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

Differences in the mechanics of takeoff in reverse and forward springboard somersaulting dives

Forward and reverse springboard somersaulting dives use similar approaches with a hurdle step prior to the final board contact phase during which forward rotation is produced in forward takeoffs and backward rotation in reverse takeoffs. This study compared forward and reverse takeoffs for joint strength, activation complexity, technique kinematics, and rotation potential. A planar 8-segment torque-driven computer simulation model of springboard diving takeoff was used to determine isometric joint strength by matching performances of a forward 2½ somersault dive and a reverse 1½ somersault dive. Activation complexity for the reverse takeoff was increased to achieve a similar closeness of match as for the forward takeoff. Takeoff technique was optimised to maximise rotation potential of forward and reverse somersaulting dives. Kinematics at touchdown, lowest point and takeoff were compared for the optimised forward and reverse takeoff simulations. It was found that the optimised reverse somersaulting dive exhibited greater isometric strength for ankle plantarflexion and shoulder flexion, greater joint torque activation complexity for ankle plantarflexion and for knee flexion. There was also less forward motion during board depression, more hip extension and knee flexion during the later stages of board recoil, less capacity for rotation potential, and greater vertical velocity at takeoff.

A Conceptual Blueprint for Making Neuromusculoskeletal Models Clinically Useful

The ultimate goal of most neuromusculoskeletal modeling research is to improve the treatment of movement impairments. However, even though neuromusculoskeletal models have become more realistic anatomically, physiologically, and neurologically over the past 25 years, they have yet to make a positive impact on the design of clinical treatments for movement impairments. Such impairments are caused by common conditions such as stroke, osteoarthritis, Parkinson’s disease, spinal cord injury, cerebral palsy, limb amputation, and even cancer. The lack of clinical impact is somewhat surprising given that comparable computational technology has transformed the design of airplanes, automobiles, and other commercial products over the same time period. This paper provides the author’s personal perspective for how neuromusculoskeletal models can become clinically useful. First, the paper motivates the potential value of neuromusculoskeletal models for clinical treatment design. Next, it highlights five challenges to achieving clinical utility and provides suggestions for how to overcome them. After that, it describes clinical, technical, collaboration, and practical needs that must be addressed for neuromusculoskeletal models to fulfill their clinical potential, along with recommendations for meeting them. Finally, it discusses how more complex modeling and experimental methods could enhance neuromusculoskeletal model fidelity, personalization, and utilization. The author hopes that these ideas will provide a conceptual blueprint that will help the neuromusculoskeletal modeling research community work toward clinical utility.

A Review of Forward-Dynamics Simulation Models for Predicting Optimal Technique in Maximal Effort Sporting Movements

The identification of optimum technique for maximal effort sporting tasks is one of the greatest challenges within sports biomechanics. A theoretical approach using forward-dynamics simulation allows individual parameters to be systematically perturbed independently of potentially confounding variables. Each study typically follows a four-stage process of model construction, parameter determination, model evaluation, and model optimization. This review critically evaluates forward-dynamics simulation models of maximal effort sporting movements using a dynamical systems theory framework. Organismic, environmental, and task constraints applied within such models are critically evaluated, and recommendations are made regarding future directions and best practices. The incorporation of self-organizational processes representing movement variability and “intrinsic dynamics” remains limited. In the future, forward-dynamics simulation models predicting individual-specific optimal techniques of sporting movements may be used as indicative rather than prescriptive tools within a coaching framework to aid applied practice and understanding, although researchers and practitioners should continue to consider concerns resulting from dynamical systems theory regarding the complexity of models and particularly regarding self-organization processes.

