Influence of optimization constraints in uneven parallel bar dismount swing simulations

Forward dynamics simulations of a dismount preparation swing on the uneven parallel bars were optimized to investigate the sensitivity of dismount revolution potential to the maximum bar force before slipping, and to low-bar avoidance. All optimization constraints were classified as 1-anatomical/physiological; limiting maximum hand force on the high bar before slipping, joint ranges of motion and maximum torques, muscle activation/deactivation timing and 2-geometric; avoiding low-bar contact, and requiring minimum landing distance. The gymnast model included torso/head, arm and two leg segments connected by a planar rotating, compliant shoulder and frictionless ball-and-socket hip joints. Maximum shoulder and hip torques were measured as functions of joint angle and angular velocity. Motions were driven by scaling maximum torques by a joint torque activation function of time which approximated the average activation of all muscles crossing the joint causing extension/flexion, or adduction/abduction. Ten joint torque activation values, and bar release times were optimized to maximize dismount revolutions using the downhill simplex method. Low-bar avoidance and maximum bar-force constraints are necessary because they reduce dismount revolution potential. Compared with the no low-bar performance, optimally avoiding the low bar by piking and straddling (abducting) the hips reduces dismount revolutions by 1.8%. Using previously reported experimentally measured peak uneven bar-force values of 3.6 and 4.0 body weight (BW) as optimization constraints, 1.40 and 1.55 revolutions with the body extended and arms overhead were possible, respectively. The bar-force constraint is not active if larger than 6.9 BW, and instead performances are limited only by maximum shoulder and hip torques. Bar forces accelerate the mass center (CM) when performing muscular work to flex/extend the joints, and increase gymnast mechanical energy. Therefore, the bar-force constraint inherently limits performance by limiting the ability to do work and reducing system energy at bar release.     

Effect of hip flexibility on optimal stalder performances on high bar

In the optimisation of sports movements using computer simulation models, the joint actuators must be constrained in order to obtain realistic results. In models of a gymnast, the main constraint used in previous studies was maximum voluntary active joint torque. In the stalder, gymnasts reach their maximal hip flexion under the bar. The purpose of this study was to introduce a model of passive torque to assess the effect of the gymnast's flexibility on the technique of the straddled stalder. A three-dimensional kinematics driven simulation model was developed. The kinematics of the shoulder flexion, hip flexion and hip abduction were optimised to minimise torques for four hip flexion flexibilities: 100°, 110°, 120° and 130°. With decreased flexibility, the piked posture period is shorter and occurs later. Moreover the peaks of shoulder and hip torques increase. Gymnasts with low hip flexibility need to be stronger to achieve a stalder; hip flexibility should be considered by coaches before teaching this skill.     

Mechanical energetic processes during the giant swing exercise before dismounts and flight elements on the high bar and the uneven parallel bars.

The purposes of this study were as follows: (1) To study the energy exchange between the body of the gymnast and the high bar and uneven parallel bars during forward and backward giant swings. (2) To examine the differences between the mechanical energy produced and the mechanical energy absorbed by the muscles during forward and backward giant swings on the high bar and the uneven parallel bars. The data were gathered during the gymnastic world championships in 1994. The experimental set up consisted of two video cameras (50 Hz) and two force measurement bars (500 Hz). A total of 101 giant swings before dismounts and flight elements performed by 33 male and 34 female gymnasts were analyzed. There are characteristically two main phases during forward and backward giant swings before dismounts and flight elements. During the first phase energy is transferred from the gymnast's body into the bar. During this phase of the backward giant swing the energy of the system decreases because the amount of energy decrease of the gymnast's body is more than the energy transferred into the high bar. An exception can be seen during the giant swings in which the gymnast used the power technique. During forward giant swings the energy of the system increases during the first phase. This occurs through active flexion of the hipjoint which produced the extra muscular energy. During the second phase energy is transferred from the bar back into the gymnast's body whose total energy increases. An increase in the energy of the system can only be achieved through muscular work. During the second phase of the backward giant swing the energy of the system increases. The forward giant swings performed on the uneven parallel bars showed a large energy loss during this phase. The energy deficit seen during the first phase of the backward giant swing can be improved by using the power technique. To achieve this the athlete must be in a bent position at the start of the giant swing exercise. Through extension at the shoulder and hip joints muscular energy can be put into the system.     

