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 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.     

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.     

Muscular activity during uphill cycling: effect of slope, posture, hand grip position and constrained bicycle lateral sways.

Despite the wide use of surface electromyography (EMG) to study pedalling movement, there is a paucity of data concerning the muscular activity during uphill cycling, notably in standing posture. The aim of this study was to investigate the muscular activity of eight lower limb muscles and four upper limb muscles across various laboratory pedalling exercises which simulated uphill cycling conditions. Ten trained cyclists rode at 80% of their maximal aerobic power on an inclined motorised treadmill (4%, 7% and 10%) with using two pedalling postures (seated and standing). Two additional rides were made in standing at 4% slope to test the effect of the change of the hand grip position (from brake levers to the drops of the handlebar), and the influence of the lateral sways of the bicycle. For this last goal, the bicycle was fixed on a stationary ergometer to prevent the lean of the bicycle side-to-side. EMG was recorded from M. gluteus maximus (GM), M. vastus medialis (VM), M. rectus femoris (RF), M. biceps femoris (BF), M. semimembranosus (SM), M. gastrocnemius medialis (GAS), M. soleus (SOL), M. tibialis anterior (TA), M. biceps brachii (BB), M. triceps brachii (TB), M. rectus abdominis (RA) and M. erector spinae (ES). Unlike the slope, the change of pedalling posture in uphill cycling had a significant effect on the EMG activity, except for the three muscles crossing the ankle's joint (GAS, SOL and TA). Intensity and duration of GM, VM, RF, BF, BB, TA, RA and ES activity were greater in standing while SM activity showed a slight decrease. In standing, global activity of upper limb was higher when the hand grip position was changed from brake level to the drops, but lower when the lateral sways of the bicycle were constrained. These results seem to be related to (1) the increase of the peak pedal force, (2) the change of the hip and knee joint moments, (3) the need to stabilize pelvic in reference with removing the saddle support, and (4) the shift of the mass centre forward.     

Effects on the crank torque profile when changing pedalling cadence in level ground and uphill road cycling

Despite the importance of uphill cycling performance during cycling competitions, there is very little research investigating uphill cycling, particularly concerning field studies. The lack of research is partly due to the difficulties in obtaining data in the field. The aim of this study was to analyse the crank torque in road cycling on level and uphill using different pedalling cadences in the seated position. Seven male cyclists performed four tests in the seated position (1) on level ground at 80 and 100 rpm, and (2) on uphill road cycling (9.25% grade) at 60 and 80 rpm.The cyclists exercised for 1 min at their maximal aerobic power. The bicycle was equipped with the SRM Training System (Schoberer, Germany) for the measurement of power output (W), torque (Nm), pedalling cadence (rpm), and cycling velocity (km h(-1)). The most important finding of this study indicated that at maximal aerobic power the crank torque profile (relationship between torque and crank angle) varied substantially according to the pedalling cadence and with a minor effect according to the terrain. At the same power output and pedalling cadence (80 rpm) the torque at a 45 degrees crank angle tended (p < 0.06) to be higher (+26%) during uphill cycling compared to level cycling. During uphill cycling at 60 rpm the peak torque was increased by 42% compared with level ground cycling at 100 rpm.When the pedalling cadence was modified, most of the variations in the crank torque profile were localised in the power output sector (45 degrees to 135 degrees).     

Measurment of pedal loading in bicycling: I. Instrumentation

This paper presents a new instrumentation system to precisely measure pedal loads and pedal position. A pedal/dynamometer unit implementing four octagonal strain rings measures all six load components between the foot and pedal. To study the relationship between foot position and loading, the pedal/dynamometer offers three degree-of-freedom adjustability. Pedal position along the pedal arc is precisely described by measuring crank arm angle and relative angle between pedal and crank arm. Linear, continuous rotation potentiometers measure the two angles. Transducer signals are sampled by a digital computer which calculates resultant loads and pedal position as functions of crank arm angle. Transducers are designed to mount on most bicycles without modification. Test subjects ride their own bicycles unconstrained on rollers so that loading data is representative of actual 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.     

