Optimization Based Bicycle Design For Equivalent Dynamics


The Strida folding bicycle is an example of an unusual bicycle design in which it is desirable for it to handle as well as a more typical bicycle.

Description

When creating new bicycle styles, designers use little more than anecdotes and intuition to guide them in design decisions that affect how the vehicle handles during maneuvering [Kooijman2013]. For example, if a designer has a very small wheeled folding bicycle in mind, is it possible for that vehicle to handle and feel the same or similar to a more typical bicycle design? If the wheels are small, what is the best location for the center of mass? What should the angle of the steer tube be? What should the wheelbase be? The designer chooses these, builds prototypes, tests the handling, and adjusts hopefully coming to a favorable handling feeling.

The vehicle's uncontrolled dynamics affect both the perceived and objective handling. We have one way fairly clear way to characterize a given bicycle's dynamics: the eigenvalues of a linear model of the vehicle. For example, if the Whipple-Carvallo model [Meijaard2007] is used to model the bicycle, there are four complex numbers at any given travel speed that fully characterize the uncontrolled dynamics. Existing good-handling bicycles have a set of characteristic eigenvalues and a related characteristic equation [Moore2010].

One possible design approach would be to specify some aspects of a bicycle's physical characteristics and then search for candidate physical characteristics that ensure this new bicycle design has dynamics as similar as possible to a bicycle that is subjectively judged to have good handling. This is what a designer does in an ad-hoc way, but these characteristics could be chosen in an optimal fashion. [Paudel2020] shows a manual method of this design process that does utilize the vehicle's dynamics.

The goal of this project is to develop a constrained optimization problem which ensures that an atypical bicycle design with some fully constrained characteristics has uncontrolled dynamics as close as possible to a typical bicycle. The optimization problem presented in [Moore2020] has similarities to this problem and can be used for initial ideas. The success of the methodology should be demonstrated with different atypical bicycles: bakfiets, folding bicycles, recumbent bicycles, etc. and potentially constructing one of the designs and testing it.

Required Skills

  • 3D multibody dynamics
  • Constrained non-linear optimization techniques
  • Proficiency in a scientific programming language
  • Metal fabrication
  • Experimental methods and dynamic measurements

References

[Meijaard2007]J. P. Meijaard, J. M. Papadopoulos, A. Ruina, and A. L. Schwab, “Linearized dynamics equations for the balance and steer of a bicycle: A benchmark and review,” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 463, no. 2084, pp. 1955–1982, Aug. 2007.
[Moore2010]J. K. Moore, M. Hubbard, D. L. Peterson, A. L. Schwab, and J. D. G. Kooijman, “An Accurate Method of Measuring and Comparing a Bicycle’s Physical Parameters,” Delft, Netherlands, Oct. 2010.
[Kooijman2013]J. D. G. Kooijman and A. L. Schwab, “A review on bicycle and motorcycle rider control with a perspective on handling qualities,” Vehicle System Dynamics, vol. 0, no. 0, pp. 1–43, doi: 10.1080/00423114.2013.824990.
[Moore2020]J. K. Moore and M. Hubbard, “Expanded Optimization for Discovering Optimal Lateral Handling Bicycles,” Padua, Italy, 2019, p. 12, doi: 10.6084/m9.figshare.9942938.v1.
[Paudel2020]M. Paudel and F. F. Yap, “Development of an improved design methodology and front steering design guideline for small-wheel bicycles for better stability and performance,” Proceedings of the Institution of Mechanical Engineers, Part P: Journal of Sports Engineering and Technology, vol. 234, no. 3, pp. 227–244, Sep. 2020, doi: 10.1177/1754337120919608.

How to Apply

Send an email to j.k.moore@tudelft.nl with the title of the project in the subject line. Include an approximately half-page motivation letter explaining why you want to work in the Bicycle Lab on this project along with your current resume or C.V.