Modelling and Stability Analysis of a Recumbent Bicycle with Oscillating Leg Masses (P131)
It has been observed in the testing of a recumbent bicycle with a very low centre of gravity that the pedalling cadence can affect the rider’s ability to control the vehicle. To understand the relationship between cadence and bicycle stability, a multibody dynamic model is created. This model has nine massive rigid bodies: the bicycle frame with fixed rider torso (with head & and arms), the front fork with handlebars, the front wheel, the rear wheel, the left thigh, the right thigh, the left shank with foot, the right shank with foot, and the cranks. Nonlinear equations of motion are compiled in Autolev, a symbolic calculator using Kane’s method for multibody dynamics (Autolev, 2005). A simulation of the bicycle slowly accelerating from its starting speed (5 m/s) to its target speed (35 m/s) is run iteratively over several gear ratios. A steering controller is implemented to stabilize the bike outside its stable stable speed range. The simulation displays the lean and steer angles as well as steering control torque. Lean angle and control torque increase significantly with cadence, and steer angle increases slightly with cadence. This relationship is used to create a shifting strategy to reduce the control effort needed by the pilot during top top-speed speed-record attempts.
Keywordsrecumbent bicycle modelling stability cadence
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- [A1]Autolev 4.1. Online Dynamics, Inc. 2005.Google Scholar
- [BH1]Bryson, A. E. and Ho, Y. C. Applied Optimal Control. Blaisdell, Waltham, MA, 1969.Google Scholar
- [C1]Carvallo, E. Theorie du movement du monocycle et de la bicyclette. In Journal de L’Ecole Polytechnique, Series 2, Part 1, Volume 5, “Cerceau et Monocycle”, pp. 119–188, 1900. Part 2, Volume 6, “Theorie de la Bicyclette”, pp.1–118, 1901.Google Scholar
- [C2]Cook, B. World human powered speed challenge 2003. Barcroft Cycles Video, Falls Church, VA, 2003.Google Scholar
- [K1]Kane, T. Fundamental kinematical relationships for single-track vehicles. In International Journal of Mechanical Science, Pergamon Press, UK, Volume 17, 1975.Google Scholar
- [M1]Matlab, version 6.5.1. Control Toolbox, lqr.m. The Mathworks, Inc., 2003.Google Scholar
- [MP1]Meijaard, J.P., Papadopoulos, J.M., Ruina A., and Schwab, A.L. Linearized dynamics equations for the balance and steer of a bicycle: A benchmark and review. Proceedings of the Royal Society A463, pp. 1955–1982, 2007.Google Scholar
- [S1]Solidworks 2005. Solidworks Corporation, 2004.Google Scholar
- [W1]Whipple, F.J.W. The stability of the motion of a bicycle. The Quarterly Journal of Pure and Applied Mathematics, Vol.. 30, pp. 312–348, 1899.Google Scholar