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1 Available online at Engineering 2 00 (2010) (2009) Engineering 8 th Conference of the International Sports Engineering Association (ISEA) Prediction of energy efficient pedal forces in cycling using musculoskeletal simulation models Franz Höchtl 1,* Harald Böhm 2, Veit Senner 1 1 Department of Sport Equipment and Materials, TU Munich, Boltzmannstr. 15, Garching, Germany 2 Behandlungszentrum Aschau GmbH, Bernauer Straße 18, Aschau i. Chiemgau, Germany Received 31 January 2010; revised 7 March 2010; accepted 21 March 2010 Abstract A biomechanical simulation model was developed to analyze energy efficient pedal forces in cycling. With a genetic optimisation algorithm muscle activation has been optimized in order to minimize metabolic energy consumption. Results show that the established mechanical definition of the Index of Efficiency is not appropriate to quantify pedaling technique, because it is not in agreement with metabolic efficiency of the biomechanical system. c Published by by Elsevier Ltd. Ltd. Open access under CC BY-NC-ND license. Keywords: cycling efficiency, hill type muscle model, genetic optimisation algorithm, multi body system, Index of Efficiency 1. Introduction To improve the transfer of human power to cycling performance, technical solutions such as elliptic chain rings, pedal-crank systems with varying lengths or independent crank arms have been developed. Since the effects of these systems are small [6, 8, 11], the present mechanism with fixed crank length and circular chain rings are most commonly used in cycling. In addition to optimise the equipment it is also possible to improve the athlete s pedalling technique. The task for athlete is hereby to maximize the motive efficiency, defined as the ratio between propulsive tangential force and the total force applied to the crank shown in Fig. 1. * Corresponding author. Tel.: ; fax: address: c 2010 Published by Elsevier Ltd. doi: /j.proeng Open access under CC BY-NC-ND license.

2 3212 F. Höchtl et al. / Engineering 2 (2010) Fig. 1: Tangential and radial forces applied on the right pedal, used for the calculation of Index of Efficiency For this purpose Davis and Hull [4] developed the Index of Efficiency (IE) to quantify the quality of pedalling technique. IE = F F 2 tan tan dϕ + F rad 2 dϕ (1) It has been shown that applying optimal oriented forces to the pedal during cycling enhances power output for comparable load magnitudes [4]. However, studies on groups on high performance and recreational cyclists did not show any correlation between power output and Index of Efficiency [3, 7]. Therefore, the purpose of this study was to demonstrate that the above mechanical definition of Index of Efficiency is not in agreement with the metabolic efficiency of the biomechanical system. In particular we want to show that radial forces, even though not being effective for propulsion are important to realize efficient transfer of muscle power to cycling performance. 2. Methods The human body model used in the simulation consists of 7 rigid bodies connected by the hip, knee, and ankle joints with one rotational degree of freedom in the sagittal plane. Segment masses, moments of inertia, and joint and center of mass locations were calculated based on regression equations [9]. The model represents a male subject with body weight and standing height of 78 kg and 183 cm. The mechanical model was driven by 8 Hill-type muscles [2] for each leg (Gluteus maximus, Illiopsoas, Vastus, Soleus and Tibialis Anterior, Hamstrings, Rectus Femoris and Gastrocnemius). The bicycle rider system was implemented in MatLab Simulink/ Simmechanics 3.0. (Mathworks Inc, Natic, US). Muscle activation for each muscle was defined as a function of crank angle by a set of 8 control nodes per 360 interpolated with sinusoidal function [2]. This model results in 64 design parameters for optimisation. A genetic algorithm strategy (MatLab, genetic algorithm and direct search toolbox 2.4) was used to optimize muscle activation functions in order to minimize the metabolic energy consumption of all muscles. The metabolic energy consumption was calculated according to [1]. To generate constant cycling movement a few constraints had to be added. The mean crank frequency should remain with an accepted tolerance of 0.01 rad/min, while the maximum divergence from the crank frequency target should stay within borders of 0.2 rad/s. The optimisation was carried out for a driving speed of 35 km/h, which corresponds to a driving resistance of 280 W, at a cadence of 90 U/min. The optimisation evaluated 20 generations of 750 individuals which took about 6 days CPU time on a dual-core 2200 MHz windows PC.

