DYNAMIC MODEL SELECTION
Me 454 | Team Suicycle | Linus Garrett, Mark Kempton, Max Broehl, Nick Cornilsen, Blair Hasler | January 25, 2010 | 1
INTRODUCTION
Objective– Find a relevant and simple model for bicycle/rider dynamics.
Methods– Search in archival literature
Results– A Multibody Model for the Simulation of Bicycle Suspension Systems
Discussion– Strengths and weaknesses of this selection
Me 454 | Team Suicycle | Linus Garrett, Mark Kempton, Max Broehl, Nick Cornilsen, Blair Hasler | January 25, 2010 | 2
METHODS
DATABASES SEARCHED & SEARCH TERMS USED
Archival literature:
Compendex database
Google Scholar
Keywords for our searches were:
bicycle dynamic model
front suspension model
interactive bicycle simulator
vibration sub-model
The following authors had multiple publications related to bicycle models:
Andy Ruina, Cornell University
M. L. Hull Professor, University of California
Robin S. Sharp, Imperial College London
Me 454 | Team Suicycle | Linus Garrett, Mark Kempton, Max Broehl, Nick Cornilsen, Blair Hasler | January 25, 2010 | 3
METHODS CONT.
Description of Article Selection Process
Selection of articles for review was determined by
Similarity to the physical system we want to model
Quality of the proposed ideas
Quality and simplicity of the mathematical formulas used to
describe the bicycle model
Most articles were rejected because their mathematical model was too
complex. Other articles were rejected because of they didn’t include
front suspension in their bicycle model.
Me 454 | Team Suicycle | Linus Garrett, Mark Kempton, Max Broehl, Nick Cornilsen, Blair Hasler | January 25, 2010 | 4
RESULTS
Based on this selection criteria we chose the model described in “A
Multibody Model for the Simulation of Bicycle Suspension Systems”.
Describes a two-dimensional mathematical model for the motion of a
bicycle-rider system with wheel suspension
Predicts vibrational stress on the rider due to uneven track
Model was evaluated by comparing its predictions with actual
measurements of accelerations on the human/bicycle system
The results show that this dynamic model is adequate for designing and
developing bicycle suspensions
Waechter, M., Riess, F., and Zacharias, N., 2002, “A Multibody
Model for the Simulation of Bicycle Suspension Systems,”
Vehicle System Dynamics, Vol 37 No. 1, pp.3–28.
Me 454 | Team Suicycle | Linus Garrett, Mark Kempton, Max Broehl, Nick Cornilsen, Blair Hasler | January 25, 2010 | 5
RESULTS CONT.
Physical and Mathematical Models
Me 454 | Team Suicycle | Linus Garrett, Mark Kempton, Max Broehl, Nick Cornilsen, Blair Hasler | January 25, 2010 | 6
RESULTS CONT.
General Equations of Motion
Me 454 | Team Suicycle | Linus Garrett, Mark Kempton, Max Broehl, Nick Cornilsen, Blair Hasler | January 25, 2010 | 7
RESULTS CONT.
Me 454 | Team Suicycle | Linus Garrett, Mark Kempton, Max Broehl, Nick Cornilsen, Blair Hasler | January 25, 2010 | 8
DISCUSSION
Strengths
Weaknesses
This model is relatively simple
Closely matches our physical system
Incorporates suspension
Model only accounts for 2D motion
(acceleration in the x and z directions,
travel of the front shock, and velocity in
the x direction)
Despite simplification, the dynamic
equations are sufficiently accurate for
designing and developing bicycle
suspension systems.
May need to modify
equations.
Modifications to
physical model are
required (remove rear
shock)
Me 454 | Team Suicycle | Linus Garrett, Mark Kempton, Max Broehl, Nick Cornilsen, Blair Hasler | January 25, 2010 | 9
APPENDIX
Me 454 | Team Suicycle | Linus Garrett, Mark Kempton, Max Broehl, Nick Cornilsen, Blair Hasler | January 25, 2010 | 10
BRIEF SUMMARY EACH ARTICLE SELECTED
1) A Multibody Model for the Simulation of Bicycle Suspension Systems
This paper describes a two-dimensional mathematical model for the motion
of a bicycle-rider system with wheel suspension. It focuses on the prediction
of vibrational stress on the rider due to uneven track. The model was
evaluated by comparing its predictions with actual measurements of
accelerations on the human/bicycle system. The results show that this
dynamic model is adequate for designing and developing bicycle
suspensions.
Waechter, M., Riess, F., and Zacharias, N., 2002, “A Multibody
Model for the Simulation of Bicycle Suspension Systems,” Vehicle
System Dynamics, Vol 37 No. 1, pp.3–28.
