Measurement of contact forces on a kayak ergometer with a sliding footrest–seat complex

Sports Eng (2009) 11:67–73 DOI 10.1007/s12283-008-0011-2 ORIGINAL ARTICLE Measurement of contact forces on a kayak ergometer with a sliding footrest–seat complex Mickaël Begon Æ Floren Colloud Æ Patrick Lacouture Published online: 26 November 2008 Ó International Sports Engineering Association 2008 Abstract Kinematic analysis is done by measurement of the position of bodies, followed by differentiation to get the accelerations of the centres of mass, and it is widely used in sport research. Another common approach is to measure the forces directly. Our intention here is to perform both a kinematic and a kinetic analysis of the same athleteequipment system, in this case an athlete on a sliding kayak ergometer, with the aim of exploring the errors that may occur with each measurement type. The kayak ergometer with a sliding trolley, instrumented by seven uniaxial force sensors and two goniometers, was placed in a filming area. The instrumentation was validated in the direction of the anteroposterior axis using Newton’s second law. Ten athletes paddled at 92 strokes per minute, following a stationary phase. The comparison between the net force and the time-derivative of the linear momentum indicated a friction level of about 20 N between the trolley and the frame. Other errors came mainly from the inertial parameters of the trunk. A first analysis of contact forces shows a large inter-subject variability, in particular for the forces applied to the footrest and the seat. M. Begon School of Sport and Exercise Sciences, Loughborough University, Ashby Road, Loughborough, Leicestershire LE11 3TU, UK M. Begon (&) Department of Kinesiology, University of Montreal, Canada Research Center, Sainte-Justine Hospital, Montreal, Canada e-mail: mickael.begon@umontreal.ca F. Colloud
P. Lacouture Laboratory of Solid Mechanics, CNRS UMR 6610, University of Poitiers, Poitiers, France Keywords Kayak
Ergometer
Instrumentation
Contact forces 1 Introduction Flatwater kayaking has been an Olympic event since the 1924 Paris Games. Performance is determined by the time to cover the race distance (i.e. 500 and 1,000 m for Olympic competitions). World-class performances require commitment from athletes over years to develop complex skills and abilities (e.g. coordination, force, physiological parameters). Kayaking is a cyclic movement composed of alternate left and right strokes. A stroke begins with the initial blade–water contact and ends with the blade–water contact on the opposite side. Hence each stroke includes a propulsion (or water phase) followed by an aerial phase and involves asymmetrical movements of the left and right limbs. For each stroke, the segments which are on the side of the propulsive blade are identified as the draw segments whereas those which are on the side of the aerial blade are identified as the thrust segments (Mann and Kearney 1980). The propulsion begins with a trunk rotation combined with a small bending of the trunk, the draw upper limb being fully extended whereas both lower limbs are flexed. The propulsion involves muscular actions for rotating the trunk, extending the draw knee while flexing the thrust knee and keeping both upper limbs as extended as possible. The propulsion phase ends at the blade exit, the thrust upper limb crossing over the athlete’s face and the draw hand reaching the level of the hip joint. As a result, kayaking requires actions of trunk, upper and lower limb muscles throughout a complex coordination. The kayaking performance can be modelled with the dynamics of the anteroposterior translation of the 68 Usually, the kinematics in the local reference frame is reproduced (see Begon et al. 2003 and Lamb 1989 for kayaking and rowing examples). The main problem is about the reproduction of contact forces on ergometer compared to the outdoor activity. On water, the difference in magnitude between the blade force and the total resistance creates change in the Kayak–Athlete–Paddle linear momentum. Conventional kayaking ergometers were constructed with static footrest and seat. The paddle tips force does not produce acceleration of the system but creates extra forces on the footrest or the seat (Begon and Colloud 2007). As for rowing (Elliot et al. 2001, Colloud et al. 2006) a solution could be to use a sliding trolley to reproduce the on-water dynamics. The purpose of the present study was to provide accurate quantitative information about both kinematics and contact forces when kayaking on an ergometer with a sliding trolley. 