Development of Multi-platform Instrumented Force Pedals for Track Cycling (P49) Jean-Marc Drouet1, Yvan Champoux1, Sylvain Dorel2
Topics: Bicycle, Measurement Systems. Abstract: The aim of this research was to develop instrumented force pedals that meet the specific requirements of track cycling. Both pedals are instrumented with eight strain gauges and provide the ability to measure normal and tangential pedalling forces. Rotary encoders are used to determine the angular position of the pedals relative to the crank arm and the angular position of the crank arm relative to the bicycle frame. One original feature is that the instrumented pedals can be fitted with interchangeable pedal platforms: the clipless LOOK CX7 and the Shimano 600 (PD-6400) with a toe-clip and strap for sprint and kilometre time trial events. It is therefore possible to measure pedal loads for all track cycling disciplines. The pedals have a very high mechanical resistance in order to withstand the pedal loads produced by track sprinters which are the highest encountered among all cycling disciplines. Their mechanical design allows the pedals to be installed on any crank arm model without requiring any crank modification. With the data acquisition system attached to a modified Camelbak pack carried by the cyclist, the pedals permit on-track pedal load measurements. Post-processing software was developed to calculate derived parameters, which include the effective power, the effectiveness index and two components of the total force: the effective force component that is the component normal to the crank arm and the force component in line with the crank arm. The derived parameter calculations and analysis can be done on site for each leg and allow specific qualities to be evaluated (peak power, peak force, etc.). Typical results for these parameters are presented in this paper. Keywords: instrumented force pedals, track cycling.
1- Introduction The measurement of pedal loads is essential in acquiring a better understanding of the pedalling process as well as providing load data for bicycle design. In designing the proposed instrumented force pedals for track cycling use, specific requirements must be 1. Mechanical Engineering Department, VélUS Group, Université de Sherbrooke, Sherbrooke, Canada E-mail: Jean-Marc.Drouet,
[email protected] 2. Laboratoire de Biomécanique et Physiologie, INSEP, Paris, France - E-mail:
[email protected]
264 The Engineering of Sport 7 - Vol. 1 addressed. One of these requirements is that the instrumented force pedals have a very high mechanical resistance to withstand the pedal loads produced by track sprinters. These loads are the highest encountered among all cycling disciplines. Even with a high load capacity, the pedals must accurately measure the pedal loads throughout the loading range. In order to be useful for all track cycling disciplines, another requirement is that the instrument force pedals be fitted with two different pedal platforms: clipless pedals and, toe-clip and strap pedals. The latter are used in sprint and kilometre time trial events. Also, considering the many different crank arm lengths used in track cycling, it would more practical and cost effective to have an instrumented force pedal design that allows for normal installation on the crank arm rather than to have a design that requires a dedicated crank arm (Alvarez and Vinyolas 1996, Rowe et al. 1998, Reiser et al. 2003). Because on-track situations such as full-power starts from a dead stop, drafting during a team event and riding on a banked track are difficult or impossible to replicate in a laboratory, on-track measurements are required to obtain realistic pedal load data in these situations. Many different pedal dynamometers have been described in the literature. Some of these dynamometers are restricted to laboratory use (Bolourchi and Hull 1985, Boyd et al. 1996, Davis and Hull 1981, Newmiller et al. 1988, Wheeler et al. 1992) while others permit load measurement outside of the laboratory. In the latter category, Alvarez and Vinyolas (1996) proposed a pedal dynamometer for road use based on a Time clipless pedal platform; Rowe et al. (1998) developed a pedal dynamometer for off-road bicycling; and Reiser et al. (2003) proposed instrumented pedals based on Shimano PD-6500 clipless pedals. These three pedal dynamometers require a dedicated crank arm with integrated bearings. Also, the maximum pedal load capacity reported by Rowe et al. (1998) and Reiser et al. (2003) is not high enough for track cycling use. Since none of these previously described pedal dynamometers satisfy the specific aforementioned requirements for track cycling use, the aim of this research was to develop instrumented force pedals that meet these requirements.