The Structure of Selected Basic Acrobatic Jumps

The aim of this study was to investigate the relationships between the internal and external structure of basic acrobatic jumps. Eleven healthy elite artistic gymnasts (9 female, 2 male) participated in this study. Participants performed the following basic ‘acrobatic’ jumps: a tucked backward somersault (TS), a piked backward somersault (PS), and a countermovement jump (CMJ). Furthermore, female gymnasts also performed the backward handspring (HS), taking off and then landing on their hands in the same place – a specific jump only for women. All jumps were initiated from a stationary upright posture and with an arms swing. Six infrared cameras, synchronized with a module for wireless measurement of the electrical activity of eight muscles, and the force plate were used. Infrared camera-recordings were made in order to obtain kinematic variables describing the movement structure of the acrobatic jumps. These variables may explain the characteristics of muscle activation (the internal structure of the movement) and ground reaction force (the external-kinetic structure of the movement). However, for various technical reasons, it was not possible to register all the specified jumps in the protocol. Moreover, the distribution normalities, estimated by the Kolmogorov-Smirnov test, differed between variables. Therefore, to compare the data, the pair-wise nonparametric Wilcoxon Signed-Ranks Test was applied. The CMJ showed the highest level of vertical impulse, velocity, and displacement followed by the TS, PS, and HS. In the take-off phase of acrobatic jumps with rotation the average muscle activation levels of the biceps femoris were significantly higher and of the rectus femoris significantly lower than in the countermovement jump.

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.

Maximising forward somersault rotation in springboard diving

Performance in the flight phase of springboard diving is limited by the amounts of linear and angular momentum generated during the takeoff phase. A planar 8-segment torque-driven simulation model combined with a springboard model was used to investigate optimum takeoff technique for maximising rotation in forward dives from the one metre springboard. Optimisations were run by varying the torque activation parameters to maximise forward rotation potential (angular momentum × flight time) while allowing for movement constraints, anatomical constraints, and execution variability. With a constraint to ensure realistic board clearance and anatomical constraints to prevent joint hyperextension, the optimised simulation produced 24% more rotation potential than a simulation matching a 2½ somersault piked dive. When 2 ms perturbations to the torque onset timings were included for the ankle, knee and hip torques within the optimisation process, the model was only able to produce 87% of the rotation potential achieved in the matching simulation. This implies that a pre-planned technique cannot produce a sufficiently good takeoff and that adjustments must be made during takeoff. When the initial onset timings of the torque generators were unperturbed and 10 ms perturbations were introduced into the torque onset timings in the board recoil phase, the optimisation produced 8% more rotation potential than the matching simulation. The optimised simulation had more hip flexion and less shoulder extension at takeoff than the matching simulation. This study illustrates the difficulty of including movement variability within performance optimisation when the movement duration is sufficiently long to allow feedback corrections.

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.

Twist limits for late twisting double somersaults on trampoline

An angle-driven computer simulation model of aerial movement was used to determine the maximum amount of twist that could be produced in the second somersault of a double somersault on trampoline using asymmetrical movements of the arms and hips. Lower bounds were placed on the durations of arm and hip angle changes based on performances of a world trampoline champion whose inertia parameters were used in the simulations. The limiting movements were identified as the largest possible odd number of half twists for forward somersaulting takeoffs and even number of half twists for backward takeoffs. Simulations of these two limiting movements were found using simulated annealing optimisation to produce the required amounts of somersault, tilt and twist at landing after a flight time of 2.0s. Additional optimisations were then run to seek solutions with the arms less adducted during the twisting phase. It was found that 3½ twists could be produced in the second somersault of a forward piked double somersault with arms abducted 8° from full adduction during the twisting phase and that three twists could be produced in the second somersault of a backward straight double somersault with arms fully adducted to the body. These two movements are at the limits of performance for elite trampolinists.

Optimal technique for maximal forward rotating vaults in men's gymnastics

In vaulting a gymnast must generate sufficient linear and angular momentum during the approach and table contact to complete the rotational requirements in the post-flight phase. This study investigated the optimization of table touchdown conditions and table contact technique for the maximization of rotation potential for forwards rotating vaults. A planar seven-segment torque-driven computer simulation model of the contact phase in vaulting was evaluated by varying joint torque activation time histories to match three performances of a handspring double somersault vault by an elite gymnast. The closest matching simulation was used as a starting point to maximize post-flight rotation potential (the product of angular momentum and flight time) for a forwards rotating vault. It was found that the maximized rotation potential was sufficient to produce a handspring double piked somersault vault. The corresponding optimal touchdown configuration exhibited hip flexion in contrast to the hyperextended configuration required for maximal height. Increasing touchdown velocity and angular momentum lead to additional post-flight rotation potential. By increasing the horizontal velocity at table touchdown, within limits obtained from recorded performances, the handspring double somersault tucked with one and a half twists, and the handspring triple somersault tucked became theoretically possible.