Me 454 | Team Suicycle | Linus Garrett, Mark Kempton, Max Broehl, Nick Cornilsen, Blair Hasler | January 25, 2010 | 11
BRIEF SUMMARY EACH ARTICLE SELECTED
2) Full Bicycle Dynamic Model for Interactive Bike Simulator
The objective of this project was to create a dynamic model of a bicycle to
use in a bike simulation system. The model needed to accurately represent
the dynamics of a bicycle in order for the simulation to respond accurately to
user input. The model was validated by several experiments and successfully
applied to the interactive bicycle simulator. This model used in this article is
closely related to the model used in the article entitled “A Multibody Model for
the Simulation of Bicycle Suspension Systems”.
He, Q., Fan, X., Ma, D., 2005, “Full Bicycle
Dynamic Model for Interactive Bike Simulator,”
ASME, Vol 5, pp.373-380.
Generalized and auxiliary coordinates of
stability submodel
Sketch of vibration submodel
Me 454 | Team Suicycle | Linus Garrett, Mark Kempton, Max Broehl, Nick Cornilsen, Blair Hasler | January 25, 2010 | 12
BRIEF SUMMARY EACH ARTICLE SELECTED
3) Linearized Dynamics Equations For The Balance And Steer Of A Bicycle
This article presents linearized equations of motion for the Whipple bicycle
model consisting of two wheels, a frame and a front assembly. For the
benchmark bicycles used, this article takes into account 3D motion of the
bicycle in order to predict steering controls. the model is more
complicated than necessary for our project. Another reason that this article
is not ideal is because the benchmark bicycles evaluated in the article do not
have front suspension.
Meijaard, J., Papadopoulos, J., Ruina, A., Schwab, A., 2007, “Linearized
Dynamics Equations For The Balance And Steer Of A Bicycle: A
Benchmark And Review,” The Royal Society, pp.1955-1982.
Configuration and dynamic variables
Me 454 | Team Suicycle | Linus Garrett, Mark Kempton, Max Broehl, Nick Cornilsen, Blair Hasler | January 25, 2010 | 13
BRIEF SUMMARY EACH ARTICLE SELECTED
4) A Dynamic System Model for Estimating Surface-Induced Frame Loads
During Off-Road Cycling
To assist in design and analysis of off-road bicycle frames, this paper reports
a dynamic model of the bicycle/rider system which estimates frame loads
for bicycles traveling over rough surfaces. To develop this model, the
frame loads at rider contact points were first measured experimentally.
Following this measurement, a dynamic system model was developed with
the aid of the commercial software package.
Wilczynski, H., Hull, M., 1994, “A Dynamic System Model for
Estimating Surface-Induced Frame Loads During Off-Road
Cycling,” ASME, Vol. 116, pp.816-822.
Me 454 | Team Suicycle | Linus Garrett, Mark Kempton, Max Broehl, Nick Cornilsen, Blair Hasler | January 25, 2010 | 14
BRIEF SUMMARY EACH ARTICLE SELECTED
5) A Model for Determining Rider Induced Energy Losses in Bicycle
Suspension Systems
This article calculates rider induced energy losses in bicycle suspension
systems. The purpose of this study was to develop and verify a dynamic
model of a seated cyclist riding an off-road bicycle up a smooth road. With
the absence of terrain irregularities, all suspension motion was rider
induced. Knowing the stiffness and dissipative characteristics of the
suspension elements, the power dissipated by the suspensions was
calculated.
Wang, L., Hull, M., 1994, ?Model for Determining
Rider Induced Energy Losses in Bicycle Suspension
System,? ASME, Vol. 54, pp.301-318.
Me 454 | Team Suicycle | Linus Garrett, Mark Kempton, Max Broehl, Nick Cornilsen, Blair Hasler | January 25, 2010 | 15
BRIEF SUMMARY EACH ARTICLE SELECTED
6) A Robotic Model (ROBI) of Autonomous Bicycle System
The goal of this project was to create a MATLAB program that would
simulate a bicycle system. The advantages of this system are that it has the
capabilities to work for multiple bicycles, be more accurate than other models
and have a user friendly GUI.
Sharma, H., Umashankar, N., 2006, “Robitic Model (ROBI) of
Autonomous Bicycle System,” Computer Society, pp.1-6.
Me 454 | Team Suicycle | Linus Garrett, Mark Kempton, Max Broehl, Nick Cornilsen, Blair Hasler | January 25, 2010 | 16
BRIEF SUMMARY EACH ARTICLE SELECTED
7) Navigation and Control of the Motion of a Riderless Bicycle
The goal of this project was to design navigation and control systems for a
robot that would utilize a bicycle for mobility. The main concern in this article
is how to control the steering system.
Yavin, Y., 1997, “Navigation and Control of the Motion of a riderless Bicycle by
Using a Simplified Dynamic Model,” Pergamon, Vol 25 No. 11, pp.67-74.
Me 454 | Team Suicycle | Linus Garrett, Mark Kempton, Max Broehl, Nick Cornilsen, Blair Hasler | January 25, 2010 | 17