Optimal initial position and technique for the front foot contact phase of cricket fast bowling: Commonalities between individual-specific simulations of elite bowlers

Group-based and individual-based studies in cricket fast bowling have identified common technique characteristics associated with ball release speed. The applicability of these findings to individual bowlers is often questioned, however, due to research approach limitations. This study aims to identify whether the optimal initial body position at front foot contact and subsequent technique to maximise ball release speed exhibit common characteristics for elite male cricket fast bowlers using individual-specific computer optimisations. A planar 16-segment whole-body torque-driven simulation model of the front foot contact phase of fast bowling was customised, evaluated, and the initial body position and subsequent movement pattern optimised, for ten elite male fast bowlers. The optimised techniques significantly increased ball release speed by 4.8 ± 1.3 ms-1 (13.5 ± 4.1%) and ranged between 37.8 and 42.9 ms-1, and in lower peak ground reaction forces and loading rates. Common characteristics were observed within the optimal initial body position with more extended front knees, as well as more flexion of the front and bowling arm shoulders than in current performances. Delays to the onset of trunk flexion, front arm and bowling arm shoulder extension, and wrist flexion were also common in the subsequent movement during the front foot contact phase. Lower front hip extensor and front shoulder flexor torques, as well as greater bowling shoulder extensor torques were also evident. This is useful knowledge for coach development, talent identification, and coaching practice.

Fifty years of performance-related sports biomechanics research

Over the past fifty years there has been considerable development in motion analysis systems and in computer simulation modelling of sports movements while the relevance and importance of functional variability of sports technique has become increasingly recognised. Technical developments for experimental work have led to increased, and still increasing, subject numbers. Increased subjects per study give better statistical power, the ability to utilise different data analyses, and thus the determination of more subtle and nuanced factors. The overall number of studies has also increased massively. Most actions in sport can, and have, been studied at some level with even the more challenging ones, such as player on player impacts, having some developing research. Computer simulation models of sports movements have ranged from simple (one or two segment) models to very complex musculoskeletal models and have used parameters ranging from the generic to individual-specific. Simple models have given insights into the key mechanics of movement while individual-specific model optimisations have been used to improve athlete performance. Our depth of understanding of the mechanics of sports techniques has increased across a wide range of sports. In the future there is likely to be more development and use of markerless motion capture, individual-specific model parameters, and more consideration of motor control aspects in the analysis of sports technique.

The limits of aerial and contact techniques for producing twist in reverse 1½ somersault dives

An angle-driven computer simulation model of aerial movement was used to determine the maximum amount of twist that can be produced in a reverse 1½ somersault dive from a three-metre springboard using various aerial and contact twisting techniques. The segmental inertia parameters of an elite springboard diver were used in the simulations and lower bounds were placed on the durations of arm and hip angle changes based on recorded performances of twisting somersaults. A limiting dive was identified as that producing the largest possible odd number of half twists. Simulations of the limiting dives were found using simulated annealing optimisation to produce the required amounts of somersault, tilt and twist after a flight time of 1.5 s. Additional optimisations were then run to seek solutions with the arms less adducted during the twisting phase. It was found that the upper limits ranged from 3½ to 5½ twists with arm abduction ranges lying between 8° and 23°. Similar results were obtained when the inertia parameters of two other springboard divers were used. It may be concluded that a reverse 1½ somersault dive using aerial asymmetrical arm and hip movements to produce 5½ twists is a realistic possibility. To accomplish this limiting dive the diver needs to be able to coordinate the timing of configurational changes with the progress of the twist with a precision of 10 ms or better.

The limits of aerial techniques for producing twist in forward 1½ somersault dives

An angle-driven computer simulation model of aerial movement was used to determine the maximum amount of twist that can be produced in a forward 1½ somersault dive from a three-metre springboard using various aerial twisting techniques. The segmental inertia parameters of an elite springboard diver were used in the simulations and lower bounds were placed on the durations of arm and hip angle changes based on recorded performances of twisting somersaults. A limiting dive was identified as that producing the largest possible whole number of twists. Simulations of the limiting dives were found using simulated annealing optimisation to produce the required amounts of somersault, tilt and twist after a flight time of 1.5 s. Additional optimisations were then run to seek solutions with the arms less adducted during the twisting phase. It was found that the upper limits ranged from two to five twists with arm abduction ranges lying between 6° and 17°. Similar results were obtained when the inertia parameters of two other springboard divers were used.

