Multivariable optimization of cycling biomechanics

Relying on a biomechanical model of the lower limb which treats the leg-bicycle system as a five-bar linkage constrained to plane motion, a cost function derived from the joint moments developed during cycling is computed. At constant average power of 200 W, the effect of five variables on the cost function is studied. The five variables are pedalling rate, crank arm length, seat tube angle, seat height, and longitudinal foot position on the pedal. A sensitivity analysis of each of the five variables shows that pedalling rate is the most sensitive, followed by the crank arm length, seat tube angle, seat height, and longitudinal foot position on the pedal (the least sensitive). Based on Powell's method, a multivariable optimization search is made for the combination of variable values which minimize the cost function. For a rider of average anthropometry (height 1.78 m, weight 72.5 kg), a pedalling rate of 115 rev min-1, crank arm length of 0.140 m, seat tube angle of 76 degrees, seat height plus crank arm length equal to 97% of trochanteric leg length, and longitudinal foot position on the pedal equal to 54% of foot length correspond to the cost function global minimum. The effect of anthropometric parameter variations is also examined and these variations influence the results significantly. The optimal crank arm length, seat height, and longitudinal foot position on the pedal increase as the size of rider increases whereas the optimal cadence and seat tube angle decrease as the rider's size increases. The dependence of optimization results on anthropometric parameters emphasizes the importance of tailoring bicycle equipment to the anthropometry of the individual.     

A mechanically decoupled two force component bicycle pedal dynamometer

A design is presented for a bicycle pedal dynamometer that measures both normal and tangential forces (i.e. driving forces). Mechanical decoupling is used to reduce the cross-sensitivity of the dynamometer to loads doing no work to propel the bicycle. This obviates the need to measure all six loads for accurate data reduction. A compact strain ring is the transducer element, and a monolithic design eliminates mechanical hysteresis between the strain ring and the dynamometer frame. The angular orientation of the dynamometer with respect to the crank arm is determined with a continuous-rotation potentiometer. Design criteria and design implementation are discussed, sample data are presented, and the performance of the dynamometer is evaluated.     

Three-dimensional knee joint loading during seated cycling.

The hypothesis which motivated the work reported in this article was that neglecting pure moments developed between the foot and pedal during cycling leads to a substantial error in computing axial and varus/valgus moments at the knee. To test this hypothesis, a mathematical procedure was developed for computing the three-dimensional knee loads using three-dimensional pedal forces and moments. In addition to data from a six-load-component pedal dynamometer, the model used pedal position and orientation and knee position in the frontal plane to determine the knee joint loads. Experimental data were collected from the right leg of 11 male subjects during steady-state cycling at 90 rpm and 225 W. The mean peak varus knee moment calculated was 15.3 N m and the mean peak valgus knee moment was 11.2 N m. Neglecting the pedal moment about the anterior/posterior axis resulted in an average absolute error of 2.6 N m and a maximum absolute error of 4.0 N m in the varus/valgus knee moment. The mean peak internal and external axial knee moments were 2.8 N m and 2.3 N m, respectively. The average and maximum absolute errors in the axial knee moment for not including the moment about an axis normal to the pedal were found to be 2.6 N m and 5.0 N m, respectively. The results strongly support the use of three-dimensional pedal loads in the computation of knee joint moments out of the sagittal plane.     

On the relation between joint moments and pedalling rates at constant power in bicycling

Joint moments are of interest because they bear some relation to muscular effort and hence rider performance. The general objective of this study is to explore the relation between joint moments and pedalling rate (i.e. cadence). Joint moments are computed by modelling the leg-bicycle system as a five-bar linkage constrained to plane motion. Using dynamometer pedal force data and potentiometer crank and pedal position data, system equations are solved on a computer to produce moments at the ankle, knee and hip joints. Cadence and pedal forces are varied inversely to maintain constant power. Results indicate that average joint moments vary considerably with changes in cadence. Both hip and knee joints show an average moment which is minimum near 105 rotations min-1 for cruising cycling. It appears that an optimum rotations min-1 can be determined from a mechanical approach for any given power level and bicycle-rider geometry.     

