Every Patient Deserves Their Turn: Turning, Padding, and Positioning
One good turn deserves another
description
Transcript of One good turn deserves another
![Page 1: One good turn deserves another](https://reader030.fdocuments.net/reader030/viewer/2022033023/56815b1c550346895dc8cd18/html5/thumbnails/1.jpg)
How to be sure your robot will turn
![Page 2: One good turn deserves another](https://reader030.fdocuments.net/reader030/viewer/2022033023/56815b1c550346895dc8cd18/html5/thumbnails/2.jpg)
My Name: Chris Hibner
Mentor FRC 51 - Wings of Fire
chiefdelphi.com: “Chris Hibner”
![Page 3: One good turn deserves another](https://reader030.fdocuments.net/reader030/viewer/2022033023/56815b1c550346895dc8cd18/html5/thumbnails/3.jpg)
Who has taken the following courses? Physics Algebra Trigonometry Calculus
![Page 4: One good turn deserves another](https://reader030.fdocuments.net/reader030/viewer/2022033023/56815b1c550346895dc8cd18/html5/thumbnails/4.jpg)
F = *N
is the “coefficient of friction” and it depends on the materials in contact.
Mg
N
F
![Page 5: One good turn deserves another](https://reader030.fdocuments.net/reader030/viewer/2022033023/56815b1c550346895dc8cd18/html5/thumbnails/5.jpg)
F (maximum friction force) = (coefficient of friction) * N (normal force)F = *N
On a level surface, N = weight
![Page 6: One good turn deserves another](https://reader030.fdocuments.net/reader030/viewer/2022033023/56815b1c550346895dc8cd18/html5/thumbnails/6.jpg)
Let’s say the mass weighs 150 lb and the coefficient of friction is 0.8. How much force is required to move the object?
F = *N F = 0.8 * 150 lb F = 120 lb
![Page 7: One good turn deserves another](https://reader030.fdocuments.net/reader030/viewer/2022033023/56815b1c550346895dc8cd18/html5/thumbnails/7.jpg)
The above example has one continuous contact area – what if there are multiple contact areas?
Nf = W*(Lcom / L)Nr = W (1 – Lcom / L)
W
Nf NrL
Lcom
![Page 8: One good turn deserves another](https://reader030.fdocuments.net/reader030/viewer/2022033023/56815b1c550346895dc8cd18/html5/thumbnails/8.jpg)
Nf = W*(Lcom / L)Nr = W (1 – Lcom / L)
If Lcom is L/2, then Nf = Nr = W/2
If Lcom is L/3, then Nf = W/3 and Nr = 2W/3
W
Nf NrL
Lcom
![Page 9: One good turn deserves another](https://reader030.fdocuments.net/reader030/viewer/2022033023/56815b1c550346895dc8cd18/html5/thumbnails/9.jpg)
F = T / rF (force at edge of wheel) = T (torque) / r
(radius of wheel)
F
T
![Page 10: One good turn deserves another](https://reader030.fdocuments.net/reader030/viewer/2022033023/56815b1c550346895dc8cd18/html5/thumbnails/10.jpg)
Simple answer: wheel “breaks free” and starts to slip.
The force from the wheel to the ground: which direction does it point?
Answer: in the direction of the force applied by the torque.
![Page 11: One good turn deserves another](https://reader030.fdocuments.net/reader030/viewer/2022033023/56815b1c550346895dc8cd18/html5/thumbnails/11.jpg)
If there is significant deflection of the surface and/or interlock between mating surfaces, the simple friction model breaks down.
Especially if interlock only occurs in one direction.
In this case, the friction model does not work in the direction with interlock. The force in this direction is more of a normal force, and not a friction force.
In the direction without interlock, the simple friction model still works well.
![Page 12: One good turn deserves another](https://reader030.fdocuments.net/reader030/viewer/2022033023/56815b1c550346895dc8cd18/html5/thumbnails/12.jpg)
These slide side-to-side. They “push-off” with normal force fore-aft.
![Page 13: One good turn deserves another](https://reader030.fdocuments.net/reader030/viewer/2022033023/56815b1c550346895dc8cd18/html5/thumbnails/13.jpg)
![Page 14: One good turn deserves another](https://reader030.fdocuments.net/reader030/viewer/2022033023/56815b1c550346895dc8cd18/html5/thumbnails/14.jpg)
Link:
http://www.real-world-physics-problems.com/physics-of-skiing.html
![Page 15: One good turn deserves another](https://reader030.fdocuments.net/reader030/viewer/2022033023/56815b1c550346895dc8cd18/html5/thumbnails/15.jpg)
The physics of skiing is not worth learning for FIRST robots. A model can be created from the simple friction model that is “close enough”. Just use different “friction coefficients” in the
different directions Dynamically changing friction coefficients is
a common way to model complex surface interaction.
