Transport Thursday 24 January 2013 Arend Schwab
-
Upload
tu-delft-transport-institute -
Category
Real Estate
-
view
160 -
download
4
Transcript of Transport Thursday 24 January 2013 Arend Schwab
![Page 1: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/1.jpg)
1
![Page 2: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/2.jpg)
Challenge the future
Delft University of Technology
The Art and Science of Bicycling
Arend L. Schwab Laboratory for Engineering Mechanics (3mE/PME) Delft University of Technology, The Netherlands
![Page 3: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/3.jpg)
3
Acknowledgement
TUDelft: Jaap Meijaard
Jodi Kooijman Nick Appelman
Cornell University: Andy Ruina Jim Papadopoulos
Andrew Dressel
J. P. Meijaard, Jim M. Papadopoulos, Andy Ruina, A. L. Schwab (2007) Linearized dynamics equations for the balance and steer of a bicycle: a benchmark and review. Proc. R. Soc. A. 463, 1955-1982.
J. D. G. Kooijman, J. P. Meijaard, Jim M. Papadopoulos, Andy Ruina, and A. L. Schwab (2011) A bicycle
can be self-stable without gyroscopic or caster effects, Science 15 April: 332(6027), 339-342.
www.bicycle.tudelft.nl
UCDavis: Mont Hubbard Jason Moore Luke Peterson
![Page 4: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/4.jpg)
4
1. Bicycle Dynamics, some observations
![Page 5: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/5.jpg)
5
Jour de Fête van Jacques Tati, 1949
Movie
![Page 6: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/6.jpg)
6
Yellow Bike in the Car Park, Cornell University, Ithaca, NY.
Experiment
![Page 7: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/7.jpg)
7
Experiment
Yellow Bike in the Car Park, Cornell University, Ithaca, NY.
![Page 8: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/8.jpg)
8
Bicycle Evolution
![Page 9: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/9.jpg)
Challenge the future
Delft University of Technology
Francis Whipple 1876-1943
1899
The Whipple/Carvallo Model (1899)
![Page 10: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/10.jpg)
10
The Whipple/Carvallo Model (1899) Modelling Assumptions:
• rigid bodies
• fixed rigid rider
• hands-free
• symmetric about vertical plane
• knife-edge wheels
• point contact, no side slip
• flat level road
• no friction or propulsion
3 velocity degrees of freedom
Note: Energy Conservative
![Page 11: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/11.jpg)
12
Linearized Eqn’s of Motion For the straight ahead upright motion with lean angle ϕ, steering angle δ and forward speed v :
21 0 2[ ] [ ] [ ]
0
v v
v
ϕ ϕ ϕδ δ δ
+ + + =
=
M C K K 0
Characteristic equation : 2 21 0 2det( [ ] [ ] [ ]) 0v vλ λ+ + + =M C K K
leads to a fourth order characteristic polynomial in eigenvalues λ: 4 3 2
3 2 1 0( ) ( ) ( ) ( ) 0a v a v a v a vλ λ λ λ+ + + + =
1 0 2
130 3 0 40 1003 27 0 96, , ,
3 0.3 0.6 1.8 27 8.8 0 2.7− − − −
= = = = − − M C K K
Standard bicycle + rider :
Assume motions: λ λϕ ϕ δ δ= =0 0,t te e
![Page 12: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/12.jpg)
13
The Whipple/Carvallo Model (1899)
3 velocity degrees of freedom:
- lean rate
- steer rate
- forward speed v
ϕδ
selfstable: 4.6 < v < 7.9 m/s
λ λϕ ϕ δ δ= =0 0,t te e
2 21 0 2det( [ ] [ ] [ ]) 0v vλ λ+ + + =M C K K
![Page 13: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/13.jpg)
18
2. Experimental validation
![Page 14: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/14.jpg)
19
Experimental Validation Instrumented Bicycle, uncontrolled
2 rate gyros:
-lean rate
-yaw rate
1 speedometer:
-forward speed
1 potentiometer
-steering angle
Laptop Computer running LabVIEW
ϕψ
v
δ
![Page 15: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/15.jpg)
20
An Experiment
![Page 16: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/16.jpg)
21
An Experiment
![Page 17: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/17.jpg)
22
Measured Data
Fit function for the lean rate: 11 2 2 3 2e [ cos( ) sin( )]tc c t c tλϕ λ λ= + +
![Page 18: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/18.jpg)
23
Compare with Linearized Results
λ2 = 5.52 [rad/s]
λ1 = -1.22 [rad/s]
forward speed:
4.9 < v <5.4 [m/s]
![Page 19: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/19.jpg)
24
Compare in a broad speed range
Conclusion: Experimental data in good agreement with linearized analysis on 3 dof model.