Goniometric measurement of hip motion in cycling while standing

The purpose of this study was to develop an instrument for quantifying the motion of the hip relative to the bicycle while cycling in the standing position. Because of the need to measure hip motion on the road as well as in the laboratory, a goniometer which locates the hip using spherical coordinates was designed. The goniometer is presented first, followed by the development of the equations that enable the distance from the joint center to the pedal spindle to be determined. The orientation of this line segment is specified by calculating two angles referenced to the frame. Also outlined are the procedures used to both calibrate the goniometer and perform an accuracy check. The results of this check indicate that the attachment point of the goniometer to the rider can be located to within 2.5 mm of the true position. The goniometer was used to record the hip movement patterns of six subjects who cycled in the standing position on a treadmill. Representative results from one test subject who cycled at 6% grade and 25 km h-1 are presented. Results indicate that the bicycle is leaned from side to side with the frequency of leaning equal to the frequency of pedalling. Extreme lean angles are +/- 6 degrees. The distance from the hip to the pedal varies approximately sinusoidally with frequency equal to pedalling rate and amplitude somewhat less than crank arm length. The absolute elevation of the hip, however, exhibits two cycles for each crank cycle. Asymmetry in the plot of elevation over a single crank cycle indicates that the pelvis rocks from side to side and that the elevation of the pelvis midpoint changes. Extreme values of the pelvis rocking angle are +/- 12 degrees. Highest pelvis midpoint elevations, however, do not occur at the same crank angles as those angles at which the pelvis rocking is extreme. It appears that the vertical motion of the hips affects pedalling mechanics when cycling in the standing position.     

How changing the inversion/eversion foot angle affects the nondriving intersegmental knee moments and the relative activation of the vastii muscles in cycling

Nondriving intersegmental knee moment components (i.e., varus/valgus and internal/external axial moments) are thought to be primarily responsible for the etiology of overuse knee injuries such as patellofermoral pain syndrome in cycling because of their relationship to muscular imbalances. However the relationship between these moments and muscle activity has not been studied. Thus the four primary objectives of this study were to test whether manipulating the inversion/eversion foot angle alters the varus/valgus knee moment (Objective 1) and axial knee moment (Objective 2) and to determine whether activation patterns of the vastus medialis oblique (VMO), vastus lateralis (VL), and tensor fascia latae (TFL) were affected by changes in the varus/valgus (Objective 3) and axial knee moments (Objective 4). To fulfill these objectives, pedal loads and lower limb kinematic data were collected from 15 subjects who pedaled with five randomly assigned inversion/eversion angles: 10 deg and 5 deg everted and inverted and 0 deg (neutral). A previously described mathematical model was used to compute the nondriving intersegmental knee moments throughout the crank cycle. The excitations of the VMO, VL, and TFL muscles were measured with surface electromyography and the muscle activations were computed. On average, the 10-deg everted position decreased the peak varus moment by 55% and decreased the peak internal axial moment by 53% during the power stroke (crank cycle region where the knee moment is extensor). A correlation analysis revealed that the VMO/VL activation ratio increased significantly and the TFL activation decreased significantly as the varus moment decreased. For both the VMO/VL activation ratio and the TFL activation, a path analysis indicated that the varus/valgus moment was highly correlated to the axial moment but that the correlation between muscle activation and the varus moment was due primarily to the varus/valgus knee moment rather than the axial knee moment. The conclusion from these results is that everting the foot may be beneficial towards either preventing or ameliorating patellofemoral pain syndrome in cycling.     

Crank inertial load affects freely chosen pedal rate during cycling.

Cyclists seek to maximize performance during competition, and gross efficiency is an important factor affecting performance. Gross efficiency is itself affected by pedal rate. Thus, it is important to understand factors that affect freely chosen pedal rate. Crank inertial load varies greatly during road cycling based on the selected gear ratio. Nevertheless, the possible influence of crank inertial load on freely chosen pedal rate and gross efficiency has never been investigated. This study tested the hypotheses that during cycling with sub-maximal work rates, a considerable increase in crank inertial load would cause (1) freely chosen pedal rate to increase, and as a consequence, (2) gross efficiency to decrease. Furthermore, that it would cause (3) peak crank torque to increase if a constant pedal rate was maintained. Subjects cycled on a treadmill at 150 and 250W, with low and high crank inertial load, and with preset and freely chosen pedal rate. Freely chosen pedal rate was higher at high compared with low crank inertial load. Notably, the change in crank inertial load affected the freely chosen pedal rate as much as did the 100W increase in work rate. Along with freely chosen pedal rate being higher, gross efficiency at 250W was lower during cycling with high compared with low crank inertial load. Peak crank torque was higher during cycling at 90rpm with high compared with low crank inertial load. Possibly, the subjects increased the pedal rate to compensate for the higher peak crank torque accompanying cycling with high compared with low crank inertial load.     

