Description

Dynamic model of a bicycle that includes both a nonlinear and linear tire model. The model includes lateral forces, self-aligning moments, relaxation length, and an input capable of applying either a force or displacement to the contact point under the rear wheel to simulate a lateral kick plate.

The model is based on the nonlinear Carvallo-Whipple model presented in [Moore2012]. The lateral nonholonomic constraints at the wheel-ground contact locations are removed and replaced with a lateral force and self-aligning moment at the contact patch. A tire carcass radius creates a toroidal tire and vertical tire compression is added.

We first presented preliminary results of this model at the ICSC 2023 conference [DellOrto2023].

[Moore2012]

Moore, J. K. (2012). Human Control of a Bicycle [Doctor of Philosophy, University of California]. http://moorepants.github.io/dissertation

[DellOrto2023]

Dell’Orto, G., Alizadehsaravi, L., Happee, R., & Moore, J. K. (2023, November 16). Kick-plate test for assessing bicycle dynamics and tyre effect [Poster]. International Cycling Safety Conference, The Hague, The Netherlands.

Usage

Create the Conda environment and activate it:

conda env create -f bicycle-kickplate-model-env.yml
conda activate bicycle-kickplate-model

After that you can run the sample simulation, e.g.:

python base_simulation.py

or recreate the plot from our ICSC 2023 poster presentation:

python icsc2023_abstract_figure.py

After model.py is run once, it generates a Python module generated_functions.py which caches the equations of motion. If you edit symbols.py or model.py you'll need to delete the generated_functions.py and rerun the model construction. Delete the generated_functions.py anytime you want to rebuild the model.

The various files in the repository are described below:

• symbols.py: contains all symbol symbol definitions
• model.py: formulates the symbolic equations of motion and generates numeric functions to evaluate them
• inputs.py: contains different function for specified inputs (kick plate displacement, steer torque, etc.)
• parameters.py: holds dictionaries mapping numerical values to all model constants
• simulate.py: simulation functions
• plot.py: plotting functions
• viz.py: sets up a pythreejs animation using PyDy
• visualize.ipynb: displays a 3D animation of the base_simualtion.py
• mplviz.py: a symmeplot animation of the motion
• simple_kick_plate_simulation.py: 1D simulation of a kick plate mass hitting the stoppers used to understand the possible acceleration profiles
• tire_data.py: Pajecka Magic formula constants for the nonlinear tire model measured from Gabriele Dell'Orto's work
• utils.py: helper functions

License

The source code and documentation in this repository are licensed under the 3-clause BSD open source software license.