Mechanical energetic processes during the giant swing before the Tkatchev exercise

The goal of this study was to examine the possibility of the utilization of high bar and uneven parallel bar elasticity by the gymnasts through muscular work during the giant swing before the Tkatchev exercise on the high bar or uneven parallel bars. The performances were gathered during the Gymnastic World Championship in 1994. The set up consisted of two video cameras (50Hz) and two force measuring bars (500Hz). Twenty giant swings before the Tkatchev exercise, nine giant swings before the Tkatchev exercise after Tkatchev on the high bar and 15 giant swings before the Tkatchev exercise on the uneven parallel bars were analyzed. The giant swings were performed by 20 male and 15 female gymnasts. There are three phases during the giant swing exercise before the Tkatchev in which the systems (high bar-human body) total energy can be changed. During the first phase, energy is transferred from the gymnast's body into the bar. A clearly effective use of the bar's elasticity during the first phase could not be found. During the second phase, energy is transferred from the bar's back into the gymnast's body whose total energy increases. An increase in the energy of the system can only be achieved through muscular work. During the second phase of the various giant swing techniques no significant (p<0.05) difference in the energy increase through muscular work could be found. During the third phase, energy is once again produced by the gymnast through extension at the hip and shoulder joints.     

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 hip joint angle on concentric knee extension torque

This study tested the hypothesis that the effect of hip joint angle on concentric knee extension torque depends on knee joint angle during a single knee extension task. Twelve men performed concentric knee extensions in fully extended and 80° flexed hip positions with maximal effort. The angular velocities were set at 30° s⁻¹ and 180° s⁻¹. The peak torque and torques attained at 30°, 50°, 70° and 90° (anatomical position = 0°) of the knee joint were compared between the two hip positions. Muscle activations of the vastus lateralis, medialis, rectus femoris and biceps femoris were determined using surface electromyography. The peak torque was significantly greater in the flexed than in the extended hip position irrespective of angular velocity. The torques at 70° and 90° of the knee joint at both angular velocities and at 50° at 180° s⁻¹ were significantly greater in the flexed than in the extended hip position, whereas corresponding differences were not found at 30° (at either angular velocity) and 50° (at 30° s⁻¹) of the knee joint. No effect of hip position on muscle activation was observed in any muscle. These results supported our hypothesis and may be related to the force–length and force–velocity characteristics of the rectus femoris.     

Investigating centre of mass stabilisation as the goal of posture and movement coordination during human whole body reaching

In the light of experimental results showing significant forward centre of mass (CoM) displacements within the base of support, this study investigated if whole body reaching movements can be executed whilst keeping the CoM fixed in the horizontal axis. Using kinematic simulation techniques, angular configurations were recreated from experimental data imposing two constraints: a constant horizontal position of the CoM and an identical trajectory of the hand to grasp an object. The comparison between recorded and simulated trials showed that stabilisation of the CoM was associated with greater backward hip displacements, which became more marked with increasing object distance. This was in contrast to recorded trials showing reductions in backward hip displacements with increasing distance. Results also showed that modifications to angular displacements were necessary only at the shoulder and hip joints, but that these modifications were within the limits of joint mobility. The analysis of individual joint torques revealed that the pattern and timing of simulated trials were similar to those recorded experimentally. Peak joint torque values showed particularly that keeping the CoM at a constant horizontal position resulted in significantly smaller ankle peak flexor and extensor torques. It may be concluded from this study that `stabilising' the CoM during human whole body reaching represents a feasible strategy, but not the one chosen by subjects under experimental conditions. Our results also do not support the idea of the CoM as the stabilised reference value for the coordination between posture and goal-directed movements. Received: 22 September 1998 / Accepted in revised form: 2 June 1999     

A mathematical high bar–human body model for analysing and interpreting mechanical-energetic processes on the high bar

The aims of this study were:

1. To study the transfer of energy between the high bar and the gymnast.

2. To develop criteria from the utilisation of high bar elasticity and the utilisation of muscle capacity to assess the effectiveness of a movement solution.