Misuse of "Power" and Other Mechanical Terms in Sport and Exercise Science Research

Despite the Système International d'Unitès (SI) that was published in 1960, there continues to be widespread misuse of the terms and nomenclature of mechanics in descriptions of exercise performance. Misuse applies principally to failure to distinguish between mass and weight, velocity and speed, and especially the terms "work" and "power." These terms are incorrectly applied across the spectrum from high-intensity short-duration to long-duration endurance exercise. This review identifies these misapplications and proposes solutions. Solutions include adoption of the term "intensity" in descriptions and categorizations of challenge imposed on an individual as they perform exercise, followed by correct use of SI terms and units appropriate to the specific kind of exercise performed. Such adoption must occur by authors and reviewers of sport and exercise research reports to satisfy the principles and practices of science and for the field to advance.

Validation of a subject specific 3-actuator torque-driven model in human vertical jumping

In this study, a forward dynamic subject specific 3-actuator torque-driven model of the human musculoskeletal system was created based on measurements of individual characteristics of a subject. Simulation results were compared with experimental vertical squat jumping with and without adding weights. By analyzing kinematic and kinetic experimental data at the instant of the toe-off for the same initial conditions, it was shown that a simple computer simulation using a suitable cost function could reproduce the real task performed by humans. This investigation is the first step in a wider project that will incorporate elastic components, and that will evaluate the advantages of the individual subject approach in modeling.

A comparison of Coulomb and pseudo-Coulomb friction implementations: Application to the table contact phase of gymnastics vaulting

In the table contact phase of gymnastics vaulting both dynamic and static friction act. The purpose of this study was to develop a method of simulating Coulomb friction that incorporated both dynamic and static phases and to compare the results with those obtained using a pseudo-Coulomb implementation of friction when applied to the table contact phase of gymnastics vaulting. Kinematic data were obtained from an elite level gymnast performing handspring straight somersault vaults using a Vicon optoelectronic motion capture system. An angle-driven computer model of vaulting that simulated the interaction between a seven segment gymnast and a single segment vaulting table during the table contact phase of the vault was developed. Both dynamic and static friction were incorporated within the model by switching between two implementations of the tangential frictional force. Two vaulting trials were used to determine the model parameters using a genetic algorithm to match simulations to recorded performances. A third independent trial was used to evaluate the model and close agreement was found between the simulation and the recorded performance with an overall difference of 13.5%. The two-state simulation model was found to be capable of replicating performance at take-off and also of replicating key contact phase features such as the normal and tangential motion of the hands. The results of the two-state model were compared to those using a pseudo-Coulomb friction implementation within the simulation model. The two-state model achieved similar overall results to those of the pseudo-Coulomb model but obtained solutions more rapidly.

Mechanics of the Fouetté turn

The Fouetté turn in classical ballet is performed repeatedly on one leg with swinging of the free limbs, producing a continued sequence of turns with one turn leading into the next. The purpose of this study was to determine the possible time history profiles of the twisting torque between the supporting leg and the remainder of the body that will allow continued performances of the Fouetté turn. Simulations were performed using a model which comprised the supporting leg and the remainder of the body to find torque profiles that maintain the initial angular velocity so that the state after one revolution is the same as the initial state. The solution space of torque profiles was determined for various rotation times and coefficients of friction between foot and floor. As the time for one revolution became shorter the solution space became smaller and for a given turn time there was a lower limit on the coefficient of friction. As the frictional coefficient became smaller the solution space became smaller and for a given coefficient there was a lower limit on the turn time. Turns of a given tempo can be performed on floors with different friction by modifying the twisting torque profile. When a turn is completed with a net change in angular velocity this can be compensated for in the next turn by adjusting the twisting torque profile.

Why do high jumpers use a curved approach?

