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.     

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.     

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.     

Reducing ground reaction forces in gymnastics’ landings may increase internal loading

The aim of this study was to use a subject-specific seven-link wobbling mass model of a gymnast, and a multi-layer model of a landing mat, to determine landing strategies that minimise ground reaction forces (GRF) and internal forces. Subject-specific strength parameters were determined that defined the maximum voluntary torque/angle/angular velocity relationship at each joint. These relationships were used to produce subject-specific ‘lumped’ linear muscle models for each joint. Muscle activation histories were optimised using a Simplex algorithm to minimise GRF or bone bending moments for forward and backward rotating vault landings. Optimising the landing strategy to minimise each of the GRF reduced the peak vertical and horizontal GRF by 9% for the backward rotating vault and by 8% and 48% for the forward rotating vault, compared to a matching simulation. However, most internal loading measures (bone bending moments, joint reaction forces and muscle forces) increased compared to the matching simulation. Optimising the landing strategy to minimise the peak bone bending moments resulted in reduced internal loading measures, and in most cases reduced GRF. Bone bending moments were reduced by 27% during the forward rotating vault and by 2% during the backward rotating vault landings when compared to the matching simulations. It is possible for a gymnast to modify their landing strategy in order to minimise internal forces and lower GRF. However, using a reduction in GRF, due to a change in landing strategy, as a basis for a reduction in injury potential in vaulting movements may not be appropriate since internal loading can increase.     

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.     

Effect of Plyometric Training on Handspring Vault Performance and Functional Power in Youth Female Gymnasts

This study aimed to determine the effect of plyometric training (PT) when added to habitual gymnastic training (HT) on handspring vault (HV) performance variables. Twenty youth female competitive gymnasts (Age: 12.5 ± 1.67 y) volunteered to participate and were randomly assigned to two independent groups. The experimental plyometric training group (PTG) undertook a six-week plyometric program, involving two additional 45 min PT sessions a week, alongside their HT, while the control group (CG) performed regular HT only. Videography was used (120 Hz) in the sagittal plane to record both groups performing three HVs for both the baseline and post-intervention trials. Furthermore, participants completed a countermovement jump test (CMJ) to assess the effect of PT on functional power. Through the use of Quintic biomechanics software, significant improvements (P < 0.05) were found for the PTG for run-up velocity, take-off velocity, hurdle to board distance, board contact time, table contact time and post-flight time and CMJ height. However, there were no significant improvements on pre-flight time, shoulder angle or hip angle on the vault for the PTG. The CG demonstrated no improvement for all HV measures. A sport-specific PT intervention improved handspring vault performance measures and functional power when added to the habitual training of youth female gymnasts. The additional two hours plyometric training seemingly improved the power generating capacity of movement-specific musculature, which consequently improved aspects of vaulting performance. Future research is required to examine the whether the improvements are as a consequence of the additional volume of sprinting and jumping activities, as a result of the specific PT method or a combination of these factors.     

Strategies in preflight for an optimal Yurchenko layout vault

An optimal Yurchenko layout vault of an elite female gymnast was identified by Koh et al. [2003. A predicted optimal performance of the Yurchenko layout vault in women's artistic gymnastics. Journal of Applied Biomechanics 19, 187-204] to require a combination of an increased body angle at horse contact and increased angular momentum for postflight than was recorded experimentally. However, the individual effect of each of these variables to producing the optimal vault is not known. The purpose of the study was to determine an appropriate strategy to teaching the optimal Yurchenko layout vault. Separate optimisations were carried out to investigate how each of these variables would change in order to produce the optimal vault identified by Koh et al. (2003). A combined optimal parameter selection and optimal control approach was used. The results suggest that when the body angle of attack at horse impact was kept low, pre-flight angular momentum had to be increased, with further gains during horse impact, to produce an optimal vault. This strategy of increasing solely the level of angular momentum needed for optimum postflight may not be attainable realistically. On the other hand, employing a larger body angle of attack required an increase in angular momentum during impact but which was attainable. Both optimisations show that increasing the vertical CM horse takeoff velocity is essential for postflight height and distance. The strategy to enhance performance should thus focus on maintaining an appropriate CM pre-flight velocity, a high level of angular momentum during pre-flight and to contact the horse with a large body angle of attack.     

Optimisation of high bar circling technique for consistent performance of a triple piked somersault dismount

The dismount from the high bar is one of the most spectacular skills performed in Men's Artistic Gymnastics. Hiley and Yeadon [2005. Maximal dismounts from high bar. Journal of Biomechanics 38, 2221-2227] optimised the technique in the backward giant circle prior to release using a computer simulation model to show that a gymnast could generate sufficient linear and angular momentum to perform a triple piked backward somersault dismount with a sufficiently large release window (the period of time during which the gymnast could release the bar and successfully complete the dismount). In the present study, it was found that when the timing of the actions at the hip and shoulder joints from the optimum simulation were perturbed by 30ms the resulting simulation could no longer meet the criteria for sufficient aerial rotation and release window. Since it is to be expected that a gymnast's technique can cope with small errors in timing for consistent performance, a requirement of robustness to timing perturbations should be included within the optimisation process. When the technique in the backward giant circle was optimised to be robust to 30ms perturbations, it was found that sufficient linear and angular momentum for a triple piked dismount could be achieved with a realistic release window.     