An angular velocity profile in cycling derived from mechanical energy analysis

The contributions of this article are twofold. One is procedure for determining the angular velocity profile in seated cycling that maintains the total mechanical energy of both legs constant. A five-bar linkage model (thigh, shank, foot, crank and frame) of seated (fixed hip) cycling served for the derivation of the equations to compute potential and kinetic energies of the leg segments over a complete crank cycle. With experimentally collected pedal angle data as input, these equations were used to compute the total combined mechanical energy (sum of potential and kinetic energies of the segments of both legs) for constant angular velocity pedalling at 90 rpm. Total energy varied indicating the presence of internal work. Motivated by a desire to test the hypothesis that reducing internal work in cycling will reduce energy expenditure, a procedure was developed for determining the angular velocity profile that eliminated any change in total energy. Using data recorded from five subjects, this procedure was used to determine a reference profile for an average equivalent cadence of 90 rpm. The phase of this profile is such that highest and lowest angular velocities occur when the cranks are near vertical and horizontal respectively. The second contribution is the testing of the hypothesis that the reference angular velocity profile serves to effectively reduce internal work for the subjects whose data were used to develop this profile over the range of pedalling rates (80-100 rpm) naturally preferred. In this range, the internal work was decreased a minimum of 48% relative to the internal work associated with constant angular velocity pedalling. The acceptance of this hypothesis has relevance to the protocol for future experiments which explore the effect of reduced internal work on energy expenditure in cycling.     

Analysis of EMG measurements during bicycle pedalling

Activity of eight leg muscles has been monitored for six test subjects while pedalling a bicycle on rollers in the laboratory. Each electromyogram (EMG) data channel was digitized at a sampling rate of 2 kHz by a minicomputer. Data analysis entailed generating plots of both EMG activity regions and integrated EMG (IEMG). For each test subject, data were recorded for five cases of pedalling conditions. The different pedalling conditions were defined to explore a variety of research hypotheses. This exploration has led to the following conclusions: Muscular activity levels of the quadriceps are influenced by the type of shoes worn and activity levels increase with soft sole shoes as opposed to cycling shoes with cleats and toeclips. EMG activity patterns are not strongly related to pedalling conditions (i.e. load, seat height and shoe type). The level of muscle activity, however, is significantly affected by pedalling conditions. Muscular activity bears a complex relationship with seat height and quadriceps activity level decreases with greater seat height. Agonist (i.e. hamstrings) and antagonist (i.e. quadriceps) muscles of the hip/knee are active simultaneously during leg extension. Regions of peak activity levels, however, do not overlap. The lack of significant cocontraction of agonist/antagonist muscles enables muscle forces during pedalling action to be computed by solving a series of equilibrium problems over different regions of the crank cycle. Regions are defined and a solution procedure is outlined.     

Bivariate optimization of pedalling rate and crank arm length in cycling

The contribution of this paper is a bivariate optimization of cycling performance. Relying on a biomechanical model of the lower limb, a cost function derived from the joint moments developed during cycling is computed. At constant average power, both pedalling rate (i.e. rpm) and crank arm length are systematically varied to explore the relation between these variables and the cost function. A crank arm length of 170 mm and pedalling rate of 100 rpm correspond closely to the cost function minimum. In cycling situations where the rpm deviates from 100 rpm, however, crank arms of length other than 170 mm yield minimum cost function values. In addition, the sensitivity of optimization results to both increased power and anthropometric parameter variations is examined. At increased power, the cost function minimum is more strongly related to the pedalling rate, with higher pedalling rates corresponding to the minimum. Anthropometric parameter variations influence the results significantly. In general it is found that the cost function minimum for tall people occurs at longer crank arm lengths and lower pedalling rates than the length and rate for short people.     

Influence of bicycle seat tube angle and hand position on lower extremity kinematics and neuromuscular control: implications for triathlon running performance

We investigated how varying seat tube angle (STA) and hand position affect muscle kinematics and activation patterns during cycling in order to better understand how triathlon-specific bike geometries might mitigate the biomechanical challenges associated with the bike-to-run transition. Whole body motion and lower extremity muscle activities were recorded from 14 triathletes during a series of cycling and treadmill running trials. A total of nine cycling trials were conducted in three hand positions (aero, drops, hoods) and at three STAs (73°, 76°, 79°). Participants also ran on a treadmill at 80, 90, and 100% of their 10-km triathlon race pace. Compared with cycling, running necessitated significantly longer peak musculotendon lengths from the uniarticular hip flexors, knee extensors, ankle plantar flexors and the biarticular hamstrings, rectus femoris, and gastrocnemius muscles. Running also involved significantly longer periods of active muscle lengthening from the quadriceps and ankle plantar flexors. During cycling, increasing the STA alone had no affect on muscle kinematics but did induce significantly greater rectus femoris activity during the upstroke of the crank cycle. Increasing hip extension by varying the hand position induced an increase in hamstring muscle activity, and moved the operating lengths of the uniarticular hip flexor and extensor muscles slightly closer to those seen during running. These combined changes in muscle kinematics and coordination could potentially contribute to the improved running performances that have been previously observed immediately after cycling on a triathlon-specific bicycle.     

