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

How to Stick the Landing: Kangaroo Rats Use Their Tails to Reorient during Evasive Jumps Away from Predators

Tails are widespread in the animal world and play important roles in locomotor tasks, such as propulsion, maneuvering, stability, and manipulation of objects. Kangaroo rats, bipedal hopping rodents, use their tail for balancing during hopping, but the role of their tail during the vertical evasive escape jumps they perform when attacked by predators is yet to be determined. Because we observed kangaroo rats swinging their tails around their bodies while airborne following escape jumps, we hypothesized that kangaroo rats use their tails to not only stabilize their bodies while airborne, but also to perform aerial re-orientations. We collected video data from free-ranging desert kangaroo rats (Dipodomys deserti) performing escape jumps in response to a simulated predator attack and analyzed the rotation of their bodies and tails in the yaw plane (about the vertical-axis). Kangaroo rat escape responses were highly variable. The magnitude of body re-orientation in yaw was independent of jump height, jump distance, and aerial time. Kangaroo rats exhibited a stepwise re-orientation while airborne, in which slower turning periods corresponded with the tail center of mass being aligned close to the vertical rotation axis of the body. To examine the effect of tail motion on body re-orientation during a jump, we compared average rate of change in angular momentum. Rate of change in tail angular momentum was nearly proportional to that of the body, indicating that the tail reorients the body in the yaw plane during aerial escape leaps by kangaroo rats. Although kangaroo rats make dynamic 3D movements during their escape leaps, our data suggest that kangaroo rats use their tails to control orientation in the yaw plane. Additionally, we show that kangaroo rats rarely use their tail length at full potential in yaw, suggesting the importance of tail movement through multiple planes simultaneously.

Functional variability in the takeoff phase of one metre springboard forward dives

In springboard diving consistency of body orientation at water entry is necessary for a good dive and is likely to be dependent on the consistency of conditions at takeoff. The aim of the present study was to investigate whether a diver modifies his technique from dive to dive during the board contact phase in order to be more consistent at takeoff in one metre springboard forward dives. Two-dimensional video analysis was used to calculate orientation and configuration angles of 12 forward pike dives and 12 forward 2½ somersault pike dives, performed by an international diver. A computer simulation model of a diver and springboard during board contact was used to obtain matching simulations of the performances and to calculate the rotation potential (angular momentum × flight time) for each dive. Simulations were used to determine the variation in conditions at maximum board depression arising from variation in touchdown conditions, and the variation in takeoff conditions arising from the variability in conditions at maximum board depression. A comparison of the simulated and performance variations implied that adjustments were made during the board contact phase for both the pike dives and the 2½ somersault pike dives. In the board depression phase, adjustments reduced the variability in the mass centre horizontal velocity at the lowest point. In the board recoil phase, adjustments reduced the variability in the horizontal velocity and rotation potential at takeoff.

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.

Kinematic and kinetic analysis of the goalkeeper's diving save in football

Kinetics and full body kinematics were measured in ten elite goalkeepers diving to save high and low balls at both sides of the goal, aiming to investigate their starting position, linear and angular momentum, and legs' contribution to end-performance. Our results showed that goalkeepers adopted a starting position with a stance width of 33 ± 1% of leg length, knee flexion angle of 62 ± 18° and hip flexion angle of 63 ± 18°. The contralateral leg contributed more than the ipsilateral leg to COM velocity (p < 0.01), both for the horizontal (2.7 ± 0.1 m·s^-1 versus 1.2 ± 0.1 m·s^-1) and for the vertical component (3.1 ± 0.3 m·s^-1 versus 0.4 ± 0.2 m·s^-1). Peak horizontal and peak angular momenta were significantly larger (p < 0.01) for low dives than for high dives with a mean difference of 55 kg·m·s^-1 and 9 kg·m²·s^-1, respectively. In addition, peak vertical momentum was significantly larger (p < 0.01) for high dives with a mean difference between dive heights of 113 kg·m·s^-1. Coaches need to highlight horizontal lateral skills and exercises (e.g. sideward push-off, sideward jumps), with emphasis on pushing-off with the contralateral leg, when training and assessing goalkeeper's physical performance.

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.

What governs successful performance of a complex whole body movement: The Kovacs release-regrasp on horizontal bar?