An object oriented implementation of the Yeadon human inertia model

We present an open source software implementation of a popular mathematical method developed by M.R. Yeadon for calculating the body and segment inertia parameters of a human body. The software is written in a high level open source language and provides three interfaces for manipulating the data and the model: a Python API, a command-line user interface, and a graphical user interface. Thus the software can fit into various data processing pipelines and requires only simple geometrical measures as input.

An object oriented implementation of the Yeadon human inertia model

We present an open source software implementation of a popular mathematical method developed by M.R. Yeadon for calculating the body and segment inertia parameters of a human body. The software is written in a high level open source language and provides three interfaces for manipulating the data and the model: a Python API, a command-line user interface, and a graphical user interface. Thus the software can fit into various data processing pipelines and requires only simple geometrical measures as input.

The limits of aerial twisting techniques in the aerials event of freestyle skiing

In the aerials event of freestyle skiing, athletes perform three somersaults with up to five twists. This study investigated the twisting limits of such movements using a computer simulation model of aerial movement. The abilities of various asymmetrical arm and hip techniques to produce twist during flight were investigated using 10 simulations to maximise twist and allow reorientation prior to landing. It was found that 4-6 twists could be produced during three somersaults. The main limiting factor was the increased whole body frontal moment of inertia due to the equipment which restricted the amount of tilt resulting from an asymmetrical arm movement. It was concluded that reductions in equipment mass might make such movements easier to achieve but would be unlikely to allow advances beyond the limits found.

The Effect of Cost Function on Optimum Technique of the Undersomersault on Parallel Bars

The undersomersault, or felge, to handstand on parallel bars has become an important skill in Men’s Artistic Gymnastics as it forms the basis of many complex variations. To receive no deductions from the judges, the undersomersault must be performed without demonstrating the use of strength to achieve the final handstand position. Two male gymnasts each performed nine undersomersaults from handstand to handstand while data were recorded using an automatic motion capture system. The highest and lowest scoring trials of each gymnast, as determined by four international judges, were chosen for further analysis. Three optimization criteria were used to generate undersomersault technique during the swing phase of the skill using a computer simulation model: minimization of peak joint torques, minimization of horizontal velocity before release, and maximization of angular momentum. The techniques used by both gymnasts could be explained using the second optimization criterion which facilitated further skill development. The first optimization criterion generated a technique advocated for beginners where strength might be expected to be a limiting factor. The third optimization criterion resulted in a different type of undersomersault movement of greater difficulty according to the FIG Code of Points.

Evaluation of a Subject-Specific, Torque-Driven Computer Simulation Model of One-Handed Tennis Backhand Ground Strokes

A torque-driven, subject-specific 3-D computer simulation model of the impact phase of one-handed tennis backhand strokes was evaluated by comparing performance and simulation results. Backhand strokes of an elite subject were recorded on an artificial tennis court. Over the 50-ms period after impact, good agreement was found with an overall RMS difference of 3.3° between matching simulation and performance in terms of joint and racket angles. Consistent with previous experimental research, the evaluation process showed that grip tightness and ball impact location are important factors that affect postimpact racket and arm kinematics. Associated with these factors, the model can be used for a better understanding of the eccentric contraction of the wrist extensors during one-handed backhand ground strokes, a hypothesized mechanism of tennis elbow.

Optimization of Backward Giant Circle Technique on the Asymmetric Bars

The release window for a given dismount from the asymmetric bars is the period of time within which release results in a successful dismount. Larger release windows are likely to be associated with more consistent performance because they allow a greater margin for error in timing the release. A computer simulation model was used to investigate optimum technique for maximizing release windows in asymmetric bars dismounts. The model comprised four rigid segments with the elastic properties of the gymnast and bar modeled using damped linear springs. Model parameters were optimized to obtain a close match between simulated and actual performances of three gymnasts in terms of rotation angle (1.5°), bar displacement (0.014 m), and release velocities (<1%). Three optimizations to maximize the release window were carried out for each gymnast involving no perturbations, 10-ms perturbations, and 20-ms perturbations in the timing of the shoulder and hip joint movements preceding release. It was found that the optimizations robust to 20-ms perturbations produced release windows similar to those of the actual performances whereas the windows for the unperturbed optimizations were up to twice as large. It is concluded that robustness considerations must be included in optimization studies in order to obtain realistic results and that elite performances are likely to be robust to timing perturbations of the order of 20 ms.

