chrisdembia / bicycleparameters

Bicycle Parameters Module

A python program designed to produce and manipulate the basic parameters needed for the Whipple bicycle model.

Description

This is code associated with the work done to measure the physical parameters of a bicycle and the rider of a bicycle. Physical parameters include but are not limited to the geometry, mass, mass location and mass distribution of the bicycle rider system. More detail can be found in our papers and the [website](http://biosport.ucdavis.edu/research-projects/bicycle/bicycle-parameter-measurement/).

Features

• Loads bicycle parameter sets from text files
• Generates the benchmark parameters for a real bicycle from experimental data
• Plots a descriptive drawing of the bicycle
• Calculates the eigenvalues for the Whipple bicycle model linearized about the upright configuration.
• Plots the eigenvalue root loci as a function of speed, both in the complex plane and as eigenvalue vs speed.

Upcoming Features

• Converts benchmark parameters to other parametrizations
• Calculates the transfer functions of the open loop system.
• Plots Bode diagrams of the open loop transfer functions.
• Ability to add a rigid rider's physical properties.
• Generates publication quality tables of parameters using LaTeX

Dependencies

These are the versions that I tested the code with, but the code will most likely work with older versions with minor adjustments.

• [Python 2.6.6](http://www.python.org/)
• [Scipy 0.9.0](http://www.scipy.org/)
• [Numpy 1.5.1](http://numpy.scipy.org/)
• [Matplotlib 0.99.3](http://matplotlib.sourceforge.net/)
• [Uncertainties 1.7.2](http://packages.python.org/uncertainties/)

Installation

For now simply clone the source code with git or download the tarball from github. Make sure you have the dependencies installed.

Set up your subdirectories like this:

/data
|
-->/bicycles
   |
   -->/Bicyclea
   |  |
   |  -->/Parameters
   |  |
   |  -->/Photos
   |  |
   |  -->/RawData
   |
   -->/Bicycleb
      |
      -->/Parameters
      |
      -->/Photos
      |
      -->/RawData

Root Directory

The root folder should contain BicycleParameters.py and the other top level files found in the source code.

Bicycles Directory

This directory contains directories for the parameter sets, raw data, and experiment photos. There should be a folder with a short name for each bicycle that you have parameter sets and/or raw data for. The short name should be a word with the first letter capitalized. Examples of Shortname include "Bianchipista", "Bike", "Mybike", "Rigidrider", "Schwintandem", "Gyrobike", etc.

Parameters directory

If you don't have any raw measurements for the bicycle, simply add a file titled ShortnameBenchmark.txt with the benchmark parameter set into the Parameters directory for the particular bicycle. Each line should have one of the 26 benchmark parameters in the following format: c = 0.080+/-0.001, where the first characters are a unique variable name, following with next an equal sign, the value of the parameter, a plus or minus symbol (+/-), and the standard deviation of the value. There can be spaces between the parts. Use 0.0 for the standard deviation if this is unknown or you don't need to know the uncertainties in other values. Use the same units as the benchmark bicycle paper for less headaches. These are the possible variables:

Required Parameters

• g : acceleration due to gravity
• c : trail
• w : wheelbase
• lam : steer axis tilt
• rR : rear wheel radius
• rF : front wheel radius
• mB : frame/rider mass
• mF : front wheel mass
• mH : handlebar/fork assembly mass
• mR : rear wheel mass
• xB : x distance to the frame/rider center of mass
• yB : y distance to the frame/rider center of mass
• xH : x distance to the frame/rider center of mass
• yH : y distance to the frame/rider center of mass
• IBxx : x moment of inertia of the frame/rider
• IByy : y moment of inertia of the frame/rider
• IBzz : z moment of inertia of the frame/rider
• IBxz : xz product of inertia of the frame/rider
• IFxx : x moment of inertia of the front wheel
• IFyy : y moment of inertia of the front wheel
• IHxx : x moment of inertia of the handlebar/fork
• IHyy : y moment of inertia of the handlebar/fork
• IHzz : z moment of inertia of the handlebar/fork
• IHxz : xz product of inertia of the handlebar/fork
• IRxx : x moment of inertia of the rear wheel
• IRyy : y moment of inertia of the rear wheel

RawData directory

If you have raw data it can come in two forms: either a file containing all the manual measurements (including the oscillation periods for each rigid body) or a file containing all the manual measurments and a set of data files containing oscillatory signals from which the periods can be estimated. The manual measurement data file should follow the naming convention ShortnameMeasure.txt and should have one variable on each line in the following format mR = 1.38+/-0.02, 1.37+/-0.02 which is the same as the previous parameter variable definition accept that multiple measurements can be included as comma separated values.

