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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
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
Pros & Cons
Pros: Simplified geometry Clearly defined equations of motion
Cons: Doesn’t account for front shock Assumes tires are rigid bodies