2- Methods The instrumented force pedals can be fitted with two interchangeable pedal platforms: the clipless LOOK CX7 platform (LOOK CYCLE International, Nevers, France) and the Shimano 600 (model PD-6400, Shimano Inc., Osaka, Japan) toe-clip and strap platform (Fig. 1a and 1b). In order to ensure that the instrumented force pedals are functionally equivalent to the original pedals, some parts of the original pedals have been used for the construction of the platform-specific bodies. These platforms are bolted to a pedal base assembly (Fig. 2), which consists of three principal elements: the ball bearing assembly, the instrumented spindle and the rotary encoder. The bearing allows the rotation of the instrumented spindle relative to the crank arm. A thin delrin rod is inserted into the hollow of the instrumented spindle and connects the encoder axle to the bearing assembly, thus allowing the encoder to measure the angular position of the instrumented spindle relative to the crank arm.
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Figure 1 - Photographs of the instrumented force pedal with the LOOK CX7 and the Shimano 600 platforms.
Figure 2 - Photograph of the instrumented force pedal base assembly (exploded view).
The instrumented force pedals measure only the mutually orthogonal force components Fx and Fz (Fig. 3). These forces were measured using a total of eight strain gauges on each pedal (Fig. 2). The strain gauges were arranged in two full Wheatstone bridges, one in the x-y plane (Fx) and the other in the y-z plane (Fz). Theoretically, the position of the strain gauges and their interconnection give bridge signals that are independent of the location of forces Fx and Fz as well as insensitive to the unmeasured loads (Fy, Mx, My and Mz). The instrumented force pedals maximum load is 2500 N. In order to withstand the pedal load, a double row angular contact ball bearing with a dynamic load rating of 10600 N was used. High strength materials were also used for the construction
266 The Engineering of Sport 7 - Vol. 1 of the pedals. Heat-treated 17-4 PH stainless steel (yield strength (Sy) = 1250 MPa) was used for the spindle and the bearing assembly. For the two platforms, 7075-T651 aluminium (Sy = 500 MPa) was used. The mass of one instrumented force pedal is 422 g with the LOOK CX7 platform and 512 g with the Shimano 600 platform (original pedals typical mass: 200 g for LOOK and 282 g for Shimano).
Figure 3 - Pedals local coordinates system with three force components (Fx, Fy, Fz), three moment components (Mx, My, Mz), the pedal angle relative to the crank ( ) and the crank angle relative to the bicycle frame () (right pedal shown).
A supplemental rotary encoder located on the bicycle frame was used (Fig. 4) to measure the angular position of the crank arm relative to the bicycle frame (). Two pulleys (transmission ratio: 1:1) and a synchronous belt were used to link the left crank to the encoder.
Figure 4 - Crank angle () measurement system.
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Measurement data from the instrumented pedals and from the encoder located on the bicycle frame are collected by a data acquisition system (model pro7, ISAAC Instruments inc., Chambly, Canada) attached to a modified Camelbak pack carried by the cyclist (Fig. 5). The pedals as well as the encoder located on the bicycle frame are wired to the data acquisition system. The electrical cables are attached to the cyclist’s legs with elastic bands and Velcro fasteners. The mass of the data acquisition system (including the Camelbak pack) is 1.2 kg. Post-processing software was developed using Matlab to calculate derived parameters, which include the effective power, the effectiveness index and two components of the total force: the effective force component that is the component normal to the crank arm and the force component in line with the crank arm. The derived parameter calculations and analysis can be done on site for each leg and allow specific qualities to be evaluated (peak power, peak force, etc.).
Figure 5 - Track cyclist and bicycle equipped with the instrumented force pedals (Shimano 600 toe-clip and strap platform) and data acquisition system attached to a modified Camelbak pack.