Quantification of structural loading during off-road cycling.

To provide data for fatigue life prediction and testing of structural components in off-road bicycles, the objective of the research described herein was to quantify the loads input to an off-road bicycle as a result of surface-induced loads. A fully instrumented test bicycle was equipped with dynamometers at the pedals, handlebars, and hubs to measure all in-plane structural loads acting through points of contact between the bicycle and both the rider and the ground. A portable data acquisition system carried by the standing rider allowed, for the first time, this loading information to be collected during extended off-road testing. In all, seven experienced riders rode a downhill trial test section with the test bicycle in both front-suspension and full-suspension configurations. The load histories were used quantitatively to describe the load components through the computation of means, standard deviations, amplitude probability density functions, and power spectral density functions. For the standing position, the coefficients of variation for the load components normal to the ground were greater than 1.2 for handlebar forces and 0.3 and 0.5-0.6 for the pedal and hub forces, respectively. Thus, the relative contribution of the dynamic loading was much greater than the static loading at the handlebars but less so at the pedals and hubs. As indicated by the rainflow count, high amplitude loading was developed approaching 3 and 5 times the weight of the test subjects at the front and rear wheels, respectively. The power spectral densities showed that energy was concentrated in the band 0-50 Hz. Through stress computations and knowledge of material properties, the data can be used analytically to predict the fatigue life of important structural components such as those for steering. The data can also be used to develop a fatigue testing protocol for verifying analytical predictions of fatigue life.     

Crank inertial load has little effect on steady-state pedaling coordination

Inertial load can affect the control of a dynamic system whenever parts of the system are accelerated ordeclerated. During steady-state pedating, because within-cycle variations in crank angular acceleration still exist, the amount of crank inertia present (which varies widely with road-riding gear ratio) may affect the within-cycle coordination of muscles. However, the effect of inertial load on steady-state pedaling coordination is almos always assumed to be negligible, since the net mechanical energy per cycle developed by muscles only depends on the constant cadence and workload. This study tests the hypothesis that under steady-state conditions, the net joint torques produced by muscles at the hip, knee, and ankle are unaffected by crank inertial load. To perform the investigation, we constructed a pedaling apparatus which could emulate the low inertial load of a standard ergometer or the high inertial load of a road bicycle in high gear. Crank angle and bilateral pedal force and angle data were collected from ten subjects instructed to pedal steadily (i.e. constant speed across cycles) and smoothly (i.e. constant speed within a cycle) against both inertias at a constant workload. Virtually no statistically significant changes were found in the net hip and knee muscle joint torques calculated from an inverse dynamics analysis. Though the net ankle muscle joint torque, as well as the one- and two-legged crank torque, showed statistically significant increases at the higher inertia, the changes were small. In contrast, large statistically significant reductions were found in crank kinematic variability both within a cycle and between cycles (i.e. cadence), primarily because a larger inertial load means a slower crank dynamic response. Nonetheless, the reduction in cadence variability was somewhat attenuated by a large statistically significant increase in one-legged crank torque variability. We suggest, therefore, that muscle coordination during steady-state pedaling is largely unaffected, though less well regulated, when crank inertial load is increased.     

Is economy of competitive cyclists affected by the anterior–posterior foot position on the pedal?

