
io
Target Time (sec)
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K for our Robot w/GearRedux
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Optimize for Distance
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Optimize for Distance
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Optimize for Distance
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Optimum GearRedux for Distance
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Optimum Ratio for Distance
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Optimum Ratio for Distance
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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 ✚