An improved accuracy six-load component pedal dynamometer for cycling

Pergamon

0021-9290(95)00177-S

TECHNICAL

AN IMPROVED

ACCURACY SIX-LOAD COMPONENT DYNAMOMETER FOR CYCLING Tom

Department

NOTE

of Mechanical

Boyd.

M.

Engineering.

L. Hull*

and

University

PEDAL

D. Wootten

of Califorma,

Davis,

CA 95616,

USA

Abstract--This paper describes a new six-load component pedal dynamometer designed for study of knee ovcrusc injury in cycling. A unique capability of the dynamometer is the ability to interface with multiple pedal platforms oi varying height while maintaining a desired elevation of the foot above the pedal spindle axis. The dynamometel was designed using a concept described in an earlier article by Quinn and Mote (1991. Erp. Mrch. 30,40 -48) which measures shear strain across multiple, thin cross-sections. An optimal design technique was used for choosing dimensions of the load measuring cross-sections. A dynamometer was designed and built using the optimal results. Calibration, accuracy results, and sample data are presented. A comparison of accuracy reveals that the new dynamometer is more accurate than previously reported instruments. Copyright c, 1996 Elsevier Science Ltd. Keywords:

Six-load

component;

Dynamometer;

Pedal; Cycling.

the previous dynamometers satisfied this requirement, the objettive of the work reported in this article was the design of a dynamometer which could be adjusted in height to fit different pedal interfaces.

INTRODUCTlON

Knee overuse injury is the most common reported injury in cycling (Dickson, 1985; Holmes et a[., 1991). Knee overuse injuries can be divided into two categories, overtraining and pathomechanical injuries (Pruitt, 1988). Overtraining results from riding in too high a gear. or riding too many miles early in the season. Pathomechanical injuries, which are the focus of this study, result from misalignment between the rider and the bicycle. While cycling with clipless pedals, the rider’s foot is constrained to a circular path in the sagittal plane with little or no motion of the sole of the foot in either the frontal or transverse planes. If the leg and foot do not travel naturally along the path of the pedal. then constraint loads are developed to maintain this path. These constraint loads produce joint loads that do not contribute to propelling the bicycle (Francis, 1988; Ruby and Hull, 1993). These joint loads are disadvantageous, since they can increase the load carried by soft tissue. It has been hypothesized that relieving some of the constraint loads developed at the foot by clipless pedals will decrease the loads transmitted through the knee during cycling for a given workload (Ruby and Hull, 1993). To accurately calculate both the varus/valgus and axial moments, which are potentially important to the study of injury at the knee, a six-load component dynamometer is needed to measure loads developed at the foot/pedal interface (Ruby er ill., 1992). Although other six-load component pedal dynamometers have been designed (Broker and Gregor, 1990; Davis and Hull. 1981; Ruby and Hull, 1993). they were not appropriate for the knee injury study to be undertaken. The dynamometer must accommodate different foot/pedal interfaces (Ruby and Hull, 1993; Wootten and Hull, 1992) which vary substantially in height. Since elevation of the foot above the pedal spindle has been shown to affect cycling biomechanics (Hull and Gonzalez. 1990). the foot must be maintained at a constant elevation if a type of constraint is to be isolated for study. Because none of

Receiwd in ,ha/,form 21 Nowrnher * Corresponding author.

DESIGN

DESCRIPTIOU

The dynamometer was designed around a concept previously described by Quinn and Mote (1991). In their article. ihey outline a procedure for designing a dynamometer which measures shear strain across thin plates called shear panel eicments (SPEs) (Fig. 1). Each SPE is designed to support force in the Y’ direction only. and to be compliant in the X’ and Z’ directions. Compliance in the X’ direction is accomplished by means of a flange on one end of the YPE. A combination of these SPEs can be used to support all six load components. The paper by Quinn and Mote presents a design table based on iinite element analysis which can be used to calculate maximum shear load that an SPE can withstand without either yieldmg 01 buckling based on its aspect ratio and thickness. Dimensions for the SPEs were calculated by interpolatine the design tables provided by Quinn and Mote and using them ;n an optimization program to obtain maximum sensitivity. Derived from previous cycling data (Stone. 1990). the maximum design loads in the pedal coordinate system of Fig. 2 were F, = 52.5 N. and F,. = 175 N, F, = 1925 N, &I, = 7 N m. ,Zf, = 7 N m n/l: = 5 Nm. To optimize the design of each SPE, the design variables of the SPE were entered into a FORTRAN program based on a non-hnear optimization routine from the 1MSL library. A grid search was used with all design variables of the SPE to provide multiple entry points into the optimization routine to eliminate any problems with local minima and maxima. The variables considered were the length. width, and thickness of the SPE and supporting flange. The constraints imposed on each SPE optimization were of two types. The first type of constraints was geometric, includmg minimum thickness and maximum length and width of each SPE. The second type of constraints concerned failure modes and decoupling. The design was constrained to withstand the maximum loading conditions mentioned above both rn shear

1995.

