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
Lynbrook Robotics Team, FIRST 846
Need 2nd relation
Lynbrook Robotics Team, FIRST 846
Need 2nd relation
m
Lynbrook Robotics Team, FIRST 846
Do the math...
m
Lynbrook Robotics Team, FIRST 846
Solve the Differential Equation
Lynbrook Robotics Team, FIRST 846
2nd Solution
Choose A = -1 so that α(0)=0
A
Lynbrook Robotics Team, FIRST 846
-1
Lynbrook Robotics Team, FIRST 846
f(x) = e-x Slope of f(x) = -f(x)
Lynbrook Robotics Team, FIRST 846
e-t/k Effect of Time constant, K
K = 1/2
K = 1
Lynbrook Robotics Team, FIRST 846
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
Lynbrook Robotics Team, FIRST 846
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)
Lynbrook Robotics Team, FIRST 846
Velocity as function of GearRedux
Lynbrook Robotics Team, FIRST 846
Effect on Velocity(t,g)
Lynbrook Robotics Team, FIRST 846
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
Lynbrook Robotics Team, FIRST 846
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 ✚