The primary purpose of this investigation was to test the hypothesis that cycling economy, as measured by rate of oxygen consumption (VO(2)) in healthy, young, competitive cyclists pedaling at a constant workrate, increases (i.e. VO(2) decreases) when the attachment point of the foot to the pedal is moved posteriorly on the foot. The VO(2) of 11 competitive cyclists (age 26.8+/-8.9 years) was evaluated on three separate days with three anterior-posterior attachment points of the foot to the pedal (forward=traditional; rear=cleat halfway between the head of the first metatarsal and the posterior end of the calcaneous; and mid=halfway between the rear and forward positions) on each day. With a randomly selected foot position, VO(2) was measured as each cyclist pedaled at steady state with a cadence of 90 rpm and with a power output corresponding to approximately 90% of their ventilatory threshold (VT) (mean power output 203.3+/-20.8 W). After heart rate returned to baseline, VO(2) was measured again as the subject pedaled with a different anterior-posterior foot position, followed by another rest period and then VO(2) was measured at the final foot position. The key finding of this investigation was that VO(2) was not affected by the anterior-posterior foot position either for the group (p=0.311) or for any individual subject (p>or=0.156). The VO(2) for the group was 2705+/-324, 2696+/-337, and 2747+/-297 ml/min for the forward, mid, and rear foot positions, respectively. The practical implication of these findings is that adjusting the anterior-posterior foot position on the pedal does not affect cycling economy in competitive cyclists pedaling at a steady-state power output eliciting approximately 90% of VT.     

Comparison of a kayaking ergometer protocol with an arm crank protocol for evaluating peak oxygen consumption

The purpose of this study was to compare a kayak ergometer protocol with an arm crank protocol for determining peak oxygen consumption (V(.-)O2). On separate days in random order, 10 men and 5 women (16-24 years old) with kayaking experience completed the kayak ergometer protocol and a standardized arm crank protocol. The kayak protocol began at 70 strokes per minute and increased by 10 strokes per minute every 2 minutes until volitional fatigue. The arm crank protocol consisted of a crank rate of 70 revolutions per minute, initial loading of 35 W and subsequent increases of 35 W every 2 minutes until volitional fatigue. The results showed a significant difference (p < 0.01) between the kayak ergometer and the arm crank protocols for relative peak V(.-)O2 (47.5 +/- 3.9 ml x kg(-1) x min(-1) vs. 44.2 +/- 6.2 ml x kg(-1) x min(-1)) and absolute peak V(.-)O2 (3.38 L x min(-1) +/- 0.53 vs. 3.14 +/- 0.64 L x min(-1)). The correlation between kayak and arm crank protocol was 0.79 and 0.90, for relative and absolute V(.-)O2 peak, respectively (both p < 0.01). The higher peak V(.-)O2 on the kayak ergometer may be due to the greater muscle mass involved compared to the arm crank ergometer. The kayak ergometer protocol may therefore be more specific to the sport of kayaking than an arm crank protocol.     

Diurnal variations in cycling kinematics

Physiological and biomechanical constraints as well as their fluctuations throughout the day must be considered when studying determinant factors in the preferred pedaling rate of elite cyclists. The aim of this study was to monitor the diurnal variation of spontaneous pedaling rate and movement kinematics over the crank cycle. Twelve male competitive cyclists performed a submaximal exercise on a cycle ergometer for 15 min at 50% of their W(max). Two test sessions were performed at 06:00 and 18:00 h on two separate days to assess diurnal variation in the study variables. For each test session, the exercise bout was divided into three equivalent 5-min periods during which subjects were requested to use different pedal rates (spontaneous cadence, 70 and 90 rev min(-1)). Pedal rate and kinematics data (instantaneous pedal velocity and angle of the ankle) were collected. The results show a higher spontaneous pedal rate in the late afternoon than in the early morning (p < 0.001). For a given pedal rate condition, there was a less variation in pedal velocity during a crank cycle in the morning than in the late afternoon. Moreover, diurnal variations were observed in ankle mobility across the crank cycle, the mean plantar flexion observed throughout the crank cycle being greater in the 18:00 h test session (p < 0.001). These results suggest that muscular activation patterns during a cyclical movement could be under the influence of circadian fluctuations.     