Evaluation of a torque-driven model of jumping for height

This study used an optimization procedure to evaluate an 8-segment torque-driven subject-specific computer simulation model of the takeoff phase in running jumps for height. Kinetic and kinematic data were obtained on a running jump performed by an elite male high jumper. Torque generator activation timings were varied to minimize the difference between simulation and performance in terms of kinematic and kinetic variables subject to constraints on the joint angles at takeoff to ensure that joints remained within their anatomical ranges of motion. A percentage difference of 6.6% between simulation and recorded performance was obtained. Maximizing the height reached by the mass center during the flight phase by varying torque generator activation timings resulted in a credible height increase of 90 mm compared with the matching simulation. These two results imply that the model is sufficiently complex and has appropriate strength parameters to give realistic simulations of running jumps for height.

Biomechanical research in artistic gymnastics: a review

Biomechanical research into artistic gymnastics has grown substantially over the years. However, most research is still skill oriented with few tries at generalization. Consequently, our understanding of the principles and bases of the sport, although improved, is still marginal with gaps in knowledge about technique attributes throughout the sport. For that reason, this review begins with an attempt to identify important variables contributing to successful performance. The review is presented in clusters of work in similar apparatuses culminating in Tables offering an 'at a glance' summary of knowledge in each cluster. The last section of the review tries to give some direction to future biomechanical research in gymnastics in issues relating to data collection--two-dimensional or three-dimensional, image size, frame rate--and analysis, such as descriptive or explanatory, simulation and optimization, and statistical issues.

Modelling the parallel bars in men's artistic gymnastics

The modelling of the parallel bars-gymnast system is considered. A 2D frontal plane model for the parallel bars apparatus is developed, enabling technique and injury analysis to be undertaken when combined with an interacting gymnast body model. We also demonstrate how such a gymnast body model may be combined with the parallel bars model by use of a simplifying symmetry consideration about the gymnast's sagittal plane. This symmetry consideration implies that just half the gymnast body and one of the two bars, are needed in the total model. We found that midpoint vertical parallel bars dynamics may be modelled by three parameters, using a single damped spring-mass model with linear force-displacement characteristics. Horizontally, as opposed to the vertical direction, bar endpoints accounted for a substantial part (35%) of the midpoint movement, demanding two serially connected springs for this direction. One spring represented the absolute horizontal movement of the bar endpoints, while the other spring represented the superimposed horizontal movement of bar midpoint relative to the endpoints. Both horizontal springs had the same characteristics as the vertical spring, giving a total of nine parameters for the three-spring bar model. Bar parameters were estimated by fitting the modelled bar movements to corresponding measured movements caused by a 140 kg lateral pendulum below the bar midpoint. Validation was then undertaken by comparing model-predicted bar movements to corresponding measurements using lateral pendulums of 100 kg and 60 kg, respectively. Finally, a gymnast handstand position was modelled and used to compare model-predicted and measured bar oscillations following a somersault backwards to a handstand position. The model gave convincing predictions of bar movements both for the 100 kg (1 period, RMS error of 7.0 mm) and 60 kg (1 period, RMS error of 3.7 mm) pendulums, as well as for the somersault landing (2 periods, RMS error of 8.1 mm).

Determination of subject-specific model parameters for visco-elastic elements

The determination of subject-specific model parameter values is necessary in order for a computer simulation model of human motion to be evaluated quantitatively. This study used an optimisation procedure along with a kinematically driven simulation model of the contact phase in running jumps to determine the elastic parameters of segmental wobbling masses and the foot-ground interface. Kinetic and kinematic data were obtained on running jumps for height and distance performed by an elite male high jumper. Stiffness and damping coefficients of the visco-elastic elements in the model were varied until the difference between simulation and performance was minimised. Percentage differences of 6% and 9% between the simulated and recorded performances were obtained in the jumps for height and distance, respectively. When the parameters obtained from the jump for height were used in a simulation of the jump for distance (and vice versa), there was poor agreement with the recorded jump. On the other hand, a common set of visco-elastic parameters were obtained using the data from both recorded jumps resulting in a mean difference of only 8% (made up of 7% and 10%) between simulation and performance that was almost as good as the individual matches. Simulations were not overly sensitive to perturbations of the common set of visco-elastic parameters. It is concluded that subject-specific elastic parameters should be calculated from more than a single jump in order to provide a robust set of values that can be used in different simulations.