Currently, all elite high jumpers use the Fosbury Flop technique with a curved approach. This suggests that the curved approach presents some clear advantage, although there is no general agreement upon the mechanism or the mechanics. This study aimed to determine the characteristics of the approach curve and to investigate how it contributes to the generation of somersault rotation. A simple theoretical model was used to demonstrate that a tightening approach curve would change the inward lean towards the centre of the curve into outwards lean. Three-dimensional video analysis was used to record the performances of two elite male high jumpers in competition. It was found that in each case the radius of the approach curve and the inward lean angle both decreased towards the end of the approach. The amount of outward lean angular velocity generated was shown to be a major proportion of the required somersault angular velocity for a jump. It was concluded that the main advantage of a curved approach was that it resulted in the generation of somersault velocity providing the curve tightened towards the end of the approach.

Coping with perturbations to a layout somersault in tumbling

Tumbling is a dynamic movement requiring control of the linear and angular momenta generated during the approach and takeoff phases. Both of these phases are subject to some variability even when the gymnast is trying to perform a given movement repeatedly. This paper used a simulation model of tumbling takeoff to establish how well gymnasts can cope with perturbations of the approach and takeoff phases. A five segment planar simulation model with torque generators at each joint was developed to simulate tumbling takeoffs. The model was customised to an elite gymnast by determining subject specific inertia and torque parameters and a simulation was produced which closely matched a performance of a layout somersault by the gymnast. The performance of a layout somersault was found to be sensitive to the approach characteristics and the activation timings but relatively insensitive to the elasticity of the track and maximum muscle strength. Appropriate variation of the activation timings used during the takeoff phase was capable of coping with moderate perturbations of the approach characteristics. A model of aerial movement established that variation of body configuration in the flight phase was capable of adjusting for takeoff perturbations that would lead to rotation errors of up to 8%. Providing the errors in perceiving approach characteristics are less than 5% or 5 degrees and the errors in timing activations are less than 7ms, perturbations in the approach can be accommodated using adjustments during takeoff and flight.

The margin for error when releasing the high bar for dismounts

In Men's Artistic Gymnastics the current trend in elite high bar dismounts is to perform two somersaults in an extended body shape with a number of twists. Two techniques have been identified in the backward giant circles leading up to release for these dismounts (J. Biomech. 32 (1999) 811). At the Sydney 2000 Olympic Games 95% of gymnasts used the "scooped" backward giant circle technique rather than the "traditional" technique. It was speculated that the advantage gained from the scooped technique was an increased margin for error when releasing the high bar. A four segment planar simulation model of the gymnast and high bar was used to determine the margin for error when releasing the bar in performances at the Sydney 2000 Olympic Games. The eight high bar finalists and the three gymnasts who used the traditional backward giant circle technique were chosen for analysis. Model parameters were optimised to obtain a close match between simulated and actual performances in terms of rotation angle (1.2 degrees ), bar displacements (0.014 m) and release velocities (2%). Each matching simulation was used to determine the time window around the actual point of release for which the model had appropriate release parameters to complete the dismount successfully. The scooped backward giant circle technique resulted in a greater margin for error (release window 88-157 ms) when releasing the bar compared to the traditional technique (release window 73-84 ms).

A method for synchronising digitised video data

This paper presents a general method for synchronising digitised video data using a mathematical approach based upon the direct linear transformation reconstruction technique. The method was tested using digitised data from genlocked video recordings of gymnastic vaulting, tumbling, high bar and rings. The mean synchronisation error was less than 0.002 s for vaulting and less than 0.001 s for the other activities.

A two-segment simulation model of long horse vaulting

The optimum pre-flight characteristics of the Hecht and handspring somersault vaults were determined using a two-segment simulation model. The model consisted of an arm segment and a body segment connected by a frictionless pin joint, simulating the vault from the Reuther board take-off through to landing. During horse contact, shoulder torque was set to zero in the model. Five independent pre-flight variables were varied over realistic ranges and an objective function was maximized to find the optimum pre-flight for each vault. The Hecht vault required a low trajectory of the mass centre during pre-flight, with a low vertical velocity of the mass centre and a low angular velocity of the body at horse contact. In contrast, the optimum handspring somersault required a high pre-flight trajectory, with a high angular velocity of the body and a high vertical velocity at horse contact. Despite the simplicity of the model, the optimum pre-flights were similar to those used in competitive performances.