2 Materials and methods The instrumented system enabled the measure of the antero-posterior forces applied to the footrest, the seat and the paddle. It disassociated forces applied to the left and right sides, thus opening the way to the measurement of asymmetric actions of the draw and thrust segments. A new kayaking ergometer was constructed based on the Etindus (French) kayak ergometer in which an air brake simulated the water drag on the blade. The flywheel was driven by two self-winding inextensible ropes linked to a paddle (1.64 m long). This ergometer differed from conventional kayaking ergometers by having a trolley that slid forward and backward along a static frame (Fig. 1). The trolley included the footrest and the seat (Fig. 2). A bungee cord linked the trolley to the rear part of the frame. The set-up possibilities offered by the trolley (e.g. height of the feet Z Trolley X Y Bu he el 1.0 Fl yw Kayak–Athlete–Paddle system. The change in velocity of this system depends on the difference between the blade force and the total resistance (i.e. aerodynamic and hydrodynamic drag). The forces applied to the footrest and to the seat are internal forces of this system. The relationship of these internal forces with the performance is not obvious. The kayaker can (1) keep his lower limbs motionless by applying forces to the footrest that counterbalance the blade force or (2) use pedalling motions that cause a longitudinal pelvis rotation (Logan and Holt 1985). The lower limb actions, added to those of the trunk and the upper limbs, increase the stroke length. A stroke technique that uses pelvis and trunk rotations around a vertical axis seems to be an adequate co-ordination to improve the performance in kayaking. However, in both cases, differences in force distribution at the contact points of the athlete with the kayak can produce the same kinematics because the forces applied to the footrest and the seat can have opposite sign. A performance assessment based on mechanical quantities requires simultaneous kinematics and kinetics data collection. To our knowledge, the instrumentation necessary for this complete investigation suitable for water and laboratory tests has not yet been developed. Kinematics investigations were initiated using ergometers. Mann and Kearney (1980) and Campagna et al. (1982) analysed the path of the wrist, elbow and shoulder in the sagittal plane. However, pelvis, trunk and upper limbs kinematics can not be assumed to be planar. Accurate measurement of the three-dimensional (3D) kinematics is difficult, specifically on-water (Sanders and Kendal 1992b) as this requires at least two calibrated cameras and a large filming area. In spite of these difficulties, Kendal and Sanders (1992, 1992a) reported on-water 3D descriptive analyses over a full stroke. On-water kinematics acquisition over successive cycles of the lower limbs, which are hidden by the cockpit of the kayak, remains challenging for the future. The scientific literature reports very few analyses of athletes’ contact forces. The main reasons concern complexity in the measurement of the blade forces (Aitken and Neal 1992) and the need of construction of robust and waterproof instrumentation. Petrone et al. (1998) designed a four-component dynamometric footrest and a six-component dynamometric seat used both on-water and on ergometer. This instrumentation measured the forces generated by athletes at three contact points (i.e. each foot and the seat). Faced with similar difficulties, outdoor sport activities (e.g. cycling, running, rowing) used ergometers. Ergometers are a reasonable alternative to field testing for training, evaluating athletes’ capacities and performing scientific investigations. Hence, 3D kinematics synchronised with contact forces are acquired in a sheltered environment. Using an ergometer to simulate a sport activity raises the question of the similarity between the two conditions. M. Begon et al. ni Go 0.2 et e om r me Fra 5m 5 3.0 e nge m 5m Fig. 1 The kayaking ergometer with the sliding trolley. Dimensions and marker locations are also shown Measurement of contact forces on a kayak ergometer with a sliding footrest–seat complex B A Fig. 2 3D views of the ergometer trolley. Middle general view of sliding trolley with the fixed footrest (a) and the adjustable seat (b). Detail view of the seat (left) and footrest (right) instrumentations: fixed part (1), force sensor (2) and part on the cross roller bearing slides (3) relative to the seat and distance between the seat and the feet) corresponded to those found by athletes on water. For each kayaking stroke, in the fixed reference frame (O, xyz), the Trolley–Athlete–Paddle system {TAP} was