Soft tissue artefacts of skin markers on the lower limb during cycling: Effects of joint angles and pedal resistance

Soft tissue artefacts (STA) are a major error source in skin marker-based measurement of human movement, and are difficult to eliminate non-invasively. The current study quantified in vivo the STA of skin markers on the thigh and shank during cycling, and studied the effects of knee angles and pedal resistance by using integrated 3D fluoroscopy and stereophotogrammetry. Fifteen young healthy adults performed stationary cycling with and without pedal resistance, while the marker data were measured using a motion capture system, and the motions of the femur and tibia/fibula were recorded using a bi-plane fluoroscopy-to-CT registration method. The STAs with respect to crank and knee angles over the pedaling cycle, as well as the within-cycle variations, were obtained and compared between resistance conditions. The thigh markers showed greater STA than the shank ones, the latter varying linearly with adjacent joint angles, the former non-linearly with greater within-cycle variability. Both STA magnitudes and within-cycle variability were significantly affected by pedal resistance (p < 0.05). The STAs appeared to be composed of one component providing the stable and consistent STA patterns and another causing their variations. Mid-segment markers experienced smaller STA ranges than those closer to a joint, but tended to have greater variations primarily associated with pedal resistance and muscle contractions. The current data will be helpful for a better choice of marker positions for data collection, and for developing methods to compensate for both stable and variation components of the STA.     

A governing relationship for repetitive muscular contraction

During repetitive contractions, muscular work has been shown to exhibit complex relationships with muscle strain length, cycle frequency, and muscle shortening velocity. Those complex relationships make it difficult to predict muscular performance for any specific set of movement parameters. We hypothesized that the relationship of impulse with cyclic velocity (the product of shortening velocity and cycle frequency) would be independent of strain length and that impulse-cyclic velocity relationships for maximal cycling would be similar to those of in situ muscle performing repetitive contraction. Impulse and power were measured during maximal cycle ergometry with five cycle-crank lengths (120-220mm). Kinematic data were recorded to determine the relationship of pedal speed with joint angular velocity. Previously reported in situ data for rat plantaris were used to calculate values for impulse and cyclic velocity. Kinematic data indicated that pedal speed was highly correlated with joint angular velocity at the hip, knee, and ankle and was, therefore, considered a valid indicator of muscle shortening velocity. Cycling impulse-cyclic velocity relationships for each crank length were closely approximated by a rectangular hyperbola. Data for all crank lengths were also closely approximated by a single hyperbola, however, impulse produced on the 120mm cranks differed significantly from that on all other cranks. In situ impulse-cyclic velocity relationships exhibited similar characteristics to those of cycling. The convergence of the impulse-cyclic velocity relationships from most crank and strain lengths suggests that impulse-cyclic velocity represents a governing relationship for repetitive muscular contraction and thus a single equation can predict muscle performance for a wide range of functional activities. The similarity of characteristics exhibited by cycling and in situ muscle suggests that cycling can serve as a window though which to observe basic muscle function and that investigators can examine similar questions with in vivo and in situ models.     

Determinants of metabolic cost during submaximal cycling.

The metabolic cost of producing submaximal cycling power has been reported to vary with pedaling rate. Pedaling rate, however, governs two physiological phenomena known to influence metabolic cost and efficiency: muscle shortening velocity and the frequency of muscle activation and relaxation. The purpose of this investigation was to determine the relative influence of those two phenomena on metabolic cost during submaximal cycling. Nine trained male cyclists performed submaximal cycling at power outputs intended to elicit 30, 60, and 90% of their individual lactate threshold at four pedaling rates (40, 60, 80, 100 rpm) with three different crank lengths (145, 170, and 195 mm). The combination of four pedaling rates and three crank lengths produced 12 pedal speeds ranging from 0.61 to 2.04 m/s. Metabolic cost was determined by indirect calorimetery, and power output and pedaling rate were recorded. A stepwise multiple linear regression procedure selected mechanical power output, pedal speed, and pedal speed squared as the main determinants of metabolic cost (R(2) = 0.99 +/- 0.01). Neither pedaling rate nor crank length significantly contributed to the regression model. The cost of unloaded cycling and delta efficiency were 150 metabolic watts and 24.7%, respectively, when data from all crank lengths and pedal speeds were included in a regression. Those values increased with increasing pedal speed and ranged from a low of 73 +/- 7 metabolic watts and 22.1 +/- 0.3% (145-mm cranks, 40 rpm) to a high of 297 +/- 23 metabolic watts and 26.6 +/- 0.7% (195-mm cranks, 100 rpm). These results suggest that mechanical power output and pedal speed, a marker for muscle shortening velocity, are the main determinants of metabolic cost during submaximal cycling, whereas pedaling rate (i.e., activation-relaxation rate) does not significantly contribute to metabolic cost.     