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 roche vault performed by elite gymnasts: somersaulting technique, deterministic model, and judges' scores

The purpose of the study was to determine the mechanical variables that are related to successful post-flight somersaulting performance of the Roche vault. The 23 Roche vaults performed during the 2000 Olympic Games were filmed by a 16-mm camera operating at 100 Hz. The 2-D direct linear transformation technique was used for spatial calibration. Approximately 60 frames were digitized per vault. The method of Hay and Reid (1988) was used to develop a deterministic model to identify the mechanical variables that govern linear and angular motions of the vault. Correlational analysis was used to establish the strength of the relationship between the mechanical variables identified and the judges' scores. Significant correlations indicated that the higher judges' scores were negatively related to five mechanical variables and positively related to seventeen variables in the model. The normalized horizontal displacement of body center of mass (CM) from the knee grasp to the peak of post-flight was the best single predictor of the judges' score and accounted for 50% of variation in the judges' score. Finally, the landing point deductions and the official horizontal distance of post-flight collectively accounted for 86% of the variance in the judges' scores.     

The margin for error when releasing the asymmetric bars for dismounts

It has previously been shown that male gymnasts using the "scooped" giant circling technique were able to flatten the path followed by their mass center, resulting in a larger margin for error when releasing the high bar (Hiley and Yeadon, 2003a). The circling technique prior to performing double layout somersault dismounts from the asymmetric bars in women's artistic gymnastics appears to be similar to the "traditional" technique used by some male gymnasts on the high bar. It was speculated that as a result the female gymnasts would have margins for error similar to those of male gymnasts who use the traditional technique. However, it is unclear how the technique of the female gymnasts is affected by the need to avoid the lower bar. A 4-segment planar simulation model of the gymnast and upper bar was used to determine the margins for error when releasing the bar for 9 double layout somersault dismounts at the Sydney 2000 Olympics. The elastic properties of the gymnast and bar were modeled using damped linear springs. Model parameters, primarily the inertia and spring parameters, were optimized to obtain a close match between simulated and actual performances in terms of rotation angle (1.2 degrees), bar displacement (0.011 m), and release velocities (<1%). 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 margins for error of the 9 female gymnasts (release window 43-102 ms) were comparable to those of the 3 male gymnasts using the traditional technique (release window 79-84 ms).     

The control of twisting somersaults

In the takeoff and early flight phase of a twisting somersault, joint coordination is based on feed-forward control whereas in the late stages of the flight phase configuration adjustments are made using feedback control to ensure accurate completion of the movement and appropriate landing orientation. The aim of this study was to use a computer simulation model of aerial movement to investigate the extent to which arm and hip movements can control twist and somersault rotation in the flight phase of a twisting somersault. Two mechanisms were considered for the control of twist in simulated target trampoline movements with flight times of 1.4 s. In the first case a single symmetrical arm adduction correction was made using delayed feedback control based on the difference between the twist rate in a perturbed simulation and the twist rate in a target movement comprising a forward somersault with 1½ twists. Final corrections were made using symmetrical arm abduction and hip flexion to adjust the twist and somersault angles. In the second case continual asymmetrical arm adduction/abduction adjustments were used to remove the tilt from a perturbed full twisting backward somersault using delayed feedback control based on twist angle and angular velocity. The first method was able to cope with perturbations to a forward somersault with 1½ twists providing the feedback time delay was less than 200 ms. The second method was able to correct a perturbed full twisting backward somersault providing the feedback time delay was less than 125 ms.     

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 effects of initial conditions and takeoff technique on running jumps for height and distance

This study used a subject-specific model with eight segments driven by joint torques for forward dynamics simulation to investigate the effects of initial conditions and takeoff technique on the performance of running jumps for height and distance. The torque activation profiles were varied in order to obtain matching simulations for two jumping performances (one for height and one for distance) by an elite male high jumper, resulting in a simulated peak height of 1.98m and a simulated horizontal distance of 4.38m. The peak height reached/horizontal distance travelled by the mass centre for the same corresponding initial conditions were then maximised by varying the activation timings resulting in a peak height of 2.09m and a horizontal distance of 4.67m. In a further two optimizations the initial conditions were interchanged giving a peak height of 1.82m and a horizontal distance of 4.04m. The four optimised simulations show that even with similar approach speeds the initial conditions at touchdown have a substantial effect on the resulting performance. Whilst the takeoff phase is clearly important, unless the approach phase and the subsequent touchdown conditions are close to optimal then a jumper will be unable to compensate for touchdown condition shortcomings during the short takeoff phase to achieve a performance close to optimum.     