accelerated forward when the anteroposterior component of the paddle tip force was higher than the bungee cord tension (FB); otherwise {TAP} was decelerated. The kayaking ergometer was instrumented to measure the contact forces between the athlete and the ergometer (Figs. 1, 2) in the direction of the anteroposterior axis (x). To measure the asymmetrical forces applied to the footrest (FFx left FFx right ) and to the seat (FSx left and FSx right ), the footrest and seat were divided into left and right independent parts (Fig. 2). Each part was instrumented by a uniaxial force sensor (Kistler 9101A; measurement range 2,000 N, tolerance of overload 500 N, linearity \ ±2% FSO and hysteresis \ 1% FSO). The electrical charge generated by the piezoelectric sensor was converted into a proportional voltage by an industrial charge amplifier (Kistler Type 5038A). Since the feet could be strapped to the footrest, the athletes [S2, S3, S5] (see Table 2) were able to generate pushing and pulling actions. The sensors, placed between a fixed part and a part mounted on cross roller bearing slides to avoid friction, were preloaded to about 500 N at the footrest in line with the results of Petrone et al. (1998) and 1,000 N at the seat. The force sensors were calibrated in situ after final assembly (Table 1). The acceleration of the part on the bearing slides caused contact forces on the footrest and the seat due to their mass (1.01 and 3.00 kg for each seat and each footrest, respectively). From the second time-derivative of the trolley position, these contact forces were removed before any analysis. Table 1 Sensitivity [N/V] of the force sensors calibrated with the chain of acquisition Footrest Seat Paddle Right 215.0 191.0 105.9 Left 212.5 191.4 96.7 Bungee cord 96.2 69 To measure the force applied to the paddle tips (FPleft and FPright ), two load cells (Entran ELPM-T2 with IAM amplifier; measurement range 500 N, linearity and hysteresis\ ±0.15% FSO) were connected at the paddle tip in series to the two ropes that linked the shaft to the flywheel. The ropes slid into two Cardan joints placed on each side of the flywheel (Fig. 3). The two axes (azimuth h and elevation /) of each goniometer were instrumented by two oneturn linear potentiometers (Megatron MUS1900-10kX— linearity \ 2% FSO) to measure the rope orientations. Then the anteroposterior components (FPx left and FPx right ) of paddle tip forces were computed from force magnitudes and rope orientations. A threshold on the rope elevation (/0) was set to determine the relative paddle position with respect to a virtual water level. The water level was expressed with respect to the height of the seat and corresponded approximately to /0 = 0°. The tension of the bungee cord (FB), that linked the trolley to the frame, was acquired using a similar load cell (Entran ELPM-T2 with IAM amplifier). The zero references of the force sensors were collected before each athlete’s test procedure. The kinematics was captured by a motion-analysis system equipped with six infrared cameras (Saga3RT—Biogesta, France) located around the ergometer in high-angle shot positions (three on each side: front, side and back). The kinematics and analog data were synchronised and acquired at a sampling frequency of 50 and 1,000 Hz, respectively. Ten flatwater athletes with international experience (25 ± 2.5 years, 1.78 ± 0.07 m and 78.2 ± 9.4 kg), two females and eight males, volunteered to take part in this study. The frequency of their training ranged from 8 to 15 sessions a week. The participants completed the following test schedule. They performed a warm-up routine on this sliding ergometer until they were confident in kayaking with this new equipment. They were recorded during a trial that included static, starting and steady paddling phases. First, the athletes remained in a static position for 5 s and then they paddled for 40 s. They were advised to paddle at a constant pace of 92 strokes per minute (spm) given by a metronome. This pace rate is a basic cadence used during aerobic training (Szanto 2004). Eighteen reflective markers were placed on body landmarks following Winter’s anthropometric model (Winter 1990): head of metatarsal II, lateral malleolus, femoral condyle, greater trochanter, acromion process, olecranon, ulnar styloid, knuckle II middle finger, left and right tragus. They defined the positions of 14 body segments: feet, legs, thighs, trunk, arms, forearms, hands and head. The segment inertia parameters were estimated using the anthropometrical model of Winter (1990). Three extra markers were placed on the trolley and the paddle tips. In a multibody system with