Mechanical muscular power output and work during ergometer cycling at different work loads and speeds

The aim of the study was to calculate the magnitude of the instantaneous muscular power output at the hip, knee and ankle joints during ergometer cycling at different work loads and speeds. Six healthy subjects pedalled a weight-braked cycle ergometer at 0, 120 and 240 W at a constant speed of 60 rpm. The subjects also pedalled at 40, 60, 80 and 100 rpm against the same resistance, giving power outputs of 80, 120, 160 and 200 W respectively. The subjects were filmed with a cine-film camera, and pedal reaction forces were recorded from a force transducer mounted in the pedal. The muscular work for the hip, knee and ankle joint muscles was calculated using a model based upon dynamic mechanics and described elsewhere. The total work during one pedal revolution significantly increased with increased work load but did not increase with increased pedalling rate at the same braking force. The relative proportions of total positive work at the hip, knee and ankle joints were also calculated. Hip and ankle extension work proportionally decreased with increased work load. Pedalling rate did not change the relative proportion of total work at the different joints.     

Optimal design parameters of the bicycle-rider system for maximal muscle power output

The purpose of this study was to find the optimal values of design parameters for a bicycle-rider system (crank length, pelvic inclination, seat height, and rate of crank rotation) which maximize the power output from muscles of the human lower limb during bicycling. The human lower limb was modelled as a planar system of five rigid bodies connected by four smooth pin joints and driven by seven functional muscle groups. The muscles were assumed to behave according to an adapted form of Hill's equation. The dependence of the average power on the design parameters was examined. The instantaneous power of each muscle group was studied and simultaneous activity of two seemingly antagonistic muscle groups was analyzed. Average peak power for one full pedal revolution was found to be around 1100 W. The upper body position corresponding to this peak power output was slightly reclined, and the pedalling rate was 155 rpm for a nominal crank length of 170 mm.     

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.     

Prediction of pedal forces in bicycling using optimization methods

The bicycle-rider system is modeled as a planar five-bar linkage with pedal forces and pedal dynamics as input. The pedal force profile input is varied, maintaining constant average bicycle power, in order to obtain the optimal pedal force profile that minimizes two cost functions. One cost function is based on joint moments and the other is based on muscle stresses. Predicted (optimal) pedal profiles as well as joint moment time histories are compared to representative real data to examine cost function appropriateness. Both cost functions offer reasonable predictions of pedal forces. The muscle stress cost function, however, better predicts joint moments. Predicted muscle activity also correlates well with myoelectric data. The factors that lead to effective (i.e. low cost) pedalling are examined. Pedalling effectiveness is found to be a complex function of pedal force vector orientation and muscle mechanics.     

Power output and work in different muscle groups during ergometer cycling

The aim of this study was to calculate the magnitude of the instantaneous muscular power output at the hip, knee and ankle joints during ergometer cycling. Six healthy subjects pedalled a weight-braked bicycle ergometer at 120 watts (W) and 60 revolutions per minute (rpm). The subjects were filmed with a cine camera, and pedal reaction forces were recorded from a force transducer mounted in the pedal. The muscular work at the hip, knee and ankle joint was calculated using a model based upon dynamic mechanics described elsewhere. The mean peak concentric power output was, for the hip extensors, 74.4 W, hip flexors, 18.0 W, knee extensors, 110.1 W, knee flexors, 30.0 W and ankle plantar flexors, 59.4 W. At the ankle joint, energy absorption through eccentric plantar flexor action was observed, with a mean peak power of 11.4 W and negative work of 3.4 J for each limb and complete pedal revolution. The energy production relationships between the different major muscle groups were computed and the contributions to the total positive work were: hip extensors, 27%; hip flexors, 4%; knee extensors, 39%; knee flexors, 10%; and ankle plantar flexors 20%.