3. To study the influence of varying segment movement upon release parameters.

For these purposes a model of the human body attached to the high bar (high bar–human body model) was developed. The human body was modelled using a 15-segment body system. The joint-beam element method (superelement) was employed for modelling the high bar. A superelement consists of four rigid segments connected by joints (two Cardan joints and one rotational–translational joint) and springs (seven rotation springs and one tension–compression spring). The high bar was modelled using three superelements. The input data required for the high bar–human body model were collected with video-kinematographic (50 Hz) and dynamometric (500 Hz) techniques. Masses and moments of inertia of the 15 segments were calculated using the data from the Zatsiorsky et al. (1984) model. There are two major phases characteristic of the giant swing prior to dismounts from the high bar. In the first phase the gymnast attempts to supply energy to the high bar–human body system through muscle activity and to store this energy in the high bar. The difference between the energy transferred to the high bar and the reduction in the total energy of the body could be adopted as a criterion for the utilisation of high bar elasticity. The energy previously transferred into the high bar is returned to the body during the second phase. An advantageous increase in total body energy at the end of the exercise could only be obtained through muscle energy supply. An index characterising the utilisation of muscle capacity was developed out of the difference between the increase in total body energy and the energy returned from the high bar. A delayed and initially slow but even reduction of hip and shoulder angles provided more advantageous release conditions. The total body energy could be improved by up to 15%, the vertical CM release velocity by up to 10% and the angular momentum by up to 35%.     

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 degrees ), 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.     

Kinetic chain of overarm throwing in terms of joint rotations revealed by induced acceleration analysis

This study investigated how baseball players generate large angular velocity at each joint by coordinating the joint torque and velocity-dependent torque during overarm throwing. Using a four-segment model (i.e., trunk, upper arm, forearm, and hand) that has 13 degrees of freedom, we conducted the induced acceleration analysis to determine the accelerations induced by these torques by multiplying the inverse of the system inertia matrix to the torque vectors. We found that the proximal joint motions (i.e., trunk forward motion, trunk leftward rotation, and shoulder internal rotation) were mainly accelerated by the joint torques at their own joints, whereas the distal joint motions (i.e., elbow extension and wrist flexion) were mainly accelerated by the velocity-dependent torques. We further examined which segment motion is the source of the velocity-dependent torque acting on the elbow and wrist accelerations. The results showed that the angular velocities of the trunk and upper arm produced the velocity-dependent torque for initial elbow extension acceleration. As a result, the elbow joint angular velocity increased, and concurrently, the forearm angular velocity relative to the ground also increased. The forearm angular velocity subsequently accelerated the elbow extension and wrist flexion. It also accelerated the shoulder internal rotation during the short period around the ball-release time. These results indicate that baseball players accelerate the distal elbow and wrist joint rotations by utilizing the velocity-dependent torque that is originally produced by the proximal trunk and shoulder joint torques in the early phase.     

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.     

Kinematics and kinetics of the racket-arm during the soft-tennis smash under match conditions

The purposes of this study were to (a) describe the racket-arm kinematics and kinetics of the soft-tennis smash during match rallies, and (b) assess the characteristics of this smash vs. the laboratory-simulated smash of our previous study. In the current study we recorded soft-tennis smash motions during match play of the 3rd East Asian Games. Racket-arm anatomical joint angular velocity and anatomical joint torque were calculated from 3-D coordinate data of 13 collected motions obtained using the direct linear transformation procedure. The results showed that most of the maximum values of the anatomical joint torques were qualitatively smaller than those of the tennis serve. Peak elbow extension, shoulder internal rotation, and elbow varus torques in match play were significantly greater than values reported for laboratory-simulated conditions. The greater forward swing torques did not result in significantly different racket head velocity, possibly because there was a significantly shorter forward swing phase in match conditions. In particular, a clear peak of the elbow extension torque during the forward swing phase was the most characteristic pattern in the smashes under match conditions, for it was 160% greater than laboratory-simulated conditions. These results supported our hypothesis that racket-arm kinematic and kinetic characteristics of the smash under match conditions differ from those under laboratory-simulated conditions. Possible explanations include the time-pressure conditions of the competitive situation in a match, and the Hawthorne effect (Hudson et al., 1986), both of which alter performance between match conditions and laboratory-simulated conditions.     

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.     

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.     