known external forces and kinematics, the 70 M. Begon et al. Table 2 Root mean square difference (N) calculated according to subject, system and trial phases Subjects Gender Mass (kg) Static Trolley Trolley–Athlete–Paddle Starting Steady Static Starting Steady 1 M 82.1 14 21 23 16 29 56 2 M 74.5 20 23 30 25 24 35 3 M 80.0 22 22 40 12 32 59 4 F 63.6 19 17 23 19 26 37 5 M 88.0 15 31 39 19 30 50 6 F 62.8 8 20 17 16 27 32 7 8 M M 75.6 86.9 20 20 21 29 32 38 17 13 27 25 39 35 9 M 90.0 29 30 33 21 34 59 10 M 78.4 43 32 40 25 34 46 Mean 21 ± 10 25 ± 5 32 ± 8 18 ± 4 29 ± 4 45 ± 11 Forces ranges sum 138 ± 133 757 ± 214 3063 ± 1716 57 ± 19 334 ± 62 431 ± 114 The sum of the range of forces gives information about the magnitude of external forces without considering direction Fig. 3 The arrows show the measured forces for both systems: Trolley and Trolley– Athlete–Paddle. Anteroposterior components of the paddle forces (FPx left and FPx right ) were computed from paddle forces ðFPleft and FPright ) and rope orientations (azimuth and elevation) given by the goniometers system of equations is over-determined. Thus, the measurement accuracy was assessed using Newton’s second law: the mechanical equality between the net force acting P on the multibody system ( Fext/S) and the time-derivative of the linear momentum of the multibody system S ðP_ S ¼ MS AS Þ in an inertial reference frame: X X Fext=S ¼ MS AS ¼ m i ai ð1Þ i where mi and ai are the mass and acceleration of the centre of mass of the ith part (i.e. body segment, paddle or trolley). Segment linear acceleration was obtained from the time histories of the segment centre of mass position by double differentiation with a 5-point numerical differentiator. Previous to this, raw kinematics data were filtered by a bi-directional second order Butterworth filter (cut-off frequency 6 Hz). According to the ergometer instrumentation, two mechanical systems were defined (Fig. 3): Trolley {T} and Trolley–Athlete–Paddle {TAP} and used to validate the different elements of the instrumentation. To obtain the {T} dynamics, only one reflective marker and five force sensors were necessary, whereas the paddle tip forces, the bungee cord tension and the segment inertial parameters were involved in the {TAP} dynamics calculation. The friction between the trolley and the frame as well as the air resistance were assumed to be zero. Newton’s second law, applied to both systems in the direction of the anteroposterior axis, yields respectively: FFx left þ FFx right þ FSx left þ FSx right þ FBx ¼ mT axT ð2Þ FPx left þ FPx right þ FBx ¼ mT axT þ mA axA þ mP axP ð3Þ To validate the instrumentation, all residual forces (E) were evaluated (Kingma et al. 1996) by: X X Fext=S þ E ¼ m i ai ð4Þ i The root mean square of E (RMSe) gave a value representing the residual forces over the known time Measurement of contact forces on a kayak ergometer with a sliding footrest–seat complex 200 100 0 -100 -200 200 100 0 -100 -200 [N] Static phase Starting phase Stable phase Trolley-Athlete-Paddle Trolley Net force Time derivative linear momentum periods: static, starting and steady phases. RMSe was compared to the inaccuracy of the time-derivative of the linear momentum. The motion analysis accuracy was determined by means of a wand with two markers placed at a known distance (345 mm) moved throughout the measurement volume. RMSe values between the three phases (static, starting and steady paddling) were also compared using nonparametric Wilcoxon tests that revealed statistical differences at a probability level of 1% (p \ 0.01). time Right side Left side Pushing 1. Footrest [N] Fig. 4 Net force and timederivative of linear momentum for the three phases (static, starting and steady paddling) and for both systems: Trolley and Trolley–Athlete–Paddle for trial of subject 2 71 600 400 200 0 -200 Pushing The average RMSe during the static phase was about 20 N (Table 2). The time-derivative of the linear momentum fluctuated around 0 N while the net force showed negative values for each system and each subject (Fig. 4). This difference remained constant for {T} whatever the phase (p [ 0.01). By contrast, RMSe for {TAP} increased significantly between the consecutive phases. However, values were less important than the cinematographic inaccuracy (the only exception was for S10 during the static phase). The maximal error in the inter-marker distance of the wand was 5.5 mm, with an error about 0.615 mm for each co-ordinate. Thus, the accuracy of the acceleration was estimated at 1.54 ms-2. As a result, the time-derivative of the linear momentum was inaccurate to 40 and 110 N for {T} and {TAP} respectively. For {TAP}, the inaccuracy increased with athlete’s mass. The RMSe for {TAP} represented a low percentage of the sum of the P range of forces ( iDFi where DFi = FPi max-FPi min) that reached an average of 3,063 N for {T} and 431 N for {TAP} in the steady paddling phase. The curves for the left and the right side forces generated at the paddle, the footrest and the seat showed antisymmetric patterns (Fig. 5). The highest forces were collected on the footrest, following by the seat and the paddle. The average peak forces (min, max) applied by one foot, one ischium and both ischia were [-300; 865], [-590; 145] and [-576; 50] newtons, respectively. The peak values specific to each kayaker are summarized in Table 3. The peak values occurred in the following time sequence: paddle (around the paddle verticality, i.e. when 400 200 0 -200 Pulling 600 3. Paddle [N] 3 Results 2. Seat [N] 600 400 200 0 0 20 40 60 Cycle [%] 80 100 0 20 40 60 Cycle [%] 80 100 Fig. 5 Mean curves of the forces measured by the sensors for the population of elite athletes (bold lines) with 95% confidence intervals above and below (thin lines) for the left and right footrests (top), seats (middle) and paddle tips (bottom). The forces were averaged and time normalized to 100% of the kayaking cycle. The cycle begins with the entry of the right blade. Figures of athletes and vertical dashed lines indicate the three characteristics positions (entry, verticality and exit) for the left and right strokes. the paddle projection on the sagittal plane is vertical), foot and seat. FxP was positive before the blade entry and the value given by the sensors of the seat and footrest could be negative corresponding to traction forces. 4 Discussion Newton’s second law was applied to both {TAP} and {T} multibody systems to assess the measurement accuracy. As 72 M. Begon et al. Table 3 Peak values (min, max) of the contact forces (N) measured by the sensors at the footrest, seat, bungee cord and paddle for each subject during the steady paddling phase Subjects Footrest Seat Bungee Paddle 1 [-15, 294] [-94, 301] [67, 93] [0, 273] 2 [-32, 521] [17, 357] [67, 98] [0, 292] 3 4 [-42, 815] [-16, 479] [-98, 588] [-10, 325] [63, 95] [54, 79] [0, 309] [0, 181] 5 [-36, 429] [-116, 439] [59, 93] [0, 305] 6 [-25, 322] [-60, 302] [58, 69] [0, 164] 7 [-28, 424] [-53, 231] [66, 97] [0, 292] 8 [14, 412] [0, 351] [67, 94] [0, 313] 9 [-9, 497] [-41, 265] [70, 104] [0, 331] 10 [-11, 469] [-34, 355] [64, 98] [0, 284] Except for the bungee cord, the peak values are for both the left and right sides RMSe is a global indicator of the accuracy, curve analysis (Fig. 4) gave complementary information about systematic or random differences. The analysis of the static phase for both systems highlighted an underestimated net force, whilst the time-derivative of the linear momentum fluctuated about the theoretical statics value of 0 N. The rope orientations inaccuracy, which gave a random error in FxP, did not explain the systematic error computed for the net force measurement; consequently, the friction between trolley and frame was not negligible. Since the residual force did not significantly increase for {T}, there should be more agreement with Newton’s second law—at low and high stroke rates—if friction was considered or reduced using linear ball (or cross roller) bearing slides. By contrast, the RMSe increased significantly for {TAP} during the trial (static, starting and steady phases). Other errors came from the time-derivative of the linear momentum of the multibody system, the numerical timederivation and the anthropometric model being both sources of error. In spite of signal processing, the noise was amplified by the calculation of acceleration. Further errors originated from the estimation of segment mass and centre of mass position. The trunk viewed as a single segment (defined by the greater trochanter and the acromion), is not suitable for further analysis of kayaking movement. The athlete’s trunk was bent forwards and rotated from left to right. In addition, the shoulder joint contributed to extend the paddle entry as far as possible. Thus, considering the trunk as a single segment does not sufficiently account for spine and sternoclavicular joint mobilities. Hatze (1980), Plagenhoef et al. (1983) and Yeadon (1990) proposed trunk models divided into four parts (abdomino-thorax, abdomino-pelvis and two shoulders) or three parts (thorax, abdomen and pelvis). These models could give a better correspondence between forces and kinematical values. This is also confirmed by previous Motion Capture studies with a kinematic analysis of shoulder–pelvis rotation as