Considerations that affect optimised simulation in a running jump for height

This study used a computer simulation model to investigate various considerations that affect optimum peak height in a running jump. A planar eight-segment computer simulation model with extensor and flexor torque generators at five joints was formulated and customised to an elite male high jumper. A simulation was matched to a recorded high jumping performance by varying the activation profiles of each of the torque generators giving a simulated peak height of 1.99m compared to the recorded performance of 2.01 m. In order to maximise the peak height reached by the mass centre in the flight phase, the activation profiles were varied, keeping the same initial conditions as in the matching simulation. Optimisations were carried out without any constraints, with constraints on the angular momentum at take-off, with further constraints on joint angles, and with additional requirements of robustness to perturbations of activation timings. A peak height of 2.37 m was achieved in the optimisation without constraints. Introducing the three constraints in turn resulted in peak heights of 2.21, 2.14 and 1.99m. With all three types of constraints included, the peak height was similar to that achieved in the recorded performance. It is concluded that such considerations have a substantial influence on optimum technique and must be included in studies using optimised simulations.     

Pole vault performance for anthropometric variability via a dynamical optimal control model

Optimal performance of a dynamical pole vault process was modeled as a constrained nonlinear optimization problem. That is, given a vaulter's anthropomorphic data and approach speed, the vaulter chose a specific take-off angle, pole stiffness and gripping height in order to yield the greatest jumping height compromised by feasible bar-crossing velocities. The optimization problem was solved by nesting a technique of searching an input-to-output mapping arising from the vaulting trajectory and a method of nonlinear sequential quadratic programming (SQP). It was suggested from the optimization results that the body's weight has an important influence on the vaulting performance beside the vaulter's height and approach speed; the less skilled vaulter should gradually adopt a longer pole to improve the performance.     

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.     

The influence of simulation model complexity on the estimation of internal loading in gymnastics landings

Evaluating landing technique using a computer simulation model of a gymnast and landing mat could be a useful tool when attempting to assess injury risk. The aims of this study were: (1) to investigate whether a subject-specific torque-driven or a subject-specific muscle-driven model of a gymnast is better at matching experimental ground reaction forces and kinematics during gymnastics landings, (2) to calculate their respective simulation run times and (3) to determine what level of model complexity is required to assess injury risk. A subject-specific planar seven-link wobbling mass model of a gymnast and a multi-layer model of a landing mat were developed for this study. Subject-specific strength parameters were determined which defined the maximum voluntary torque/angle/angular velocity relationship about each joint. This relationship was also used to produce subject-specific 'lumped' muscle models for each joint. Kinetic and kinematic data were obtained during landings from backward and forward rotating gymnastics vaults. Both torque-driven and muscle-driven models were capable of producing simulated landings that matched the actual performances (with overall percentage differences between 10.1% and 18.2%). The torque-driven model underestimated the internal loading on joints and bones, resulting in joint reaction forces that were less than 50% of those calculated using the muscle-driven model. Simulation time increased from approximately 3 min (torque driven) to more than 10 min (muscle driven) as model complexity increased. The selection of a simulation model for assessing injury risk must consider the need for determining realistic internal forces as the priority despite increases in simulation run time.     

Kinetic and kinematic adjustments during perturbed walking across visible and camouflaged drops in ground level

Walking in even the most familiar environment posesses a challenge to humans due to continuously changing surface conditions such as compliance, slip, or level. These changes can be visible or invisible due to camouflage. In order to prevent falling, camouflaged changes in the ground level in particular require a quick response of the locomotor system. For ten subjects we investigated kinematics and ground reaction forces of two consecutive contacts while they were walking across visible (drops of 0, −5 and −10 cm at second contact) and camouflaged (drops of 0 or −5 cm, and drops of 0 or −10 cm at second contact) changes in the ground level. For both situations we found significant kinetic and kinematic adjustments during the perturbed second contact but also one step earlier, in the preparatory first contact. During walking across visible changes in the ground level, second peak ground reaction force at first contact decreased whereas the drop height increased at the second contact. In addition, at the end of this first contact the ankle and knee were more flexed and the trunk was more erect compared to level walking. During the perturbed second contact, first peak ground reaction force increased with drop height, whereas kinematic adjustments at touchdown were less. The visual perception of the perturbation facilitated prior adaptations. During walking across camouflaged changes in ground level such a visually guided preadaptation was not possible and the adaptations prior to the perturbation were less than those observed during walking across visible changes in the ground. However, when stepping into a camouflaged drop, the kinetic and kinematic adjustments became more obvious and they increased with increasing camouflaged drop height.     

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 2.0 s. 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.