Looking for a dynamic model of a bicycle and
rider system:
- Simple
- Clear
- Compliant with Simulink

Search Terms:
“dynamic bicycle model”
 “simple linear bicycle model”
 “basic bicycle model”
 “Simulink”



Models that included a rider (many didn’t)
Background and derivation for the Equations
of Motion

Relatively simple Equations of Motion

Obtainable inputs

Position

Velocity

Acceleration
“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)
Center of Mass:
C1: Rear wheel
C2: Upper portion of the rider
C3: Bicycle frame & lower portion of the rider
C4: Handlebar assembly
C5: Front wheel
Rotational Joints:
O1: Rear wheel
O2: Rider’s torso (about the seat)
O3: Stem/headset (for steering)
O4: Front wheel
Center of Mass:
C1: Rear wheel
C2: Upper portion of the rider
C3: Bicycle frame & lower portion of the rider
C4: Handlebar assembly
C5: Front wheel
Rotational Joints:
O1: Rear wheel
O2: Rider’s torso (about the seat)
O3: Stem/headset (for steering)
O4: Front wheel
Position Vectors
r1  rz1
r2  r1  O1O2  O2C2
r3  r1  O1C3
r4  r1  O1O3  O3C4
r5  r1  O1O3  O3C5
Angular Velocity
Linear Velocity
vO1  v1  1r1
.
1   rw y
vO 2  v1  3 XO1O2
.
2   rw z
v2  vO 2  2 XO2O2
v3  v1  3 XO1C3
.
3   rw z
vO 3  v1  3 XO1O2
.
4   rw z
v4  vO 3  4 XO3C4
.
5  4   fw y4
v5  vO 3  4 XO3O4
Complete Force Balance
* Can use the time derivative of velocity to find acceleration
Pros:
 Simplified geometry
 Clearly defined equations of motion
Cons:
 Doesn’t account for front shock
 Assumes tires are rigid bodies
Questions?
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.