1105

Technical

~Bose

(Dynamometer

Note

Body)

.tom bracket

1

Y’ Flange I

Fig. 1. Shear panel element

(SPE).

strength and in buckling with a factor of safety of 1.2. Additionally, the flanges were constrained to have a compliance in the X and Z’ directions which was greater than 100 times that of the compliance of the panel in the Y’ direction. This ensures that the X’- and Z’-direction loads supported by the flanges will be negligible compared to the corresponding Y’ direction load supported by other panels. The dynamometer was designed so that any load incurred at the foot/pedal interface is supported solely by seven SPEs. One end of each SPE is attached to a main body supported by the crank hanger (described below). At the other end. the SPE flange is attached to the pedal cage to which foot/pedal interface constraint loads are applied. The seven SPEs are positioned such that four SPEs support and measure loads in the Z direction, two SPEs support and measure loads in the X direction, and one SPE supports loads in the Y direction (Fig. 3).

x Fig. 2. Pedal dynamometer local coordinate formed by X and Z is parallel to the bicycle rotate about Y.

MAIN

.ACRANK

HANGER

system. The plane frame. X and Z can

BODY

ATTACHMENT

Fig. 3. Dynamometer interior construction. Six SPEs are shown. The seventh is hidden from view. oriented similarly to the one shown on the bottom, and translated back in the - Y direction.

It is

Technical

Fig. 4. Photograph

of dynamometer

Note

showing

encoder

and crank

hanger.

-

SPE 1

-o-

SPE 2

-t-

SPE 3

--ct

SPE 4

--t-

SPE 5

-

SPE 6

-t-

SPE 7

-0.006 (NJ

Fig. 5. Sample

Moments are supported by combinations of these seven SPEs. In this manner, all six load components are supported. and the strain from the SPEs can be measured and individual loads can be resolved using a calibration matrix described below. To measure the shear strain across each SPE, two 90” strain gauge rosettes mounted along the axis of principal strain were attached to each face of the SPE panel in a full Wheatstone bridge configuration. The bridge configuration rendered it insensitive

calibration

plot (F-).

to bending and axial strain. All seven bridges were powered in parallel. Each bridge was balanced externally at zero load. To meet the variable height requirement of the dynamometer, the dynamometer body was designed to interface with multiple crank hangers (Fig. 4). Different hangers can be produced to match any height needed for various pedal platforms. Completing the dynamometer is an encoder system used to measure the angle of the dynamometer relative to the crank arm

II08

Technical

(Fig. 2). The encoder is an eight bit absolute encoder, giving a resolution of 256 discrete angles in a 360” rotation. The encoder is mounted on the side of the crank hanger (Fig. 4) and has a geared belt drive connected to matched gears on the encoder shaft and crank arm.

CALIBRATION

Following construction, the dynamometer was calibrated using a previously designed apparatus (Hull and Davis, 1981). This apparatus uses a system of cables, pulleys, and weights to apply each of the six load components according to the coordinate system in Fig. 2 at a chosen coordinate center origin. Because each of the six load components was applied individually, both direct sensitivity and cross-sensitivity were evaluated. Thus, the calibration procedure generated a matrix, C(7 x 6) that was used to relate each set of 7 voltage outputs acquired during a data run, V (1 x 7), to the corresponding load components, L (1 x 6). A best-fit linear relationship of the form VC = L was the goal of the procedure. To calculate C, a series of known loads was applied to the dynamometer one load component at a time. Starting at zero, a particular load component’s magnitude was increased incrementally to a positive maximum and then decreased to a negative minimum and finally brought back to zero. There were approximately 37 steps in each of the six load components for a total of 224 load steps. At each load component step. voltages were recorded with a personal computer. After this was done for each load component, two full matrices of loads and voltages existed: V (224 x 7) and L (224 x 6). C was then deduced using a matrix regression calculation (Strang, 1988). A sample plot of the individual load component calibrations (Fig. 5) illustrates that all cross-sensitivities are linear and can be decoupled using the C matrix. Hysteresis was less than 0.5 N for all force components and less than 0.1 Nm for all moment components. An accuracy check was performed in which known or actual loads were applied to the dynamometer. These were then compared to the instrument predicted or apparent loads. In each case, combined loads were applied in order to observe the instrument’s accuracy under conditions better approximating those it would see in use. Maximum absolute errors. and RMSE error for the entire accuracy check were determined (Table 1). The largest force error of 6.40 N was seen in the F, direction under application of five simultaneous loads. The largest moment error of 0.44 N m was seen during a separate application of five simultaneous loads. The RMSE error for force data is bounded by 3.21 N. while the RMSE error for moments is bounded by 0.21 N m. The natural frequency was determined along the z-axis to characterize the dynamic performance capabilities of the instrument. With the foot/pedal interface of Wootten and Hull (1992), the natural frequency was 280 Hz.