Measuring running speed using photocells

Photocell timing systems are used routinely to measure running speeds. In this study, the accuracy of such systems was evaluated using centre of mass speed estimates from three-dimensional video analysis as criteria. One subject ran at five nominal speeds (5-9 m x s(-1)) for each of five separations (1.6-2.4 m) between consecutive photocells. Running speeds were calculated from the photocell data using single beam and double beam systems. For single beam systems, the start of the first break of a beam and the start of the longest break of a beam were used as trigger criteria. For double beam systems, the first occurrence of both beams being broken and the start of the longest double break were used as trigger criteria. Root mean square speed errors were smaller for the double beam systems. The longest break criterion gave smaller root mean square errors than the first break criterion. In general, errors in speed were smaller for greater photocell separations. An error of 0.1 m x s(-1) was achieved using a single beam system set at hip height with a longest break criterion for photocell separations of around two stride lengths. The advantage of using a double beam system is that it achieves this accuracy without the need to adjust photocell separation for different stride lengths.

Pre-flight characteristics of Hecht vaults

This study reports the techniques used by gymnasts to perform the Hecht vault and compares them with techniques used for the handspring somersault vault (Takei and Kim, 1990). Our main aim was to establish how the pre-flight characteristics of the Hecht vault influence post-flight performance. Data were obtained on 27 elite gymnasts performing the Hecht vault at the 1993 Canadian National Championships using two-dimensional video analysis with the direct linear transformation (DLT) technique. The maximum height reached by the mass centre during post-flight was significantly correlated (P < 0.001) with the vertical velocity of the mass centre and the body angle at horse contact. The backwards rotation of the body was significantly correlated (P = 0.015) with the shoulder angle at horse contact. The competition score was significantly correlated (P = 0.043) with the body angle at horse contact and was also related to the maximum height of the mass centre during post-flight. For the Hecht vault, the gymnasts had longer, lower and faster pre-flights with slower rotation at horse contact compared with the handspring somersault vaults.

The biomechanics of the human in flight

I used a computer simulation model of aerial movement to investigate the techniques for producing and controlling rotations of the human body during free flight. I found that the rotational motion can change from a twisting somersault to a nontwisting somersault by flexing at the hips at a suitable time. Twist may be produced in the aerial phase by means of asymmetrical movements of arms or hips, which result in a tilting of the longitudinal axis away from the plane perpendicular to the angular momentum vector. Asymmetrical movements may also remove the tilt and stop the twist. Elite performances of twisting somersaults are characterized by a large contribution from aerial twisting techniques. A progression of movements is presented for learning a double somersault with one and a half twists in the second somersault.

The control of non-twisting somersaults using configuration changes

Theoretical analyses have shown that rotations of a rigid body about the principal axis corresponding to the intermediate principal moment of inertia are unstable. This poses a potential problem for gymnasts who perform double somersaults without twist in a layout configuration. A computer simulation model is used to investigate configurational strategies for controlling such movements. It is shown that the build up of twist is not reduced by abduction of the arms but can be controlled by adopting a configuration with sufficient body flexion. For somersaults with a straight body, control in the form of asymmetrical arm abduction accelerations, based upon twist angular velocity and angular acceleration, is capable of preventing a build up of twist providing that the feedback time delay is less than a quarter somersault.

The future of performance-related sports biomechanics research

An overview of performance-related research in sports biomechanics is presented describing the relevant techniques of data analysis and data processing together with the methods used in experimental and theoretical studies. Advances in data collection and processing techniques which are necessary for the future development of sports biomechanics research are identified. The difficulties associated with experimental studies in sports biomechanics are described with examples of the different approaches that have been used. The strengths and weaknesses of theoretical studies are discussed with examples drawn from a number of sports. It is concluded that progress in performance-related research will result from the application of a suitable combination of theoretical and experimental approaches to those sports in which technique is the primary requirement for success.