Maximal dismounts from high bar

In men's artistic gymnastics the triple straight somersault dismount from the high bar has yet to be performed in competition. The present study used a simulation model of a gymnast and the high bar apparatus (J. Appl. Biomech. 19(2003a) 119) to determine whether a gymnast could produce the required angular momentum and flight to complete a triple straight somersault dismount. Optimisations were carried out to maximise the margin for error in timing the bar release for a given number of straight somersaults in flight. The amount of rotation potential (number of straight somersaults) the model could produce whilst maintaining a realistic margin for error was determined. A simulation model of aerial movement (J. Biomech.23 (1990) 85) was used to find what would be possible with this amount of rotation potential. The model was able to produce sufficient angular momentum and time in the air to complete a triple straight somersault dismount. The margin for error when releasing the bar using the optimum technique was 28 ms, which is small when compared with the mean margin for error determined for high bar finalists at the 2000 Sydney Olympic Games (55 ms). Although the triple straight somersault dismount is theoretically possible, it would require close to maximum effort and precise timing of the release from the bar. However, when the model was required to have a realistic margin for error, it was able to produce sufficient angular momentum for a double twisting triple somersault dismount.

Factors influencing performance in the Hecht vault and implications for modelling

This paper investigated the factors that influence Hecht vault performance and assessed the level of model complexity required to give an adequate representation of vaulting. A five-segment planar simulation model with a visco-elastic shoulder joint and a torque generator at the shoulder joint was used to simulate the contact phase in vaulting. The model was customized to an elite gymnast by determining subject-specific segmental inertia and joint torque parameters. The simulation model was matched to a performance of the Hecht vault by varying the visco-elastic characteristics of the shoulders and the arm-horse interface and the activation time history of the shoulder torque generator until the best match was found. Perturbing the matching simulation demonstrated that appropriate initial kinematics are necessary for a successful performance. Fixing the hip and knee angles at their initial values had a small effect with 3 degrees less rotation. Applying shoulder torque during the contact phase also had a small effect with only a 7 degrees range in landing angles. Excluding the hand segment from the model was found to have a moderate effect with 15 degrees less rotation and the time of contact reduced by 38%. Removing shoulder elasticity resulted in 50 degrees less rotation. The use of a five-segment simulation model confirmed that the use of shoulder torque plays a minor role in vaulting performance and that having appropriate initial kinematics at touchdown is essential. However, factors such as shoulder elasticity and the hands which have previously been ignored also have a substantial influence on performance.

Optimal Knee Extension Timing in Springboard and Platform Dives from the Reverse Group

Optimized computer simulation, using a mathematical model of a diver, was employed to gain insight into the primary mechanical factors responsible for producing height and rotation in dives from the reverse group. The performance variable optimized was the total angular displacement of the diver as measured from last contact to the point where the diver's mass center passed the level of the springboard or platform. The times of onset, and lengths of activation for the joint torque actuators, were used as the control variables for the optimization process. The results of the platform simulation indicated that the magnitude of the hip torque was approximately twice that generated by the knee joint during the early extension phase of the takeoff. Most of the knee extension for the simulation model coincided with the period of reduced hip torque during the later phase of takeoff, suggesting that the knee torque served mainly to stabilize the lower limbs so that the force from the powerful hip extension could be delivered through to the platform. Maintaining a forward tilt of the lower legs (~50° from the horizontal) during hip and knee extension appeared to be paramount for successful reverse somersaults. Although the movement pattern exhibited by the springboard model was limited by the torque activation strategy employed, the results provided insight into the timing of knee extension. Peak knee extension torque was generated just prior to maximum springboard depression, allowing the diver's muscular efforts to be exerted against a stiffer board. It was also apparent that the diver must maintain an anatomically strong knee position (~140°) at maximum depression to resist the large upward force being exerted by the springboard against the diver's feet. The optimization process suggested that, as the number of reverse somersaults increases, both the angle of the lower legs with respect to the springboard and the angle of knee extension at completion of takeoff should decrease.