SAMPLE

DATA

Sample data were collected with the dynamometer for one subject. The 80 kg male with over 10 years of riding experience rode a Trek 1200 on a Schwinn Velodyne at a workrate of 250 W and 90 rpm. After a warm up period of 5 min at a workrate of 180 W and two minutes at 250 W, data were collected for 10 s. The subject was wearing shoes designed to interface with clipless pedals. The two degree of freedom pedal interface described by Wootten and Hull (1992) was mounted to the dynamometer with both rotations fixed. The crank angle is measured clockwise from top dead center when facing the crank. Loads are measured at the bottom center of the cleat directly above the pedal spindle axis. Data averaged over 12 cycles indicate that extreme values of all load components occurred during the downstroke (O’-18Oq [Fig. 6(a) and (b)]. For the force components [Fig. 6(a)]. the

Note extremes of F, and EZ were in phase (90 100‘). whereas the extreme for F, occurred earlier at 60“. For the moment components [Fig. 6(b)], the patterns of the absolute values of hl, and M, were similar in magnitude and phase. For the load point selected (i.e. bottom of the cleat), M, was the largest of the three moments. The pattern of M, was similar to that of F,. except that they were opposite in sign. This relationship has been explained previously (Hull and Davis. 1981 I. The extreme values and corresponding phasing for all load components were comparable to those reported for previous six-load component dynamometers (Table 2).

DISCUSSIOI\I

The six-load component pedal dynamometer was designed to study knee overuse injury in cycling. The objective was to design a dynamometer that could be used in conjunction with variable height pedal interfaces and maintain the elevation of the foot at a specified height above the pedal spindle axis. Other main criteria were that it be capable of measuring static loads and produce an accurate estimate of the pedal constraint loads. Although other dynamometer designs have been described (Broker and Gregor, 1990; Davis and Hull, 1981; Ruby and Hull, 1993) none met all of the above criteria. Accordingly. the design of a new dynamometer was undertaken. To maintain foot elevation despite different heights of foot/pedal interfaces. the dynamometer was designed to mount to the crank with varying size crank hangers. By constructmg a different crank hanger for each pedal interface of different height, the dynamometer can accommodate foot/pedal platforms over a broad range of height. For example, it can accommodate the adjustable pedal platform discussed by Wootten and Hull (1992) as pictured in Fig. 4. Although it would have been possible to build one crank hanger long enough to accommodate the tallest pedal platform and use shims to raise the height of shorter platforms, building separate crank hangers made it possible to raise the dynamometer as high as possible for each pedal platform for maximum ground clearance. Maximum clearance between the dynamometer and the ground makes it useable for data collection on rollers, treadmill and open road cycling where turning can bring the dynamometer closer to the ground. Additionally, using separate hangers for each platform minimizes the weight of the dynamometer-pedal platform system. Another criterion was the ability to measure static load. Piezoelectric dynamometers, such as that by Broker and Gregor (1990), have capacitance built into their signal conditioning electronics which causes the output signal to decay with time. The time constant of this decay is long enough that the decay effect is negligible on data taken during short intervals. However, as can be seen in the sample data [Fig. 6(a) and (b)], not all load components have a zero average, so extended warm-up periods will cause the dynamometer to drift. The capacitor must then be reset at zero load, between warm-up and data collection. This interrupts the protocol of cycling studies. The strain gauge nature of the design ensures static load measurement capability which simplifies the experimental protocol. Quantities calculated to indicate the accuracy of the dynamometer were cross-sensitivity, linearity. and hysteresis. Although all channels exhibited small amounts of cross-sensitivity. (i.e. load components activating channels not designed to register resultant strain from that load component), the crosssensitivity was linear in nature and was accounted for in the calibration matrix, C, used to resolve the loads from the strain measurements. Additionally, all the primary channels designed to respond to each individual load responded linearly. The lowest R-squared value from regression for any channel designed to respond to the load being applied was 0.998. The lowest R-squared value for a cross-sensitive channel responding to a load it was not intended to measure was 0.877. Hysteresis was bounded by 0.5 N for forces and 0.1 N m for moments. To assess the inaccuracy from all three factors above acting simultaneously, an accuracy check was performed. The accuracy