![Page 20: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/20.jpg)
25
3. Bicycle Selfstability
![Page 21: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/21.jpg)
26
Selfstable: automagic control?
We balance an inverted pendulum by accelerating the support in the
direction of the fall.
How do we balance a bicycle?
![Page 22: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/22.jpg)
27
Selfstable: automagic control?
Balance the bicycle by steer into the fall!
( lateral acceleration contact point: a ≈ v2/w δ )
v
a
δ
We balance an inverted pendulum by accelerating the support in the
direction of the fall.
![Page 23: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/23.jpg)
28
Anecdote
LEGO Mindstorms NXT Bicycle, built by Joep Mutsaerts, MSc TUDelft
![Page 24: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/24.jpg)
29
Automagic control? Steer-into-the-fall !
Control Law: SteerMotorVoltage=8*LeanRate
LEGO Mindstorms NXT Bicycle, built by Joep Mutsaerts, MSc TUDelft
![Page 25: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/25.jpg)
30
A selfstable bicycle
Yellow Bike in the Car Park (slow motion), Cornell University, Ithaca, NY.
![Page 26: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/26.jpg)
31
A bicycle is selfstable because ….
5 km/h 25 km/h Gyroscopic effect of the front wheel?
(Klein & Sommerfeld 1910) Trail on the front wheel?
(David Jones 1970)
![Page 27: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/27.jpg)
32
4. Control and Handling
![Page 28: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/28.jpg)
33
How do we control the mostly unstable bicycle?
by steer and balance
![Page 29: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/29.jpg)
36
How do we steer and balance? • A. van Lunteren and H. G. Stassen. On
the variance of the bicycle rider’s
behavior. In Proceedings of the 6th Annual Conference on Manual Control, April 1970.
• David Herbert Weir. Motorcycle Handling Dynamics and Rider Control and the Effect of Design Configuration on Response and Performance. PhD thesis,
University of California, LA, 1972.
![Page 30: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/30.jpg)
37
80% elderly 75% single vehicle
Relevance
Number of seriously injured
Year
60% of the accidents are among the elderly, they just fall over !
![Page 31: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/31.jpg)
38
A Ride into Town Measure rider control on an instrumented bicycle
3 rate gyros: Lean, Yaw and Steer
1 steer angle potentiometer
2 forward speed
1 pedal cadence pickup
1 video camera
Compac Rio data collection
![Page 32: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/32.jpg)
39
A ride into Town
![Page 33: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/33.jpg)
40
A Ride into Town
![Page 34: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/34.jpg)
41
Treadmill experiments
Vrije Universiteit Amsterdam , 3 x 5 m treadmill, vmax=35 km/h
![Page 35: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/35.jpg)
42
Treadmill experiments
A first ride…
![Page 36: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/36.jpg)
43
Rider Control Observations Treadmill Experiments Camera Bicycle – Normal Cycling, Pedaling
![Page 37: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/37.jpg)
44
Rider Control Observations Treadmill Experiments Camera Bicycle – Towing
![Page 38: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/38.jpg)
45
Rider Control
• 31 markers xyz-coor. • Sample freq 100 Hz • Sample time 1 min One run is 600,000
numbers. Data reduction by
Principal Component Analysis (PCA).