Maximising somersault rotation in tumbling

Performing complex somersaulting skills during the flight phase of tumbling requires the generation of linear and angular momenta during the approach and takeoff phases. This paper investigates how approach characteristics and takeoff technique affect performance with a view to maximising somersault rotation in tumbling. A five-segment planar simulation model, customised to an elite gymnast, was used to produce a simulation which closely matched a recorded performance of a double layout somersault by the elite gymnast. Three optimisations were carried out to maximise somersault rotation with different sets of initial conditions. Using the same initial linear and angular momentum as the double layout somersault and varying the joint torque activation timings allowed a double straight somersault to be performed with 19% more rotation potential than the actual performance. Increasing the approach velocity to a realistic maximum of 7 ms(-1) resulted in a 42% reduction in rotation potential when the activation timings were unchanged but allowed a triple layout somersault to be performed with an increase of 31% in rotation potential when activation timings were re-optimised. Increasing also the initial angular momentum to a realistic maximum resulted in a 4% reduction in rotation potential when the activation timings were unchanged but allowed a triple straight somersault to be performed with a further increase of 9% in rotation potential when activation timings were re-optimised. It is concluded that the limiting factor to maximising somersault rotation is the ability to generate high linear and angular velocities during the approach phase coupled with the ability to adopt consonant activation timings during the takeoff phase.

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).

Practical Use of Airborne Simulation in a Release-Regrasp Skill on the High Bar

The aim of this study was to objectively predict individual improvements in a release-regrasp tkatchev skill. The prediction was based on a kinematic analysis of failed and successful trials. The modification of release conditions, and the correction of hip and shoulder joint motions during the aerial phase of failed trials, were determined by considering the successful trials as target executions. Computer simulations were used to confirm the effect of the corrected parameters on the flight trajectory and angular motion of the body over the bar. The results indicated that when time of release is initiated earlier, this presents a major problem the gymnast must overcome in order to grasp the bar. Moreover, the moment when the body’s center of gravity is vertically above the bar represents a critical instant for the gymnast in initiating the hip and shoulder movements. The rotation motion analysis of the segments indicated that the stabilization motion of the upper limbs could be a good strategy for improving the failed tkatchev. This study showed that simple computer simulation using hypothetical data based upon real data could be an effective tool for improving acrobatic skills.

Evaluation of a Torque-Driven Simulation Model of Tumbling

The use of computer simulation models in studies of human movement is now widespread. Most of these models, however, have not been evaluated in a quantitative manner in order to establish the level of accuracy that may be expected. Without such an evaluation, little credence should be given to the published results and conclusions. This paper presents a simulation model of tumbling takeoffs which is evaluated by comparing the simulation output with an actual performance of an elite gymnast. A five-segment planar model was developed to simulate tumbling takeoffs. The model comprised rigid foot, leg, thigh, trunk + head, and arm segments with two damped linear springs to represent the elasticity of the tumbling track/ gymnast interface. Torque generators were included at the ankle, knee, hip, and shoulder joints in order to allow each joint to open actively during the takeoff. The model was customized to the elite gymnast by determining subject-specific inertia and torque parameters. Good agreement was found between actual and simulated tumbling performances of a double layout somersault with 1% difference in the linear and angular momenta at takeoff. Allowing the activation timings of the four torque generators to vary resulted in an optimized simulation that was some 0.32 m higher than the evaluation simulation. These simulations suggest the model is a realistic representation of the elite gymnast, since otherwise the model would either fail to reproduce the double layout somersault or would produce a very different optimized solution.

Experimental Simulation of an Airborne Movement: Applicability of the Body Segment Parameter Estimation Methods

The purpose of this study was twofold: (a) to investigate the effect of the method of body segment parameter (BSP) estimation on the accuracy of the experimental simulation of a complex airborne movement; and (b) to assess the applicability of selected BSP estimation methods in the experimental simulation. It was hypothesized that different BSP estimation methods would provide different simulation results. A sensitivity analysis was performed to identify the BSP items and segments responsible for the inter-method differences in the simulation accuracy. The applicability of the estimation methods was assessed based on the simulation results and the number of anthropometric parameters required. Ten BSP estimation methods classified into 3 groups (4 cadaver-based, 4 gamma mass scanning-based, and 2 geometric) were employed in a series of experimental simulations based on 9 double-somersault-with-full-twist H-bar dismounts performed by 3 male college gymnasts. The simulated body orientation angles were compared with the corresponding observed orientation angles in computing the simulation errors. The inclination and twist simulation errors revealed significant (p < .05) differences among the BSP estimation groups and methods. It was concluded that: (a) the method of BSP estimation significantly affected the simulation accuracy, and more individualized BSP estimation methods generally provided more accurate simulation results; (b) the mass items, and the lower leg and thorax/ abdomen were more responsible for the intermethod differences in the simulation accuracy than other BSP items and segments, respectively; (c) the ratio methods and the simple regression methods were preferable in simulation of the somersaulting motion due to the fewer anthropometric parameters required; (d) the geometric models and the cadaver-based stepwise regression method were superior to the other methods in the simulation of the complex airborne motion with twist.