Technical

Table Current

1. Accuracy dynamometer

RMSE

Fx W) F, (N) F: PJ) Mx Wm) My Wm)

3.21

6.1

3.04 2.06 0.21

6.4

RMSE

previous

4.1

dynamometers

(1993,

1995)

Ruby

and Hull

Absolute

RMSE

13.2 5.9 27.5 0.6 0.6 0.7

7.1 1.7 2.6

6.1 3.3 14.1 0.3 0.29

0.42 0.23 0.44

200

with

Stone and Hull

Absolute

0.11 0.17

K (NW

comparison

1109

Note

0.55

0.16 0.04 0.34

T

150

(1993)

A

100 50 $ 8 b y.

0 -50 -100 ~

-150

Fx

--”

FV

-

-250

-

-

Fz

4

-I

-300

0

90

180 Crank

angla

270

380

(Dog)

4

2

0 I f

-2

r”

-4

-

Mx

-6

i

ws-8

-

-

-

, 0

” Mv

-

Mz

I I

90

270

180 Crank

angle

360

lDsgl

Fig. 6. Sample loads measured at foot/pedal interface. Data were taken at a workrate of 250 W and 90 rpm and averaged over 12 crank cycles. (a) Force components; (b) moment components.

check revealed the dynamometer to have an absolute error for multiple loading conditions bounded by 6.4 N for forces and 0.44 N m for moments. The inaccuracy is well within the acceptable range for studying knee overuse injury.

In addition to quantifying dynamometer performance under static loads, the ability to register dynamic loads was also determined. In making this determination, the natural frequency was measured with the interface of Wootten and Hull (1992)

Technical Note Table 2. Extreme value and phase comparison with previous dynamometers Current dynamometer Workrate = 250 W

Fx (N Fy (N) F: N M, PM M, (Nm) ME OW

Stone (1990) Workrate = 2 1I W

Extreme

Phase (“I

Extreme

Phase (“I

150 - 60 - 260 ~ 4.5 ~ 7.2 3.5

60 90 110 75 70 95

130 - 90 - 475 2.2 - 3.1 4.3

40 85 85 160 40 0

which had a mass of 0.65 kg and was found to be 280 Hz. However, this value is not representative of the natural frequency in practice. Since the dynamometer also supports the leg, some fraction of its mass affects the natural frequency. In experiments with other pedal dynamometers in our laboratory, the apparent mass of the leg in either the weighted (i.e. standing) or unweighted (i.e. seated) case was the same and included the mass of the shoe plus the foot. For a foot mass of 0.9 kg (Drillis and Contini, 1966) and a shoe mass of 0.4 kg, the adjusted natural frequency is 58% of the measured natural frequency. Note that this adjustment assumes that the dynamometer per se is massless which leads to a conservative (i.e. underestimated) adjustment. The adjusted natural frequency of 172 Hz gives the dynamometer a flat response region of 40 Hz to within 5% accuracy (Doebelin, 1990). This is sufficiently high to accurately indicate not only pedal loads due to muscular action but also pedal loads due to inertial loading developed in riding over rough terrain (Wilczynski and Hull, 1994). The new six-load component dynamometer offers accuracy improvement over previous six-load component dynamometers for the purposes of knee injury study. The modified dynamometer used in the studies by Stone (1990) and Stone and Hull (1993,199s) had a reported accuracy check with absolute errors of up to 27.5 N in force measurement, and 0.7 N m in moment measurement and maximum RMSE errors bounded by 14.1 N and 0.55 Nm for force and moment components, respectively. The reported RMSE errors of the dynamometer used in the study by Ruby and Hull (1993) were bounded by 7.1 N for force and 0.34 N m for moments. In comparison, the dynamometer presented herein has both absolute and RMSE error bounds lower than those reported by Stone and Hull (1993, 1995) and Ruby and Hull (1993) (Table 1).