Calibration was performed by applying force and moment loads to measure the direct sensitivity of the in-plane loads (Fx and Fz) and both the calibratable and noncalibratable cross-sensitivities (Rowe et al. 1998). The calibratable sensitivity matrix (V/N, normalized for gain and input voltage ) and the non-calibratable sensitivity matrix (V/N or V/Nm, normalized for gain and input voltage) are given by equations (1) and (2) respectively. Moment My was not considered because it is produced by the pedal bearing friction and can be ignored. (1) (2) Using the extreme loading amplitudes indicated in Table 1, the maximum total root mean square error of the instrumented pedal was found to be 1.6% FS (Full Scale) for Fx and 1.5% FS for Fz. The hysteresis was also determined from the calibration data and it was
268 The Engineering of Sport 7 - Vol. 1 found that hysteresis introduced a maximum error of 0.9% FS. The instrumented pedal repeatability and reproducibility have been assessed by successive calibration. They were found to be less than 1% FS. The natural frequency along the x and z axis was determined using the pedal stiffness and assuming half the weight of a 75 kg cyclist clipped onto the pedal. The natural frequencies for both directions were about 125 Hz. The resolution of the rotary encoders mounted on the instrumented force pedals was 0.4º. A zeroing adjustment for both components of force (Fx and Fz) and pedal angle ( ) was carried out before each measurement session. All the signals were acquired at a sampling rate of 1 kHz (USB data acquisition, ISAAC Instruments inc., Chambly, Canada) and stored on a computer.
Table 1 - Pedal loads for the evaluation of the direct sensitivities and the cross-sensitivities.
3- Results Different experimental sessions in field conditions (i.e. on a track) were carried out, demonstrating the ability of these instrumented force pedals to provide a good quantity of relevant information. The present data describe an example of some measured and calculated derived variables obtained for an elite cyclist (i.e. world class sprinter) during a specific 125 m all-out effort. The athlete was asked to perform maximal effort and encouraged to produce the greatest possible acceleration. A starting block was used for the start and the cyclist naturally adopted a standing position throughout the exercise. Following the test session, raw data stored in the acquisition system were uploaded on a computer for subsequent analysis. The typical time course of the raw data (Fx, Fz, pedal angle of the left pedal and crank angle) measured by the device are presented on Fig. 6. Fz reached very high negative values during each downstroke phase and especially at the beginning of the sprint (>2200 N) while non-negligible positive values (almost 400 N) were observed during the upstroke phases. Oscillations between positive and negative values were also observed for Fx but the magnitude remained much lower (between -500 N and +600 N).
Figure 6 - Measured and calculated derived variables for a world class sprinter during a specific 125 m all-out effort.
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Based on Fx, Fz, the pedal angle and the crank angle (Fig. 6), the total force was calculated by trigonometry and resolved into two components: one orthogonal to the crank (effective force) and another along the crank (ineffective force). A time derivative of the crank angle was used to obtain crank angular velocity and hence the power output (i.e. the product of effective torque and crank angular velocity). Evolution of total and effective forces on the left pedal, crank angular velocity and total power output (i.e. on both pedals) is depicted in Fig. 6. The effective force remained positive throughout the test (except during the last 2-3 seconds): although the effective force produced during the downstroke was very high (peak value > 2200 N), the value during the upstroke was also significant (>500 N), which highlights the importance of all zones of the crank cycle in carrying out the maximal acceleration of the system.