Application of the joint coordinate system to three-dimensional joint attitude and movement representation: a standardization proposal

The selection of an appropriate and/or standardized method for representing 3-D joint attitude and motion is a topic of popular debate in the field of biomechanics. The joint coordinate system (JCS) is one method that has seen considerable use in the literature. The JCS consists of an axis fixed in the proximal segment, an axis fixed in the distal segment, and a "floating" axis. There has not been general agreement in the literature on how to select the body fixed axes of the JCS. The purpose of this paper is to propose a single definition of the body fixed axes of the JCS. The two most commonly used sets of body fixed axes are compared and the differences between them quantified. These differences are shown to be relevant in terms of practical applications of the JCS. Argumentation is provided to support a proposal for a standardized selection of body fixed axes of the JCS consisting of the axis ê1 embedded in the proximal segment and chosen to represent flexion-extension, the "floating" axis ê2 chosen to represent ad-abduction, and the axis ê3 embedded in the distal segment and chosen to represent axial rotation of that segment. The algorithms for the JCS are then documented using generalized terminology.

Hand placement techniques in long horse vaulting

In this study, the effects of two different hand placement techniques used by gymnasts to perform Tsukahara and Kasamatsu long horse vaults were examined. Selected linear and angular flight descriptors were calculated to determine whether those gymnasts making initial hand contact on the end of the horse gained additional lift, range or rotation when compared to those gymnasts making the more traditional initial hand contact on top of the horse. Three-dimensional cine-film analysis using the Direct Linear Transformation (DLT) was used to obtain data on 17 elite gymnasts competing in the 1991 World Student Games at Sheffield, UK. The gymnasts were divided into two groups according to the techniques used: group E in which the first hand contact was made on the vertical surface of the near end and the second on the top of the horse, and group T in which both hands were placed on top of the horse. The vertical and horizontal motion of each gymnast's mass centre and the somersault rotation during pre-flight (board take-off to horse contact) and post-flight (horse take-off to ground landing) were determined. The projections of linear displacements of each gymnast's mass centre onto a vertical plane were determined from the three-dimensional mass centre co-ordinates, and somersault angles were calculated using the line joining the midpoints of each gymnast's shoulders and knees. Whole body mass centre linear velocity and somersault angular velocity were determined using quintic splines.(ABSTRACT TRUNCATED AT 250 WORDS)

Twisting techniques used by competitive divers

At the 1991 World Student Games, eight reverse 1 1/2 somersault dives with 2 1/2 twists were recorded during the men's finals in the 1 m and 3 m springboard diving competitions using two video cameras. Angles describing body configuration were determined from video data and were input, together with initial orientation angle values and angular momentum components, into a computer simulation model of aerial movement in order to predict body orientation in space. Mean absolute deviations between simulation and video after the completion of one twist were 0.02 rev for somersault, 2.3 degrees for tilt and 0.04 rev for twist. Contributions to the tilt angle after one twist were used as measures of the twisting potential of various techniques and were determined using simulations based on modifications of the video data. Seven of the eight competitors produced the majority of the tilt using aerial techniques which were predominantly asymmetrical movements of the arms and hips, although the mean contribution from contact techniques amounted to one-third of the total tilt.

The biomechanics of twisting somersaults. Part II: Contact twist

A simulation model and a rigid body model are used to investigate twisting initiated during the take-off or contact phase. It is shown that it is possible to produce a full twist solely by building up angular momentum in the arms during the contact phase. This method is only half as effective as building up momentum in the whole body during contact. The introduction of twist into a somersault changes the somersault rate by less than 1%. By timing arm adduction appropriately, it is possible to take advantage of nutation and boost the initial value of the tilt angle and so obtain a greater twist rate. Twist may be stopped by the action of piking, since the motion changes from the twisting mode to the wobbling mode of rigid body motion. Transition to and from these two modes can be used to increase or decrease the tilt angle and twist rate.

The biomechanics of twisting somersaults. Part III: Aerial twist

A simulation model and a rigid body model are used to evaluate aerial twisting techniques. It is found that when somersault is not present, a number of cycles of segment counter-rotation are required to produce one twist. When somersault is present, twist may be introduced by producing tilt using asymmetrical movements of the arms, chest or hips about the sagittal plane. The same asymmetrical movements may be used to remove tilt, although the effectiveness of these techniques is dependent upon body configuration and the direction of somersault.

