Biomechanics: optimal bike dimensions

3M-Seminar 2014, Group work, Modelling of a cyclist's leg in Simulink

Advisor: Daniel Häufle

Students: Karoline Binder, Johannes Kübler, Laura Niebling, Thomas Obst

Introduction

In competitive cycling, speed and thus success are proportional to power. On a bicycle, the power is equivalent to

P=M*f (1.1)

the torque on the crankset M and the cadence f, while

M=l_k*F_tang (1.2)

with cranklength l_k and the tangential force F_tang.

The force on the pedal is generated by various muscles and a variable of relationship of resulting levers, angles and speed. In order to maximize the power output and increase performance, these conditions have to be analyzed.

To get started, the system from hip to foot including a crankset will be modelled with one degree of freedom and using one muscle, the quadriceps femoris muscle.

Model and Task

Based on the tutorial on the Simulink model of an arm, the system of one leg including the crankset will be modeled. The following assumptions and simplifications will be made:

• Both hip and crank arm are fixed in the coordinate system.

• Hinge joints connect thigh to hip, thigh (length l_O) and lower leg (l_U) via the knee,foot to crank arm (l_K) and the crank arm in the bottom bracket. Modeling of the ankle will be neglected.

• All bones are considered massless.

• The muscular model will be reduced to one muscle, the quadriceps femoris muscle. Derived from the presented arm model, it will consist of a muscle, a spring and a damper.

Figure 1 : Geometry and model elements

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podcast_bike.mov

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Haeufle, D F B, M Günther, A Bayer, and S Schmitt. 2014. “Hill-Type Muscle Model with Serial Damping and Eccentric Force-Velocity Relation.” Journal of Biomechanics 47 (6) 1531–1536 http://dx.doi.org/10.1016/j.jbiomech.2014.02.009

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