4- Discussion One of the design requirements for the instrumented pedals was that they be able to withstand the very high loads applied by track sprinters. As can be imagined, the severe consequences for the cyclist in the event of mechanical failure of the pedals during high force and high-speed runs are such that this design criterion is an important safety issue. Finite elements analysis (FEA) was used to evaluate stress levels in the pedal. The selected ball bearing was also experimentally tested to verify its mechanical resistance. Functional equivalence of the force pedals with the original LOOK CX7 and Shimano 600 pedals was also a design requirement. With the LOOK CX7 platform, the instrumented force pedals allow for normal engagement and disengagement of the LOOK Delta cleat and for full use of the cleat’s floating angle. For the Shimano 600 platform, the original toe-clips are used. The double straps go underneath the pedals and are held securely in place using tie-wrap fasteners. To avoid contact between the right pedal and the track when riding on the steep banking of a track, another consideration was that the pedals be compact. The use of high strength materials permitted us to reduce the pedals size. FEA was also used to ensure that no mechanical interference occurs between the pedals components under maximum load conditions. A consequence of reducing the pedal size was the reduction of pedal mass, which is of importance considering the high accelerations encountered in track cycling. During the design process, FEA was used for the optimization of the area moment of inertia of the instrumented area of the spindle in order to increase sensitivity. It was also used to determine the corner radius at each end of the instrumented area of the spindle. The stress concentration in the vicinity of these radii was taken into account to determine the location of the strain gauges and to numerically ensure low cross-sensitivities. The accuracy of the in-plane forces was established through calibration by evaluating the direct sensitivity and also by measuring the influence of the other load components. Extreme loadings were considered and it was established that the influence of non-measured loads is small. The direct cross-sensitivity between measured forces Fx and Fz is also small and does not contribute significantly to measurement error. For the measured forces, the linearity is very good and the hysteresis is small. The first natural
270 The Engineering of Sport 7 - Vol. 1 frequency of 125 Hz is high enough to assume a dynamic flat response of the instrumented pedals within the operational measured frequency band of interest of 0-30 Hz. The aerodynamic drag of the data acquisition system located on the back of the cyclist was a concern in high-speed runs (over 60 km h-1). Slower times were observed for 200-m sprints during which the cyclist is in a low crouch and the acquisition system is exposed to airflow. The electrical cables connecting the pedals to the acquisition system were attached to the external side of the cyclist’s legs. It was reported that when routed this way, the cables do not interfere with leg movement even at very high pedalling cadence (over 160 rev min-1). The data presented in this paper constitute a typical sample from among the different possibilities allowed by this new device. The device allows researchers and coaches to analyse the data using practical concerns while providing relevant and useful information that reflects not only the muscular capacity but also the technical abilities of the cyclist. Among the technical aspects that can be measured are the maximal effective force and power output, the index of asymmetry and the index of effectiveness.
5- Conclusion In this paper, instrumented force pedals that meet the specific requirements of track cycling were presented. They are functionally equivalent to the original LOOK CX7 and Shimano 600 pedals and provide accurate measurements of the mutually orthogonal force components Fx and Fz with very low cross-sensitivities. Considering that these instrumented force pedals are a research tool as well as a tool for use in the field, multiple perspectives are offered for the future in terms of scientific approaches to training.
6- References [AV1] Alvarez G. and Vinyolas J. A New Bicycle Pedal Design for On-Road Measurement of Cycling Forces. In Journal of Applied Biomechanics, 12(1):130-142, 1996. [BH1] Bolourchi F. and Hull M.L. Measurement of Rider Induced Loads During Simulated Bicycling. In International Journal of Sport Biomechanics, 1(4):308-329, 1985. [BH2] Boyd T., Hull M.L. and Wooten D. An improved accuracy six-load component pedal dynamometer for cycling. In Journal of Biomechanics, 29(8):1105-1110, 1996. [DH1] Davis R.R. and Hull M.L. Measurement of pedal loading in bicycling: II. Analysis and results. In Journal of Biomechanics, 14(12):857-872, 1981. [HD1] Hull M.L. and Davis R.R. Measurement of pedal loading in bicycling: I. Instrumentation. In Journal of Biomechanics, 14(12):843-856, 1981. [NH1] Newmiller J., Hull M.L. and Zajac F.E. A mechanically decoupled two force component bicyle pedal dynamometer. In Journal of Biomechanics, 21(5):375-386, 1988. [RH1] Rowe T., Hull M.L. and Wang E.L. A Pedal Dynamometer for Off-Road Bicycling. In Journal of Biomechanical Engineering, 120(1):160-164, 1998. [RP1] Reiser II R.F., Peterson M.L. and Broker J.P. Instrumented bicycle pedals for dynamic measurement of propulsive cycling loads. In Sport Engineering, 6(1):41-48, 2003.
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[WG1] Wheeler J.B., Gregor R.J. and Broker J.P. A Dual Piezoelectric Bicycle Pedal With Multiple Shoe/Pedal Interface Compatibility. In International Journal of Sport Biomechanics, 8(3):251258, 1992.