The ski physics was brought up to show a point: when interlock occurs, slipping can occur in one direction without affecting the friction in the transverse direction.
![Page 16: One good turn deserves another](https://reader030.fdocuments.net/reader030/viewer/2022033023/56815b1c550346895dc8cd18/html5/thumbnails/16.jpg)
Title: Drive Train Basics (How to be sure your robot will turn)
Link: http://www.chiefdelphi.com/media/papers/1443
![Page 17: One good turn deserves another](https://reader030.fdocuments.net/reader030/viewer/2022033023/56815b1c550346895dc8cd18/html5/thumbnails/17.jpg)
Prior to 2003, there were no rules on materials that interact with the carpet.
Metal to carpet contact was common, and cleated wheels and treads were also common.
Omni-wheels were very common
![Page 18: One good turn deserves another](https://reader030.fdocuments.net/reader030/viewer/2022033023/56815b1c550346895dc8cd18/html5/thumbnails/18.jpg)
Cleated wheels and treads follow skiing physics very closely. This is due to “trenching” of the cleat in between the carpet fibers.The radius in the transverse direction
moves the fibers out of the way in that direction (see picture on previous slide).
Starting in 2003, FIRST outlawed cleated wheels. Wheels with symmetric friction are now the norm.
![Page 19: One good turn deserves another](https://reader030.fdocuments.net/reader030/viewer/2022033023/56815b1c550346895dc8cd18/html5/thumbnails/19.jpg)
The 2003 paper is entirely accurate for symmetric wheels.
If you design your drive train using the 2003 paper – it will still turn. The 2003 paper is overly conservative for symmetric wheels.
If you want to design at the limit of turning, you can be more accurate. However, I wouldn’t recommend designing at the turning limit.
![Page 20: One good turn deserves another](https://reader030.fdocuments.net/reader030/viewer/2022033023/56815b1c550346895dc8cd18/html5/thumbnails/20.jpg)
Assumptions for the simple case:Same torque at all 4 wheelsCOM is left/right centeredSame wheels at all 4 corners, and friction is
same in all directions.
Lwb
Ltw
Lcom
![Page 21: One good turn deserves another](https://reader030.fdocuments.net/reader030/viewer/2022033023/56815b1c550346895dc8cd18/html5/thumbnails/21.jpg)
General case:
(See appendix for derivation)
122
wb
twwb
comx
LL
L
WLF
![Page 22: One good turn deserves another](https://reader030.fdocuments.net/reader030/viewer/2022033023/56815b1c550346895dc8cd18/html5/thumbnails/22.jpg)
Worst case – Lcom is Lwb/2:
2
14
wb
tw
whl
LL
WF
![Page 23: One good turn deserves another](https://reader030.fdocuments.net/reader030/viewer/2022033023/56815b1c550346895dc8cd18/html5/thumbnails/23.jpg)
To be sure your robot will turn:1.Use the 2003 paper or the above friction
equation to determine the force at the wheel needed to make the robot turn.
2.Know the stall torque of your motor. Better yet, use the motor torque at peak power.
3.Twhl = Ffrict * Rwhl (Torque at the wheel = friction force * wheel radius)
4.GearRatio = Tmotor / TwhlDon’t forget to account for losses due to
gearing (10% per stage is a good rule), and add some safety margin.
![Page 24: One good turn deserves another](https://reader030.fdocuments.net/reader030/viewer/2022033023/56815b1c550346895dc8cd18/html5/thumbnails/24.jpg)
Introduce the students to Led Zeppelin. Just kidding.
What causes it?Ever see a stop sign flutter in the wind?
Wind force
Spring torque(from sign post)
![Page 25: One good turn deserves another](https://reader030.fdocuments.net/reader030/viewer/2022033023/56815b1c550346895dc8cd18/html5/thumbnails/25.jpg)
How road sign flutter relates to a robot.
How to stop it: increase torsional stiffness of the frame. Gussets closed box sections (not open channel
sections) Truss shapes
F
F
Spring torqueFrom Frame
Top view of frame:
![Page 26: One good turn deserves another](https://reader030.fdocuments.net/reader030/viewer/2022033023/56815b1c550346895dc8cd18/html5/thumbnails/26.jpg)
There is no substitute for doing a gear calculation.
