DYNAMIC MODEL OF A BICYCLE

Introduction

Looking for a dynamic model of a bicycle and rider system:

- Simple- Clear- Compliant with Simulink

The Search

Search Terms: “dynamic bicycle model” “simple linear bicycle model” “basic bicycle model” “Simulink”

Filtering

Models that included a rider (many

didn’t)

Background and derivation for the

Equations of Motion

Relatively simple Equations of Motion

Obtainable inputs

Required Outputs

Position

Velocity

Acceleration

Model We Chose

“Implementation of the Interactive Bicycle Simulator with Its Functional Subsystems”

-Application of article is a bicycle simulator

-Simulator relies on dynamic model-Shows equations of motion for 3-D

bicycle and rider model (we’ll simplify to 2-D)

“Points of Interest”Center of Mass:C1: Rear wheel C2: Upper portion of the riderC3: Bicycle frame & lower portion of the riderC4: Handlebar assemblyC5: Front wheel

Rotational Joints:O1: Rear wheelO2: Rider’s torso (about the seat)O3: Stem/headset (for steering)O4: Front wheel

Model

Center of Mass:C1: Rear wheel C2: Upper portion of the riderC3: Bicycle frame & lower portion of the riderC4: Handlebar assemblyC5: Front wheel

Rotational Joints:O1: Rear wheelO2: Rider’s torso (about the seat)O3: Stem/headset (for steering)O4: Front wheel

Equations

Position Vectors

1 1

2 1 1 2 2 2

3 1 1 3

4 1 1 3 3 4

5 1 1 3 3 5

r rz

r r OO O C

r r OC

r r OO O C

r r OO O C

Equations

Angular Velocity Linear Velocity.

1

.

2

.

3

.

4

.

5 4 4

rw

rw

rw

rw

fw

y

z

z

z

y

1 1 1 1

2 1 3 1 2

2 2 2 2 2

3 1 3 1 3

3 1 3 1 2

4 3 4 3 4

5 3 4 3 4

O

O

O

O

O

O

v v r

v v XOO

v v XO O

v v XOC

v v XOO

v v XO C

v v XO O

Equations

Complete Force Balance

* Can use the time derivative of velocity to find acceleration

Pros & Cons

Pros: Simplified geometry Clearly defined equations of motion

Cons: Doesn’t account for front shock Assumes tires are rigid bodies

Questions?

Reference

Yin, Song, and Yuehong Yin. "Implementation of the Interactive Bicycle Simulator with Its Functional Subsystems." Journal of Computing and Information Science in Engineering. 7. (2007): 160-166.