The biomechanics of twisting somersaults. Part IV: Partitioning performances using the tilt angle

A method is presented for determining the contributions made by contact and aerial twisting techniques in filmed performances of twisting somersaults. An 11-segment simulation model is used to determine the effects of removing asymmetries about the sagittal plane. Tilt contributions are determined for four competitive movements performed by an elite trampolinist. It is found that even in movements in which the twist is evident at take-off, aerial techniques make a greater contribution than contact techniques.

The biomechanics of twisting somersaults. Part I: Rigid body motions

This series of four papers comprises a theoretical investigation into twisting somersaults. Both simple and complex mathematical models are used to provide an understanding of the mechanics of the production and removal of twist in somersaults. Various twisting techniques are evaluated and a method is developed for the partitioning of an actual performance into contributions from these twisting techniques. In Part I, analytical solutions for the torque-free rotational motion of a rigid body are derived. It is shown that there are two distinct modes of motion which may be characterized as a twisting somersault and a wobbling somersault. The phenomenon of unstable rotations about the intermediate principal axis is explained in terms of these two modes.

Mechanical analysis of the landing phase in heel-toe running

Results of mechanical analyses of running may be helpful in the search for the etiology of running injuries. In this study a mechanical analysis was made of the landing phase of three trained heel-toe runners, running at their preferred speed and style. The body was modeled as a system of seven linked rigid segments, and the positions of markers defining these segments were monitored using 200 Hz video analysis. Information about the ground reaction force vector was collected using a force plate. Segment kinematics were combined with ground reaction force data for calculation of the net intersegmental forces and moments. The vertical component of the ground reaction force vector Fz was found to reach a first peak approximately 25 ms after touch-down. This peak occurs because, in the support leg, the vertical acceleration of the knee joint is not reduced relative to that of the ankle joint by rotation of the lower leg, so that the support leg segments collide with the floor. Rotation of the support upper leg, however, reduces the vertical acceleration of the hip joint relative to that of the knee joint, and thereby plays an important role in limiting the vertical forces during the first 40 ms. Between 40 and 100 ms after touch-down, the vertical forces are mainly limited by rotation of the support lower leg. At the instant that Fz reaches its first peak, net moments about ankle, knee and hip joints of the support leg are virtually zero. The net moment about the knee joint changed from -100 Nm (flexion) at touch-down to +200 Nm (extension) 50 ms after touch-down. These changes are too rapid to be explained by variations in the muscle activation levels and were ascribed to spring-like behavior of pre-activated knee flexor and knee extensor muscles. These results imply that the runners investigated had no opportunity to control the rotations of body segments during the first part of the contact phase, other than by selecting a certain geometry of the body and muscular (co-)activation levels prior to touch-down.

Elongation and forces of ankle ligaments in a physiological range of motion

The purposes of this study were: (1) to measure the distances between the insertion sites of selected ankle ligament fibers, (2) to measure the force-elongation characteristics of isolated bone-ligament-bone preparations, and (3) to relate the force measurements to angular positions of the ankle. The findings can be used to discuss clinically the correlation between possible ligament injuries and associated foot movement. Three fresh cadaveric ankles were dissected to expose the anterior talofibular ligament, the calcaneofibular ligament, and the superficial deltoid ligament. The ankles were first mounted on a fixture, and insertion to insertion distances of the ligament fibers were measured for selected positions of the ankle/subtalar joint. Bone-ligament-bone preparations were then removed, returned to their anatomical length and uniaxial force-extension testing was performed. The forces in each ligament were recorded for distances corresponding to those measured in situ for various ankle positions. These results allowed: (1) estimation of the forces in these three ligaments in various ankle positions, (2) identification of positions where ligaments were carrying no force, and (3) identification of positions where they carry large forces. The clinical analysis reveals that the anterior talofibular ligament is sensitive to excessive plantarflexion or dorsiflexion, the calcaneofibular ligament is sensitive to excessive inversion or eversion as well as dorsiflexion or plantarflexion, and that the deltoid ligament appears to be sensitive to plantarflexion, external rotation, and eversion. The fact that all three ligaments tested demonstrated different ranges of tension supports the view that there are optimal positions for testing ankle ligament integrity.