CONCLUSIONS A six-load component pedal dynamometer based on measuring shear strain across thin cross-sections has been constructed. It has several features necessary for knee overuse injury study. It is adjustable in height to allow mounting of different pedal interface platforms. It is capable of measuring static load and has no non-linear cross-sensitivity. Errors are bounded by 6 N, and 0.44 Nm for measurement of forces and moments, respectively. The dynamometer is acceptable for the study of knee overuse injury by means of testing pedal interfaces which allow rotations between the foot and pedal. For those interested in reproducing the dynamometer, complete manufacturing drawings and parts list can be obtained from Professor M. L. Hull. Acknowtedgements-Special thanks are extended to Shimano Corporation of Osaka, Japan for its support of this project.

Ruby et al. (1992) Workrate = 225 W Phase (‘)

Extreme 130 - 50 - 310 -3 - 3.3 - 1.8

70 100 115 55 70 45

Broker and Gregor (1990) Workrate = 300 W Extreme --___ 50 -- 120 - 350 2.1 N/A N/A

Phase i’- 1 85 45 100 95 N/A N/A

REFERENCES

Broker, J. P. and Gregor, R. J. (1990) A dual piezoelectric element force pedal for kinetic analysis of cycling. Int. J. Sports

Biomech.

6, 394403.

Davis, R. R. and Hull, M. L. (198 1) Measurement of pedal loading in cycling: II. analysis and results. J. Biomechanics 14,857-872. Dickson, T. B. (1965) Preventing overuse cycling injuries. Physician & Sports Med. 13, 116123. Doebelin, E. 0. (1990) Measurement Systems Application and Design (4th Edn), Cb 3, Section 3.3. McGraw-Hill, San Francisco, CA. Drillis, R. and Contini, R. (1966) Body segment parameters. Technical Report No. 1166.03, Department of Health, Education, and Welfare, Washington, DC. Francis, P. R. (1988) Pathomechanics of the lower extremity in cycling. In Medical and Scientific Aspects of Cycling (Edited by Burke, E. R. and Newsom, M. M.), pp. 3-16 Human Kinetics Books, Champaign, IL. Holmes, J. C., Pruitt, A. L. and Whalen, N. J. (1991) Cycling knee injuries. Cycling Sci. 3, 11-14. Hull, M. L. and Davis, R. R. (1981) Measurement ofpedal loading in cycling: I. instrumentation. .J. Biomechanics 14, 84>856. Hull, M. L. and Gonzalez, H. K. (1990) The effect of pedal platform height on cycling biomechanics. Int. J. Sports Biomech. 6, l-17. Pruitt, A. L. (1988) The cyclist’s knee: anatomical and biomechanical considerations. In Medical and Scientific Aspects ofcycling (Edited by Burke, E. R. and Newsom, M. M.), pp. 3-16. Human Kinetics Books, Champaign, IL. Quinn, T. P. and Mote, C. D., Jr (1991) Optimal design of an uncoupled six-degree-of-freedom dynamometer. Exp. Mech. 30, 4&48. Ruby, P. and Hull, M. L. (1993) Response ofintersegmental knee loads to foot/pedal platform degrees of freedom in cycling. J. Biomechanics 26, 1327-1340. Ruby, P., Hull, M. L. and Hawkins, D. (1992) Three dimensional knee joint loading during seated cycling. J. Biomechanics 25, 41-53. Stone, C. (1990) Rider/bicycle interaction loads during seated and standing treadmill cycling. M.S. thesis, Department of Mechanical Engineering, University of California, Davis. Stone, C. and Hull, M. L. (1993) Rider/bicycle interaction loads during standing treadmill cycling. J. Appl. Biomech. 9,202-218. Stone, C. and Hull, M. L. (1995) The effect of rider weight on rider induced loads during common cycling situations. J. Biomech.

28, 365-375.

Strang, G. (1988) Linear Algebra and Its Applications (3rd Edn), p. 156. Harcourt, Brace and Jovanovich, Orlando, FL. Wilczynski, H. and Hull, M. L. (1994) A dynamic system model for estimating surface induced frame loads during off-road cycling. J. Mech. Design 116, 816-822. Wootten, D. and Hull, M. L. (1992) Design and evaluation of a multi-degree-of-freedom foot-pedal interface for cycling. Int. J. Sports Biomech. 8, 152-164.