reported in Petrone et al. (2006). Nevertheless, the RMSe remained lower than the cinematographic inaccuracy for all subjects, systems and trial phases, with only one exception. The results of this experimental study were thus satisfactory and validated the instrumentation. The validation of the sliding ergometer gave information on contact forces for a population of elite athletes. Our values were noticeably different from those measured on water by Petrone et al. (1998). In their study, normal forces applied to the footrest ranged from -152 to 444 N and from -128 to 6 N for the seat at a stroke rate of 90 spm. The difference in the range of forces could be explained by the athletes’ different levels (4 versus 15 h training per week), by the tilt of the footrest and probably by the mechanism of the two ergometers (fixed versus sliding seat and footrest complex). The force applied to the footrest was higher for the draw foot and close to zero for the thrust foot. The athletes who used straps around the feet [S2, S3, S5] applied pulling actions to the footrest and the seat. These forces allowed pelvis rotation and compensated for the moment of the paddle tip force. The compression force measured on the seat indicated that the athletes applied extra forces to the footrest. The athletes seemed to anticipate the paddle tip force in order to avoid their knees collapsing when the paddle force increased sharply. Hence an increase in the paddle force decreased only the seat force and the athlete was able to continue the pelvis rotation. The paddle force was slightly positive before the blade–water contact. On the ergometer, the flywheel torque depends mainly on the paddle tip velocity and acceleration. In flatwater paddling, the blade should enter into the water with a velocity to offset the velocity of the boat. This paddle velocity created paddle force just before the time corresponding to blade– water contact. The elevation threshold (/0) defining the water plane is coherent. Moreover, the ropes were selfwinding to keep them in tension. Due to this tension, the paddle tip force was always positive. Therefore, it will be important for the estimation of the propulsion to assert a null force outside the water phase. This description of average curves must be moderated in regard to the large confidence intervals, in particularly for FxF and FxS. Although each athlete reproduced precisely the contact force time histories for each cycle, there was a strong variability between athletes, the main difference being the magnitude of the forces. Although the athletes in the present study were of international level, they produced different force patterns. In competition, they paddled at similar boat velocities, except for the women (S4 and S6). The inter-subject variability of the blade force was mainly explained by the Measurement of contact forces on a kayak ergometer with a sliding footrest–seat complex difference in the subjects’ masses. The relationship between the boat velocity and the forces applied to the seat and footrest is not obvious. Indeed, the dynamics of the lower limbs is not completely constrained to maximise the performance. Contrary to rowing, actions of the lower limbs do not accelerate the system because the seat and the footrest are used to set the athlete in the boat. Thus, the direction of these forces could be opposite. Their large variability showed a range of techniques which may be related to the efficiency of the kayaking movement. This hypothesis is supported by Ackland et al. (2003) and Ong et al. (2005) who found no significant differences among Olympic athletes in physical size and equipment set-up. Moreover, Ong et al. (2006) showed that the performance decreased when the boat set-up varied from the preferred position. 5 Conclusion The present study explored the value and limits of a kayakergometer with a sliding trolley that was instrumented with uniaxial force sensors combined with a motion analysis system. This ergometer is suitable for assessing the performance using the paddle tip forces and the coordination between left and right sides. For example, the analysis of the pelvis rotation combined with the measurement of forces applied to footrest and seat could better explain the inter-athlete variability. Future practical applications of this methodology should help both athletes and coaches to gain a better understanding of how changes in technique relate to mechanical principles. Acknowledgments This study was support by a grant from the French Office of Youth and Sports. We thank those who participated in this study. 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