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.

Current issues in the mechanics of athletic activities. A position paper

This position paper reviews current research topics in the study of athletic activities, which biomechanists would consider to be important or contentious issues, and focuses on critically evaluating what needs to be done in future research. It concludes that there remain many unresolved issues in the mechanics of athletic activities, many of which overlap with other disciplines. These issues relate to injury mechanisms, the control and co-ordination of movement, and ways of providing biomechanical feedback to enhance performance in athletic activities. Research to address these important issues will increasingly become more question than discipline orientated, must focus more on mechanisms than description, and will involve teams of researchers interacting on interdisciplinary problems.

Twisting Double Somersault High Bar Dismounts

At the 1988 Seoul Olympic Games, four double somersault dismounts with one twist and four double somersault dismounts with two twists were filmed using two 16 mm cameras during the men's horizontal bar competitions. Contributions to tilt angle reached at the midtwist position, determined using computer simulations based on modifications of the data obtained from film, were used as measures of the twisting potential of various techniques. The amount of tilt produced was greater when total twist was greater and when the body was tucked rather than straight. The twisting techniques used varied with the timing of the twist within the two somersaults. Contact contributions were larger when there was more twist in the first somersault. When there was little or no twist in the first somersault, the major contribution came from aerial techniques that comprised mainly arm movements and asymmetrical hip movements in the flight phase.

Effects of the Method of Body Segment Parameter Estimation on Airborne Angular Momentum

Ten body segment parameter (BSP) estimation methods were selected to compute the BSPs of 3 collegiate male gymnasts: cadaver-based methods (Group C, 4 methods), mass scanning-based methods (Group M, 4 methods) and geometric methods (Group G, 2 methods). Angular momenta of nine double somersault with full twist H-bar dismounts performed by the 3 gymnasts were computed. Each trial was processed 10 times using 10 sets of BSPs obtained from the estimation methods. Intergroup and intermethod comparisons of the airborne angular momenta were made. It was concluded that the method of BSP estimation affected the magnitude of airborne angular momentum but did not affect the magnitude of angular momentum fluctuation during the airborne phase.

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.

Twisting Techniques Used in Dismounts from the Rings

At the 1992 Olympic Games six full twisting double somersault dismounts were recorded with two video cameras during the rings individual apparatus finals in the men's Artistic Gymnastics competition. 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. Mean absolute deviations between simulation and video after the completion of one half twist were 0.01 rev for somersault, 2.8° for tilt, and 0.08 rev for twist. When the estimate of the initial tilt angle was adjusted by up to 1° these deviations fell to 1.6° for tilt and 0.02 rev for twist. All 6 competitors produced the majority of the tilt using aerial techniques that were predominantly asymmetrical movements of the arms. Contributions to the subsequent removal of tilt were determined using reverse simulations, and again arm movements were the main contributors.

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.

A prediction of an optimal performance of the handspring 1 1/2 front salto longhorse vault

The handspring 1 1/2 front salto vault in the tucked position is deemed to be an important high-level vault. It was the compulsory vault of the 1988 Olympics and is a building block for more advanced skills in the handspring family. The purpose of this study was to predict an individual's optimal performance of a handspring 1 1/2 front salto vault. An assessment of the athlete's present performance ability was determined using cinematographical analysis of three trials. These trials were judged as being typical high-level performances of the vault. Secondly, an objective function was identified based on the performance result of points awarded. The objective function was composed of those performance variables that, if maximized, would result in minimal deductions. Postflight height and distance were identified as those variables. Angular momentum was included in a penalty function form to ensure that sufficient angular momentum was present for successful completion of the skill. A Lagrangian approach was used to derive the equations of motion and a Rayleigh-Ritz procedure, using fifth-degree polynomials, was used to represent and discretize the state variables. The predicted optimal performance of the skill displayed greater virtuosity in postflight height, distance and angular momentum when compared to the individual's best trial performance. The results of this study generally fall within the limits observed for elite vaulters.

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.