# Looking for a dynamic model of a bicycle and rider system: - Simple - Clear - Compliant with Simulink.

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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: C 1 : Rear wheel C 2 : Upper portion of the rider C 3 : Bicycle frame & lower portion of the rider C 4 : Handlebar assembly C 5 : Front wheel Rotational Joints: O 1 : Rear wheel O 2 : Rider’s torso (about the seat) O 3 : Stem/headset (for steering) O 4 : Front wheel

Center of Mass: C 1 : Rear wheel C 2 : Upper portion of the rider C 3 : Bicycle frame & lower portion of the rider C 4 : Handlebar assembly C 5 : Front wheel Rotational Joints: O 1 : Rear wheel O 2 : Rider’s torso (about the seat) O 3 : Stem/headset (for steering) O 4 : Front wheel

Position Vectors

Angular VelocityLinear Velocity

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.

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