3 F. Höchtl et al. / Engineering 2 (2010) Fig. 2: Rigid body model with leg muscles and bike rider system. 3. Results Fig. 3 shows the simulated optimal tangential and radial pedal forces. At the top dead center (TDC at 0 crank angle) both tangential and radial force are close to zero. With increasing crank angle tangential force rises to a maximum of 400 N during the downstroke at about 100. After this maximum the curve decreases until it changes direction in the bottom dead center (BDC). In the second half rotation the tangential force is always negative with a minimum of -100 N occurring at about 260. Since the force is negative it is acting against the direction of propulsion. From the radial force curve it is obvious that during the whole rotation radial non propulsive pedal forces are present. The curve characteristic is similar to the tangential force, with a phase shift of about 30 to greater angle values. Fig. 3: Tangential and radial pedal forces for minimized metabolic energy consumption

4 3214 F. Höchtl et al. / Engineering 2 (2010) Fig 4: Pedal force direction and magnitude during crank rotation Fig. 4 visualises the resulting pedal forces during one rotation. Obviously the forces are mostly vertically orientated At TDC and BDC the tangential forces are close to zero at the same time considerable radial forces are dominant. In sector IV pedal forces are even orientated against rotation direction. Using these calculated pedal forces the IE (Fig. 5) shows rather low values being only 35% for the overall crank rotation. Only in sector II considerable high values of 90% are reached, while in sector I 34% and in sector IV only 15% of the total pedal force is propulsive. In sector III 85% of the pedal force retards the crank motion. Fig. 5: Index of Efficiency for sectors of crank rotation

5 F. Höchtl et al. / Engineering 2 (2010) Conclusion Considerable radial pedal forces were obtained when muscle activation was optimized for minimal metabolic energy consumption. Consequently IE results in relatively low values in all sectors - except for sector II. It can be concluded that the traditional definition of efficiency of motion, which is based on the reduction of radial forces in all sectors, might not be appropriate to describe pedalling technique properly. Instead it is concluded that for optimal pedalling technique a certain amount of radial pedal force is needed. Further analysis of muscle mechanics contribution to sectors work distribution will follow to fully understand the biomechanical explanation of our findings. References [1] Bhgarva J.A. et al., A phenomenological model for estimating metabolic energy consumption in muscle contraction. Journal of Biomechanics 37: 81-88, [2] Böhm H. et al., Contribution of muscle series elasticity to maximum performance in drop jumping. Journal of Applied Biomechanics 22: 3 13, [3] Böhm H. et al., Effects of short-term training using SmartCranks on cycle work distribution and power output during cycling. European Journal of Applied Physiology, 103: , [4] Davis R.R., Hull M.L., The effect of rider weight on rider-induced loads during common cycling situations. Journal of Biomechanics 14: , [5] Gressmann H, Fahrradphysik und Biomechanik. Delius Klasing Verlag, Bielefeld, Germany, 50-55, [6] Hue O. et al., Enhancing cycling performance using an eccentric chainring. Medicine and Science in Sports and Exercise 33: , [7] Korff T. et al., Effect of Pedaling Technique on Mechanical Effectiveness and Efficiency in Cyclists. Medicine and Science in Sports and Exercise 39(6): , [8] Lucia A. et al., Effects of the rotor pedalling system on the performance of trained cyclists during incremental and constant-load cycle-ergometer tests. International Journal of Sports Medicine 25(7): , [9] NASA Reference Publication 1024, Volume 1, Chapter IV, [10] Zamparo P, et al., Mechanical efficiency of cycling with a newly developed pedal-crank. Journal of Biomechanics 35: , 2002.

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