My current work is focused on investigating the general circular motions of the benchmark bicycle model.  The parameters for this model are described by Meijaard et al., and what I am doing is generating steady turning level curves of yaw rate (or one of the wheel rates) and steer torque in the lean - steer plane.  In a steady turn, lean and steer are fixed (hence their rates are zero, rear frame pitch is determined from the holonomic constraint, and rear frame pitch rate is zero), but the wheel(s) are spinning and the bicycle is yawing.  In certain special cases, one of the wheels may spin about its axle while the other doesn't spin about its axle but instead spins only about the contact point.  For this reason, I am convinced that using the yaw rate as a parameter of the circular motions is better than using either of the wheel rates, because in any configuration besides upright zero steer, there will be a yaw rate.  The upright zero steer configuration has been well studied by Meijaard et al. for a set of benchmark parameters, my goal is to study motions away from this configuration, but using the same parameters.

In the interest of better serving the research community that is interested in bicycle dynamics, I set out to do create the following software tools and make them (and their source code) publicly available:

• Holonomic constraint solver.  Lean, frame pitch, and steer are not independent coordinates if both wheels are required to touch the ground.  This tool will allow you to numerically specify two out of the three, then calculate the third.
• Nonholonomic constraint solver. 
• Equations of motion.  Be able to numerically specify two independent coordinates (lean and steer, lean and pitch, or pitch and steer) and three independent generalized speeds (really only the time derivatives of generalized coordinates, the simplest case) that you are considering to be independent, and solve for the time derivatives of these three independent generalized speeds.  Also will allow for a flag that allows you to specify if you want the time derivatives of the dependent generaliized speeds.
• Eigenvalues of equations of motion when linearized about an arbitrary configuration.  Five independent quantities need to be specified:  two independent coordinates and three rates.
• Animations of nonlinear simulation results that show the four rigid bodies of the bicycle:  Rear wheel, front wheel, rear bicycle frame with rigidly attached rider, and front fork/handlebar assembly.  Include ground reaction forces.
• Parameter converter between the parameters used by Meijaard et al., and those I use (I don't use wheelbase, head angle complement, and trail; instead I use those that Franke et al. used).
• Generalized coordinates converter between Basu-Mandal and Meijaard and my coordinates.

Each small subtask will be programmed as a C/C++ function.  SWIG interface files to Python will be created in order to allow Python scripts to utilize compiled code to quickly perform numerical studies.  These functions will be part of a C/C++ library that I will make available here.  My goal is to have many of these tasks complete by the end of February 2009.