On the organizing role of nonmuscular forces during performance of a giant circle in gymnastics

Five elite gymnasts performed giant circles on the high bar under different conditions of loading (without and with 6-kg loads attached to the shoulders, waist or ankles). Comparing the gymnasts' kinematic pattern of movement with that of a triple-pendulum moving under the sole influence of nonmuscular forces revealed qualitative similarities, including the adoption of an arched position during the downswing and a piked position during the upswing. The structuring role of nonmuscular forces in the organization of movement was further reinforced by the results of an inverse dynamics analysis, assessing the contributions of gravitational, inertial and muscular components to the net joint torques. Adding loads at the level of the shoulders, waist or ankles systematically influenced movement kinematics and net joint torques. However, with the loads attached at the level of the shoulders or waist, the load-induced changes in gravitational and inertial torques provided the required increase in net joint torque, thereby allowing the muscular torques to remain unchanged. With the loads attached at the level of the ankles, this was no longer the case and the gymnasts increased the muscular torques at the shoulder and hip joints. Together, these results demonstrate that expert gymnasts skillfully exploit the operative nonmuscular forces, employing muscle force only in the capacity of complementary forces needed to perform the task.     

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.     

The need for muscle co-contraction prior to a landing

In landings from a flight phase the mass centre of an athlete experiences rapid decelerations. This study investigated the extent to which co-contraction is beneficial or necessary in drop landings, using both experimental data and computer simulations. High speed video and force recordings were made of an elite martial artist performing drop landings onto a force plate from heights of 1.2, 1.5 and 1.8 m. Matching simulations of these landings were produced using a planar 8-segment torque-driven subject-specific computer simulation model. It was found that there was substantial co-activation of joint flexor and extensor torques at touchdown in all three landings. Optimisations were carried out to determine whether landings could be effected without any co-contraction at touchdown. The model was not capable of landing from higher than 1.05 m with no initial flexor or extensor activations. Due to the force–velocity properties of muscle, co-contraction with net zero joint torque at touchdown leads to increased extensor torque and decreased flexor torque as joint flexion velocity increases. The same considerations apply in any activity where rapid changes in net joint torque are required, as for example in jumps from a running approach.     

The effect of arm swing on lower extremities in vertical jumping

Although it is known that an arm swing can enhance the performance in vertical jumping, the mechanisms through which this enhancement occurs are not yet clearly described. The purpose of this study was to examine how arm swing affects the lower extremity torque, power and work in vertical jumping and to gain an insight into the mechanisms that enable the arm swing to increase jump height. Five subjects maximally performed two types of vertical squat jumps with (SJA) and without (SJ) an arm swing from a force platform. All performances were videotaped with a high-speed video camera (200 Hz). The jump heights, joint torques, power and work were calculated by combining kinematic and kinetic data. It was confirmed that arm swing enhanced the jump height significantly (p<0.01). The work by the hip and by the ankle was significantly augmented by arm swing (p<0.05 and p<0.01, respectively). However, the work by the knee was significantly smaller in SJA (p<0.05). The total work by the three lower extremity joints (ankle, knee and hip) was significantly larger in SJA (p<0.05). The increase of the lower extremity work by the arm swing (31.4 J) was about twice as large as the work done by the shoulder and elbow in SJA (16.3 J). It was concluded that the increment of jump height resulted mainly from the increase of the lower extremity work, which is considered to have been brought about by the additional load on the lower extremity due to the arm swing.     

Alignment of the human body in standing

Alignment of the body in typical symmetrical standing was studied by photographing fifteen subjects in profile on a reaction board. Two aspects of alignment were studied: (1) the anteroposterior position of the body landmarks of knee joint, hip joint, shoulder joint, and ear, compared to the ankle joint; and (2) the positions of the partial centers of gravity above the knee and hip, as a measure of how the body is balanced above these joints. The knee, hip, shoulder, and ear were forward of the ankle in all subjects. On average, the knee was 3.8 (+/- 2.0), the hip 6.2 (+/- 1.3) the shoulder 3.8 (+/- 1.9), and the ear 5.9 (+/- 1.6) cm (+/-S.D.) anterior to the ankle. The positions of landmarks were positively correlated with one another but not highly. The position of the center of gravity could be predicted well from the positions of the landmarks within individual subjects' data, but not across subjects. The centers of gravity above the knee and hip were calculated by subtracting the mass and position of the segments below the joint from the whole-body center of gravity. The center of gravity above the knee was located on average 1.4 (+/- 1.1) cm in front of the joint, and that of the hip 1.0 (+/- 1.6) cm behind the trochanter. Thus, at both knee and hip in typical standing, there exist slight gravitational torques tending to extend the joints.     

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.