James W. Kamman, Ph.D.
Associate Professor Emeritus
Mechanical & Aerospace Engineering
Western Michigan University
Home Up Control Demonstrator Motion Control Sled Inverted Pendulum Hand Cycle Hydraulic Bike Model

Parker Hannifin Motion and Control Laboratory
Senior Design Project

Hybrid Mechanical/Hydraulic Simulation of a Bicycle1

A numerical model to simulate the two-dimensional, rigid-body dynamic motion of a bicycle with a mechanical-hydraulic drive system was developed in this project. The bicycle is driven by a set of pedal forces which diminish with increasing crank speed. Velocity drivers (modeling gearing constraints) are used to connect the shaft of the crank to a hydraulic pump-and-motor drive system and the shaft of the hydraulic motor to the rear wheel. Velocity drivers are also used to model rolling constraints associated with the rotational and translational motion of the front and rear wheels. The model includes the effects of mass, inertia, gravity, wind resistance, rolling resistance, mechanical and hydraulic efficiencies, and hydraulic flow losses. For more details, see the report referenced below.

The model was developed using the MATLAB/Simulink/SimMechanics/SimHydraulics family of computational software.


1 Peter M. Bombara, Levi J. Scheenstra, and Bradley E. Thomas, Simulation of a Hydraulic Powertrain, Mechanical and Aeronautical Engineering Report No. ME 1004-01, Western Michigan University, April 2010.

Pedal Force Actuation System

Pedal Forces (lb)

Pedal Forces on Crank End 1 (lb)

Pedal Forces on Crank End 2 (lb)

Hydraulic Drive System

SimMechanics/SimHydraulics Interface

SimHydraulics Subsystem

Bicycle Velocity (ft/s) in Different Gears (level ground, no wind)
Effects of Hills on Bicycle Velocity (ft/s) (no wind)

Bicycle Velocity (ft/s)

(Uphill = blue;  Level = black;  Downhill = red)

Pedal Forces Downhill (lb)

Pedal Forces Uphill (lb)

Effects of Wind on Bicycle Velocity (ft/s)

(Tailwind = red;  No Wind = blue;  Headwind = green)

Complete Model Diagram (Simulink/SimMechanics/SimHydraulics)