Relation between the ankle joint angle and the maximum isometric force of the toe flexor muscles

The purpose of this study was to investigate the relationships between the ankle joint angle and maximum isometric force of the toe flexor muscles. Toe flexor strength and electromyography activity of the foot muscles were measured in 12 healthy men at 6 different ankle joint angles with the knee joint at 90 deg in the sitting position. To measure the maximum isometric force of the toe flexor muscles, subjects exerted maximum force on a toe grip dynamometer while the activity levels of the intrinsic and extrinsic plantar muscles were measured. The relation between ankle joint angle and maximum isometric force of the toe flexor muscles was determined, and the isometric force exhibited a peak when the ankle joint was at 70–90 deg on average. From this optimal neutral position, the isometric force gradually decreased and reached its nadir in the plantar flexion position (i.e., 120 deg). The EMG activity of the abductor hallucis (intrinsic plantar muscle) and peroneus longus (extrinsic plantar muscle) did not differ at any ankle joint angles. The results of this study suggest that the force generation of toe flexor muscles is regulated at the ankle joint and that changes in the length-tension relations of the extrinsic plantar muscle could be a reason for the force-generating capacity at the metatarsophalangeal joint when the ankle joint angle is changed.     

Diurnal Variations in Cycling Kinematics

Physiological and biomechanical constraints as well as their fluctuations throughout the day must be considered when studying determinant factors in the preferred pedaling rate of elite cyclists. The aim of this study was to monitor the diurnal variation of spontaneous pedaling rate and movement kinematics over the crank cycle. Twelve male competitive cyclists performed a submaximal exercise on a cycle ergometer for 15 min at 50% of their W_max. Two test sessions were performed at 06:00 and 18:00 h on two separate days to assess diurnal variation in the study variables. For each test session, the exercise bout was divided into three equivalent 5‐min periods during which subjects were requested to use different pedal rates (spontaneous cadence, 70 and 90 rev min^?1). Pedal rate and kinematics data (instantaneous pedal velocity and angle of the ankle) were collected. The results show a higher spontaneous pedal rate in the late afternoon than in the early morning (p < 0.001). For a given pedal rate condition, there was a less variation in pedal velocity during a crank cycle in the morning than in the late afternoon. Moreover, diurnal variations were observed in ankle mobility across the crank cycle, the mean plantar flexion observed throughout the crank cycle being greater in the 18:00 h test session (p < 0.001). These results suggest that muscular activation patterns during a cyclical movement could be under the influence of circadian fluctuations.     

A method for biomechanical analysis of bicycle pedalling

This paper reports a new method, which enables a detailed biomechanical analysis of the lower limb during bicycling. The method consists of simultaneously measuring both the normal and tangential pedal forces, the EMGs of eight leg muscles, and the crank arm and pedal angles. Data were recorded for three male subjects of similar anthropometric characteristics. Subjects rode under different pedalling conditions to explore how both pedal forces and pedalling rates affect the biomechanics of the pedalling process. By modelling the leg-bicycle as a five bar linkage and driving the linkage with the measured force and kinematic data, the joint moment histories due to pedal forces only (i.e. no motion) and motion only (i.e. no pedal forces) were generated. Total moments were produced by superimposing the two moment histories. The separate moment histories, together with the pedal forces and EMG results, enable a detailed biomechanical analysis of bicycle pedalling. Inasmuch as the results are similar for all three subjects, the analysis for one subject is discussed fully. One unique insight gained via this new method is the functional role that individual leg muscles play in the pedalling process.     

In vivo hip joint loads and pedal forces during ergometer cycling

The rising prevalence of osteoarthritis and an increase in total hip replacements calls for attention to potential therapeutic activities. Cycling is considered as a low impact exercise for the hip joint and hence recommended. However, there are limited data about hip joint loading to support this claim. The aim of this study was to measure synchronously the in vivo hip joint loads and pedal forces during cycling. The in vivo hip joint loads were measured in 5 patients with instrumented hip implants. Data were collected at several combinations of power and cadence, at two saddle heights.Joint loads and pedal forces showed strong linear correlation with power. So the relationship between the external pedal forces and internal joint forces was shown. While cycling at different cadences the minimum joint loads were acquired at 60 RPM. The lower saddle height configuration results in an approximately 15% increase compared to normal saddle height.The results offered new insights into the actual effects of cycling on the hip joint and can serve as useful tools while developing an optimum cycling regimen for individuals with coxarthrosis or following total hip arthroplasty. Due to the relatively low contact forces, cycling at a moderate power level of 90 W at a normal saddle height is suitable for patients.     