Wider is better – the higher the Ltw/Lwb ratio is, the easy is will be for your robot to turn.But be careful – you don’t want your robot
to flip over during acceleration.Ways to compromise:1.6 wheel drive with dropped center wheel2.8 wheel drive with dropped center 4
COM at the center of the robot is worst for turning. Moving the COM forward or rearward helps the robot turn.
![Page 27: One good turn deserves another](https://reader030.fdocuments.net/reader030/viewer/2022033023/56815b1c550346895dc8cd18/html5/thumbnails/27.jpg)
If all else fails:Consider using high friction wheels on one
end of the robot, and low friction wheels on the other end.
Consider wheels with asymmetric friction:1.Omni wheels2.Consider machining a radius or slope to the
side of hard wheels:
![Page 28: One good turn deserves another](https://reader030.fdocuments.net/reader030/viewer/2022033023/56815b1c550346895dc8cd18/html5/thumbnails/28.jpg)
2Nf 2NrL
LcomW
(2) 02 0
(1) 022 0
comwbfr
frz
WLLNM
WNNF
![Page 29: One good turn deserves another](https://reader030.fdocuments.net/reader030/viewer/2022033023/56815b1c550346895dc8cd18/html5/thumbnails/29.jpg)
Solve equation 2 for Nf:
Substitute into eq 1 and solve for Nr:
(3) 2 wb
comf L
LWN
(4) 12
22
2
wb
comr
wb
comr
fr
L
LWN
L
LWWN
NW
N
![Page 30: One good turn deserves another](https://reader030.fdocuments.net/reader030/viewer/2022033023/56815b1c550346895dc8cd18/html5/thumbnails/30.jpg)
Lwb
Ltw
Lcom
Fy Fy
FyFy
Fx
Fx
Fx
Fx
(5)
:Ffor Solve
022
:0
y
0
wb
twxy
wbytwx
L
LFF
LFLF
M
![Page 31: One good turn deserves another](https://reader030.fdocuments.net/reader030/viewer/2022033023/56815b1c550346895dc8cd18/html5/thumbnails/31.jpg)
(7)
:is magnitude whose,F and F of sum vector theis F
(6) 2
:above theinto (3) eq from N Substitute
:friction of force maximum theexceed
must wheel theof force the turn,start to To
22_
yxwhl_f
_
f
_
xyfwhl
wb
comfwhl
ffwhl
FFF
L
LWF
NF
![Page 32: One good turn deserves another](https://reader030.fdocuments.net/reader030/viewer/2022033023/56815b1c550346895dc8cd18/html5/thumbnails/32.jpg)
12
21
:Fxfor solve Now
2
:(8) into (5) eq Substitute
(8) 2
:(6) eq into (7) eq Substitute
2
2
2
2
2
22
wb
twwb
comx
wb
com
wb
twx
wb
comx
wb
twx
wb
comxy
LL
L
WLF
L
LW
L
LF
L
LWF
L
LF
L
LWFF
![Page 33: One good turn deserves another](https://reader030.fdocuments.net/reader030/viewer/2022033023/56815b1c550346895dc8cd18/html5/thumbnails/33.jpg)
JVN mechanical design calculator: http://www.chiefdelphi.com/media/papers/2755
apalrd Battery Voltage in Robot Drivetrain Simulation and Modeling: http://www.chiefdelphi.com/media/papers/2750
![Page 34: One good turn deserves another](https://reader030.fdocuments.net/reader030/viewer/2022033023/56815b1c550346895dc8cd18/html5/thumbnails/34.jpg)
![Page 35: One good turn deserves another](https://reader030.fdocuments.net/reader030/viewer/2022033023/56815b1c550346895dc8cd18/html5/thumbnails/35.jpg)
![Page 36: One good turn deserves another](https://reader030.fdocuments.net/reader030/viewer/2022033023/56815b1c550346895dc8cd18/html5/thumbnails/36.jpg)
![Page 37: One good turn deserves another](https://reader030.fdocuments.net/reader030/viewer/2022033023/56815b1c550346895dc8cd18/html5/thumbnails/37.jpg)
![Page 38: One good turn deserves another](https://reader030.fdocuments.net/reader030/viewer/2022033023/56815b1c550346895dc8cd18/html5/thumbnails/38.jpg)
![Page 39: One good turn deserves another](https://reader030.fdocuments.net/reader030/viewer/2022033023/56815b1c550346895dc8cd18/html5/thumbnails/39.jpg)
![Page 40: One good turn deserves another](https://reader030.fdocuments.net/reader030/viewer/2022033023/56815b1c550346895dc8cd18/html5/thumbnails/40.jpg)