Full Human Motion Capture, Optotrack active marker system
![Page 39: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/39.jpg)
46
Rider Control Full Human Motion Capture, Optotrack active marker system
3 x 5 m treadmill at the Vrije Universiteit Amsterdam
![Page 40: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/40.jpg)
47
Rider Control Treadmill Experiments Full Human Motion Capture - Normal Cycling, Pedaling
![Page 41: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/41.jpg)
48
Rider Control Treadmill Experiments, Full Human Motion Capture – PCA Motion Groups
![Page 42: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/42.jpg)
49
Rider Control Treadmill Experiments, Full Human Motion Capture - Compare
5 km/h 25 km/h
![Page 43: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/43.jpg)
50
Rider Control: Conclusions
• During normal bicycling the dominant upper body motions: lean, bend, twist and bounce, are all linked to the pedaling motion.
• We hypothesize that lateral control is mainly done by steering since we observed only upper body motion in the pedaling frequency.
• If upper body motions are used for control then this control is in the
pedaling frequency. • When pedaling at low speed we observe lateral knee motions which are
probably also used for control.
![Page 44: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/44.jpg)
51
5. Selfstability, revisited
![Page 45: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/45.jpg)
52
A bicycle is selfstable because ….
5 km/h 25 km/h Gyroscopic effect of the front wheel? Trail on the front wheel?
![Page 46: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/46.jpg)
53
Gyroscopic Effect? Klein & Sommerfeld 1910
Felix Klein (1849-1925)
from the Klein bottle
Arnold Sommerfeld (1868-1951)
81 Nobel prize nominations
Fritz Noether (1884-1941)
brother of Emmy
![Page 47: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/47.jpg)
56
Gyroscopic Effect? Klein & Sommerfeld 1910
Two sign errors:
Two sign errors corrected.
![Page 48: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/48.jpg)
57
Trail? Jones 1970
![Page 49: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/49.jpg)
58
Trail? Jones 1970
Jones calculated handlebar torque via the derivative of system gravitational (potential) energy H with respect to steer angle at fixed lean. But careful analysis on the full dynamical system (linearized equations of motion) shows:
![Page 50: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/50.jpg)
61
Two-mass-skate (TMS) bicycle Only 8 bicycle parameters
Two point masses and wheels are replaced by skates
Only 8 non-zero bicycle parameters
![Page 51: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/51.jpg)
63
Two-mass-skate (TMS) bicycle Stable when….
Stable when front mass mH is within shaded area, where
Eigenvalue plot
Stable without Gyroscopic or Trail effect!
![Page 52: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/52.jpg)
65
Two-mass-skate (TMS) bicycle Experimental Bicycle
Wheelbase 0.75 m, point masses 2 kg, 99.5 % gyro free, trail -4 mm
![Page 53: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/53.jpg)
68
Two-mass-skate (TMS) bicycle Basic Experiment
J. D. G. Kooijman, J. P. Meijaard, Jim M. Papadopoulos, Andy Ruina, and A. L. Schwab (2011) A bicycle can be self-stable without gyroscopic or caster effects, Science 15 April: 332(6027), 339-342.
![Page 54: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/54.jpg)
71
End of story? Rolling backwards, unstable.
![Page 55: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/55.jpg)
72
Counterexample Stable with rear wheel steering
A bicycle with ‘rear wheel steering’ which shows a stable forward speed range. The steer axis is just in front of the rear wheel and is vertical. The heavy front assembly has a center of mass in front of the front wheel. This rear wheel steered design has a stable forward speed range to the right of the rightmost vertical line, from 3 m/s to infinity.
JBike6
![Page 56: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/56.jpg)
73
Counterexample Stable with rear wheel steering
![Page 57: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/57.jpg)
74
Counterexample Stable with rear wheel steering
![Page 58: Transport Thursday 24 January 2013 Arend Schwab](https://reader034.fdocuments.in/reader034/viewer/2022052623/559af3111a28abbd708b46bc/html5/thumbnails/58.jpg)
75
Conclusions • Bicycles can be selfstable, not necessarily due to gyros or trail. • To balance a bicycle it has to steer into the fall. • Bicycles are mainly controlled by steering, little by upper body motions. • We still know very little about how we humans control the bicycle.
• Identify the human controller in bicycling.
• Define and determine handling qualities of a bicycle.
Future Work
Thank you for your attention
www.bicycle.tudelft.nl