Arm crank ergometer is reliable and valid for measuring aerobic capacity during submaximal exercise

Measuring physical fitness becomes more important. Yet most instruments depend upon the function of the lower extremities. Hence, we investigated whether an adapted submaximal arm crank test on an ergometer for the upper body is reliable to use, and if the submaximal test for the arm crank ergometer is valid compared to the test on the bicycle ergometer. Different types of reliability measures of the adapted submaximal test on an arm crank ergometer were assessed in healthy volunteers, such as test-retest, interobserver, interergometer, and between arm crank and bicycle ergometer. A crossover design was used. The measurements were proportionally distributed over 30 volunteers. Based on the intraclass correlation coefficient (ICC) and the magnitude of within-person differences, we revealed a good reliability of the submaximal test. For the test-retest reliability, the ICC was 0.76, the interobserver reliability was 0.82, and the interergometer reliability 0.63. In addition, the criterion validity was also tested by comparing the calculated VO2max during the submaximal test on the arm crank ergometer and on the bicycle ergometer. Between VO2max on the arm crank and bicycle ergometer, an ICC of 0.64 was found. The results of the submaximal test on the arm crank ergometer are reliable and valid as compared with those on the bicycle crank ergometer. We showed that the submaximal test on the arm crank ergometer is suitable for measuring physical fitness in healthy people. We expect that disabled people can use this submaximal test on the arm crank ergometer for measuring their physical fitness, also.     

An ultrasound based non-invasive method for the measurement of intrinsic foot kinematics during gait

Soft tissue artefact (STA) and marker placement variability are sources of error when measuring the intrinsic kinematics of the foot. This study aims to demonstrate a non-invasive, combined ultrasound and motion capture (US/MC) technique to directly measure foot skeletal motion. The novel approach is compared to a standard motion capture protocol. Fourteen participants underwent instrumented barefoot analysis of foot motion during gait. Markers were attached to foot allowing medial longitudinal arch angle and navicular height to be determined. For the US/MC technique, the navicular marker was replaced by an ultrasound transducer which was secured to the foot allowing the skeletal landmark to be imaged. Ultrasound cineloops showing the location of the navicular tuberosity during the walking trials were synchronised with motion capture measurements and markers mounted on the probe allowed the true position of the bony landmark to be determined throughout stance phase. Two discrete variables, minimum navicular height and maximum MLA angle, were compared between the standard and US/MC protocols. Significant differences between minimum navicular height (P=0.004, 95% CI (1.57, 6.54)) and maximum medial longitudinal arch angle (P=0.0034, 95% CI (13.8, 3.4)) were found between the measurement methods. The individual effects of STA and marker placement error were also assessed. US/MC is a non-invasive technique which may help to provide more accurate measurements of intrinsic foot kinematics.     

The influence of seat configuration on maximal average crank power during pedaling: a simulation study

Manipulating seat configuration (i.e., seat tube angle, seat height and pelvic orientation) alters the bicycle-rider geometry, which influences lower extremity muscle kinematics and ultimately muscle force and power generation during pedaling. Previous studies have sought to identify the optimal configuration, but isolating the effects of specific variables on rider performance from the confounding effect of rider adaptation makes such studies challenging. Of particular interest is the influence of seat tube angle on rider performance, as seat tube angle varies across riding disciplines (e.g., road racers vs. triathletes). The goals of the current study were to use muscle-actuated forward dynamics simulations of pedaling to 1) identify the overall optimal seat configuration that produces maximum crank power and 2) systematically vary seat tube angle to assess how it influences maximum crank power. The simulations showed that a seat height of 0.76 m (or 102% greater than trochanter height), seat tube angle of 85.1 deg, and pelvic orientation of 20.5 deg placed the major power-producing muscles on more favorable regions of the intrinsic force-length-velocity relationships to generate a maximum average crank power of 981 W. However, seat tube angle had little influence on crank power, with maximal values varying at most by 1% across a wide range of seat tube angles (65 to 110 deg). The similar power values across the wide range of seat tube angles were the result of nearly identical joint kinematics, which occurred using a similar optimal seat height and pelvic orientation while systematically shifting the pedal angle with increasing seat tube angles.