The simulation of aerial movement--II. A mathematical inertia model of the human body

A mathematical inertia model which permits the determination of personalized segmental inertia parameter values from anthropometric measurements is described. The human body is modelled using 40 geometric solids which are specified by 95 anthropometric measurements. A 'stadium' solid is introduced for modelling the torso segments using perimeter and width measurements. This procedure is more accurate than the use of elliptical discs of given width and depth and permits a smaller number of such solids to be used. Inertia parameter values may be obtained for body models of up to 20 segments. Errors in total body mass estimates from this and other models are discussed with reference to the unknown lung volumes.

The simulation of aerial movement--III. The determination of the angular momentum of the human body

A method is presented for determining the angular momentum of the human body about its mass centre for general three-dimensional movements. The body is modelled as an 11 segment link system with 17 rotational degrees of freedom and the angular momentum of the body is derived as a sum of 12 terms, each of which is a vector function of just one angular velocity. This partitioning of the angular momentum vector gives the contribution due to the relative segmental movement at each joint rather than the usual contribution of each segment. A method of normalizing the angular momentum is introduced to enable the comparison of rotational movements which have different flight times and are performed by athletes with differing inertia parameters. Angular momentum estimates were calculated during the flight phases of nine twisting somersaults performed on trampoline. Errors in film digitization made large contributions to the angular momentum error estimates. For individual angular momentum estimates the relative error is estimated to be about 10% whereas for mean angular momentum estimates the relative error is estimated to be about 1%.

The simulation of aerial movement--IV. A computer simulation model

A computer simulation model of human airborne movement is described. The body is modelled as 11 rigid linked segments with 17 degrees of freedom which are chosen with a view to modelling twisting somersaults. The accuracy of the model is evaluated by comparing the simulation values of the angles describing somersault, tilt and twist with the corresponding values obtained from film data of nine twisting somersaults. The maximum deviations between simulation and film are found to be 0.04 revolutions for somersault, seven degrees for tilt and 0.12 revolutions for twist. It is shown that anthropometric measurement errors, from which segmental inertia parameters are calculated, have a small effect on a simulation, whereas film digitization errors can account for a substantial part of the deviation between simulation and film values.

The simulation of aerial movement--I. The determination of orientation angles from film data

Quantitative mechanical analyses of human movement require the time histories of the angles which specify body configuration and orientation. When these angles are obtained from a filmed performance they may be used to evaluate the accuracy of a simulation model. This paper presents a method of determining orientation angles and their rates of change from film data. The stages used comprise the synchronization of data obtained from two camera views, the determination of three-dimensional coordinates of joint centres, the calculation of an angle from a sequence of sine and cosine values and the curve fitting of angles using quintic splines. For each stage, other possible approaches are discussed. Original procedures are presented for obtaining individual error estimates of both the film data and the calculated angles to permit the automatic fitting of quintic splines for interpolation and differentiation and for deriving the time history of an angle as a continuous function from a sequence of sine and cosine values. The method is applied to a forward somersault with 1 1/2 twists and the average error estimate of 17 orientation angles is obtained as 2.1 degrees.

The appropriate use of regression equations for the estimation of segmental inertia parameters

Linear regression equations are commonly used in conjunction with experimental data to provide linear relationships between quantities which are dimensionally distinct. In many cases theoretical relationships between such quantities are known and can be used as a basis for non-linear regression equations. This study compares linear and non-linear approaches for estimating the segmental moments of inertia from anthropometric measurements using the data of Chandler et al. [Chandler et al. (1975) Investigation of inertial properties of the human body. AMRL Technical Report 74-137, Wright Patterson Air Force Base. OH.] Right limb data were used to derive the equations while left limb data were used as a cross-validation sample to evaluate the inertia estimates calculated from the equations. For the limb segments the standard error estimates had average values of 21% for the linear equations and 13% for the non-linear equations. Data on a 10 yr-old boy was used to compare the two approaches outside the sample range. The mean percentage residuals were 286% for the linear equations and 20% for the non-linear equations. A set of non-linear equations is provided.