Required Parameters

• aB1 : perpendicular distance from the pendulum axis to the rear axle center, first orienation [m]
• aB2 : perpendicular distance from the pendulum axis to the rear axle center, second orienation [m]
• aB3 : perpendicular distance from the pendulum axis to the rear axle center, third orienation [m]
• aH1 : perpendicular distance from the pendulum axis to the front axle center, first orienation [m]
• aH2 : perpendicular distance from the pendulum axis to the front axle center, second orienation [m]
• aH3 : perpendicular distance from the pendulum axis to the front axle center, third orienation [m]
• alphaB1 : angle of the head tube with respect to horizontal, first orientation [deg]
• alphaB2 : angle of the head tube with respect to horizontal, second orientation [deg]
• alphaB3 : angle of the head tube with respect to horizontal, third orientation [deg]
• alphaH1 : angle of the steer tube with respect to horizontal, first orientation [deg]
• alphaH2 : angle of the steer tube with respect to horizontal, second orientation [deg]
• alphaH3 : angle of the steer tube with respect to horizontal, third orientation [deg]
• dF : distance the front wheel travels [m]
• dP : diameter of the calibration rod [m]
• dR : distance the rear wheel travels [m]
• f : fork offset [m]
• g : acceleration due to gravity [m/s**2]
• gamma : head tube angle [deg]
• lF : front wheel compound pendulum length [m]
• lP : calibration rod length [m]
• lR : rear wheel compound pendulum length [m]
• mB : frame mass [kg]
• mF : front wheel mass [kg]
• mH : fork/handlebar mass [kg]
• mP : calibration rod mass [kg]
• mR : rear wheel mass [kg]
• nF : number of rotations of the front wheel
• nR : number of rotations of the rear wheel
• TcB1 : frame compound pendulum oscillation period [s]
• TcF1 : front wheel compound pendulum oscillation period [s]
• TcH1 : fork/handlebar compound pendulum oscillation period [s]
• TcR1 : rear wheel compound pendulum oscillation period [s]
• TtB1 : frame torsional pendulum oscillation period, first orientation [s]
• TtB2 : frame torsional pendulum oscillation period, second orientation [s]
• TtB3 : frame torsional pendulum oscillation period, third orientation [s]
• TtF1 : front wheel torsional pendulum oscillation period, first orientation [s]
• TtH1 : handlebar/fork torsional pendulum oscillation period, first orientation [s]
• TtH2 : handlebar/fork torsional pendulum oscillation period, second orientation [s]
• TtH3 : handlebar/fork torsional pendulum oscillation period, third orientation [s]
• TtP1 : calibration torsional pendulum oscillation period [s]
• TtR1 : rear wheel torsional pendulum oscillation period [s]
• w : wheelbase [m]

Geometry Option

The default option is to provide the wheelbase, fork offset, head tube angle and the wheel radii, but there is a secondary option for the geometric variables using the perpendicular distances from the steer axis to the wheel centers and the distance between their respective intersection points. To use these, simply replace w, gamma, and f with:

• h1 : distance from the base of the height gage to the top of the the rear wheel axis [m]
• h2 : distance from the table surface to the base of the height gage [m]
• h3 : distance from the table surface to the top of the head tube [m]
• h4 : height of the top of the front wheel axle [m]
• h5 : height of the top of the steer tube [m]
• d1 : outer diameter of the head tube [m]
• d2 : diameter of the dummy rear axle [m]
• d3 : diameter of of the dummy front axle [m]
• d4 : outer diameter of the steer tube [m]
• d : inside distance between the rear and the front axles with the fork reversed [m]

The details of these measurements can be found in our [raw data sheet](http://bit.ly/jIeKKB) and on our [website](http://biosport.ucdavis.edu/research-projects/bicycle/bicycle-parameter-measurement/frame-dimensions).

Fork/Handlebar Separation

The measurement of the fork and the handlebar as two rigid bodies is also supported. See the example bicycle called Rigid for more details.

Notes

• The periods (T) are not required if you provide oscillation signal data files.
• You have to specify at least three orientations, and currently you can specify up to 6 orientation for each rigid body.

Pendulum Data Files

If you have raw signal data that the periods can be estimated from, then these should be included in the RawData directory. There should be at least one file for every period in the ShortnameMeasured.txt file. Currently the only supported file is a Matlab mat file with these variables:

• data : signal of a decaying oscillation
• sampleRate : sample rate of data in hertz

The files should be named in this manner [Shortname][Part][Pendulum][Orientation][Trial].mat where:

• Shortname is the shortname of the bicycle
• Part is either Fork, Frame, Rwheel, or Fwheel
• Orientation is either First, Second, Third, Fourth, Fifth, or Sixth
• Trial is an integer greater than or equal to 1

### Photos directory The Photos folder should contain photos of the bicycle parts hung as the various pendulums in the various orientations. The filename should follow the conventions of the raw signal data files.

Example Code

`python from bicycleparameters import bicycleparameters as bp rigid = bp.Bicycle('Rigid') rigid.parameters['Benchmark'] rigid.plot_bicycle_geometry() speeds = bp.np.linspace(0., 10., num=100) rigid.plot_eigenvalues_vs_speed(speeds)`

ToDo

• Add the root loci plots.
• Add Bode plots.
• Merge the table generation code.
• Make a bike comparison function.
• Separate the general dynamics functions to another module
• Start using some other covention other than camel case for the file names.

References

The methods associated with this software were built on these previous works, among others.

1. Kooijman, J. D. G., Schwab, A. L., and Meijaard, J. P. (2008). Experimental validation of a model of an uncontrolled bicycle. Multibody System Dynamics, 19:115–132.
2. Kooijman, J. D. G. (2006). Experimental validation of a model for the motion of an uncontrolled bicycle. MSc thesis, Delft University of Technology.
3. Roland J R ., R. D., and Massing , D. E. A digital computer simulation of bicycle dynamics. Calspan Report YA-3063-K-1, Cornell Aeronautical Laboratory, Inc., Buffalo, NY, 14221, Jun 1971. Prepared for Schwinn Bicycle Company, Chicago, IL 60639.
4. Moore, J. K., Hubbard, M., Peterson, D. L., Schwab, A. L., and Kooijman, J.

   D. G. (2010). An accurate method of measuring and comparing a bicycle's physical parameters. In Bicycle and Motorcycle Dynamics: Symposium on the Dynamics and Control of Single Track Vehicles, Delft, Netherlands.

5. Moore, J. K., Kooijman, J. D. G., Hubbard, M., and Schwab, A. L. (2009). A Method for Estimating Physical Properties of a Combined Bicycle and Rider. In Proceedings of the ASME 2009 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, IDETC/CIE 2009, San Diego, CA, USA. ASME.