DYNAMIC MODEL SELECTION

1Me 454 | Team Suicycle | Linus Garrett, Mark Kempton, Max Broehl, Nick Cornilsen, Blair Hasler | January 25, 2010 |

DYNAMIC MODEL SELECTION


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


METHODS

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

DATABASES SEARCHED & SEARCH TERMS USED


METHODS CONT.

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.

Description of Article Selection Process


RESULTSBased 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 suspensionPredicts vibrational stress on the rider due to uneven trackModel was evaluated by comparing its predictions with actual measurements of accelerations on the human/bicycle systemThe 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.


RESULTS CONT.

Physical and Mathematical Models


RESULTS CONT.General Equations of Motion


RESULTS CONT.


DISCUSSION

Strengths Weaknesses

This model is relatively simpleClosely matches our physical system Incorporates suspensionModel 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)


APPENDIX


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.


BRIEF SUMMARY EACH ARTICLE SELECTED2) 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”.

Sketch of vibration submodelGeneralized and auxiliary coordinates of stability submodel

He, Q., Fan, X., Ma, D., 2005, “Full Bicycle Dynamic Model for Interactive Bike Simulator,” ASME, Vol 5, pp.373-380.


BRIEF SUMMARY EACH ARTICLE SELECTED3) 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.

Configuration and dynamic variables

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.


BRIEF SUMMARY EACH ARTICLE SELECTED4) 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.


BRIEF SUMMARY EACH ARTICLE SELECTED5) 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.



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.



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.

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DYNAMIC MODEL SELECTION

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