Low back configuration changes following osteopathic therapy: A pilot study

The effects of one session of manipulation by an osteopath on lumbo-sacral configuration were examined in ten out-patients with low back pain. Each patient was measured three times, twice before and once immediately after treatment. In each measurement session the patient executed six forward or six lateral flexions whilst continuous primary, and associated secondary, rotations were recorded using a Coda Scanner. The effects of the treatment were also assessed subjectively by the osteopath and by the patients. Significant treatment effects, not necessarily improvements, were observed in the secondary asymmetry angles of five patients. All four patients judged by the osteopath to have responded to his treatment were found included within these five. Patient evaluations of the effectiveness of treatment in improving movement were not closely related either to the judgements of the osteopath or to the measurements of change. Relevance This study seeks to establish the feasibility of measuring and evaluating the changes arising from the effects of osteopathic manipulation with a view to establishing future collaborative studies to determine the effects of manipulation.

A method for the assessment of area-elastic surfaces

A method is presented for the evaluation of area-elastic surfaces using two subject tests. Deformations and jump heights are determined for 12 sprung floor samples to accuracies of 0.12 mm and 0.4 cm respectively, using filming techniques. It is found that the deformation of a floor sample is dependent on both the subject group and the dimensions of the floor sample. The method showed significant differences in deformation values of the 12 floor samples but only small differences in jump heights.

The influence of construction strategies of sprung surfaces on deformation during vertical jumps

The purpose of this paper is to assess the influence of variations in the construction of area-elastic surfaces on the local deformation of these surfaces during an actual movement of athletes. Area-elastic surfaces were systematically varied in construction to allow the discussion of the influence of: (a) the number; (b) the spacing of the sleepers; (c) the material of the lowest sleeper; (d) variations of the second layer; (e) variations of the top surface; and (f) addition of a special padding element between the first and second sleepers on maximum deformation. Deformation data were collected using high-speed film from a group of recreational athletes and a group of national team athletes (volleyball) performing a drop jump. The differences in maximum deformation between the various surfaces tested were about 100% from the lowest to the highest value for the recreational athletes and about 1,000% for the national team athletes. The differences in deformation were primarily influenced by the number of sleepers used and/or by construction elements which are close to the top of the surface (top layer, second layer, add rubber padding, number of sleepers). The one sleeper system consistently had the lowest values of maximum deformation.

Biomechanical aspects of playing surfaces

The purpose of this paper is to discuss some biomechanical aspects of playing surfaces with special focus on (a) surface induced injuries, (b) methodologies used to assess surfaces and (c) findings from various sports. The paper concentrates primarily on questions related to load on the athlete's body. Data from epidemiological studies suggest strongly that the surface is an important factor in the aetiology of injuries. Injury frequencies are reported to be significantly different for different surfaces in several sports. The methodologies used to assess surfaces with respect to load or performance include material tests and tests using experimental subjects. There is only little correlation between the results of these two approaches. Material tests used in many standardized test procedures are not validated which suggests that one should exercise restraint in the interpretation of these results. Point elastic surfaces are widely studied while area elastic surfaces have received little attention to date. Questions of energy losses on sport surfaces have rarely been studied scientifically.

The damaging punch

The mechanical properties of a boxing punch have been determined using several techniques. The results are consistent with the medical consequences of boxing discussed in the report of the Board of Science and Education Working Party on boxing. Data were gathered from a world ranked British professional heavyweight, Frank Bruno, as he punched an instrumented, padded target mass suspended as a ballistic pendulum. Within 0.1 s of the start the punch had travelled 0.49 m and attained a velocity on impact of 8.9 m/s. The peak force on impact of 4096N (0.4 ton), attained within 14 ms of contact, represents a blow to the human head of up to 6320N (0.63 ton). The transmitted impulse generated an acceleration of 520 m/s2 (53 g) in the target head. For comparison an equivalent blow would be delivered by a padded wooden mallet with a mass of 6 kg (13 lbs) if swung at 20 mph.