The Kovacs is a release and regrasp skill performed on the horizontal bar in men׳s artistic gymnastics. It is a popular skill in elite competitive gymnastics with over 40% of male gymnasts performing a variation of the Kovacs at the London 2012 Olympics. In the qualifying competition 84% of Kovacs were successfully regrasped, with the remaining 16% resulting in a fall. The aim of the present study was to determine why some gymnasts are more successful than others at regrasping the bar, with a secondary aim to determine how a less successful gymnast could alter his technique in order to become more successful. Nine performances of the Kovacs by each of two gymnasts, one 100% successful and one 11% successful, were analysed to determine differences in release and regrasp parameters. The technique of the less successful gymnast was optimised using a computer simulation model to increase the percentage of catches (success rate). The successful gymnast had larger and more consistent release windows and a radial velocity towards the bar at regrasp. The less successful gymnast had higher horizontal velocity at release and a mean radial velocity away from the bar at regrasp. Optimising his simulated technique increased the rate of success from 11% to 93%. The actions prior to release were performed earlier than in the recorded performances leading to a more vertical path of the mass centre at release and a radial velocity towards the bar at regrasp.

Analysis of angular momentum effect on swimming kick-start performance

The aim of this study was to analyse the mechanics of rotation and the temporal, angular and kinematics variables during the aerial phase for the kick-start with respect to the grab start. Nine elite swimmers (70.0 ± 7.7 kg; 178 ± 9.4 cm; 24.5 ± 5.3 years; 824 ± 119 FINA points scoring) performed the starts on the OMEGA OSB11 starting block followed by 5 m gliding at maximum velocity. Nineteen comparisons of kinematics variables across start technique were performed with critical alpha adjusted using a Holm's correction to maintain an experiment-wise type I error rate of p <0.05. The differences were statistically evaluated by T-test and Wilcoxon test. Significant advantages for the kick-start were observed in all temporal variables (except in the flight time) and in the vertical take-off velocity. Similarities in the centre of mass angular momentum at take-off (120.89 ± 17.66, 126.61 ± 13.51 s(-1).10(-3), p-value <0.294; kick-start and grab start) caused that KS did not increase the temporal advantages obtained on the block at 5 m distance. Two different rotational movements were found for both techniques. A displacement of the rear leg and front leg on the block and during the flight respectively permits a higher lower limbs position relative to the trunk at hands entry for kick-start. However, larger rotational movement of the trunk characterized grab start. It was concluded that shorter block times and rotational displacements of the lower limbs on the block and flight phase are the key of the best performance for kick-start at 5 m distance.

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.

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.

Consistency of performances in the Tkatchev release and re-grasp on high bar

The Tkatchev on the high bar is a release and re-grasp skill in which the gymnast rotates in a direction during flight opposite to that of the preceding swing. Since the release window is defined as the time during which the gymnast has appropriate linear and angular momentum to ensure the bar can be re-grasped, it was speculated that the release windows for this skill would be smaller than for dismounts that are less constrained. One senior male gymnast competing at national standard performed 60 Tkatchev trials. A four-segment planar simulation model of the gymnast and high bar was used to determine the release windows in 10 successful and 10 unsuccessful performances of the Tkatchev recorded using a Vicon motion analysis system. Model parameters were optimized to obtain a close match between simulations and recorded performances in terms of rotation angle (1 degree), bar displacements (0.01 m), and release velocities (1%). Each matched 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 Tkatchev successfully. The release windows for the successful trials were small compared with those of dismounts. The unsuccessful trials were associated with later release and later timing of the actions at the shoulders and hips.

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.

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.

Parameter Determination for a Computer Simulation Model of a Diver and a Springboard

This study used kinematic data on springboard diving performances to estimate viscoelastic parameters of a planar model of a springboard and diver with wobbling masses in the trunk, thigh, and calf segments and spring dampers acting at the heel, ball, and toe of the foot segment. A subject-specific angle-driven eight-segment model was used with an optimization algorithm to determine viscoelastic parameter values by matching simulations to four diving performances. Using the parameters determined from the matching of a single dive in a simulation of another dive resulted in up to 31% difference between simulation and performance, indicating the danger of using too small a set of kinematic data. However, using four dives in a combined matching process to obtain a common set of parameters resulted in a mean difference of 8.6%. Because these four dives included very different rotational requirements, it is anticipated that the combined parameter set can be used with other dives from these two groups.

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.

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 & 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°), 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).

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.

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.

Factors Influencing the Performance of Springboard Dives of Increasing Difficulty

Major factors influencing the ability of divers to perform nontwisting springboard dives of increasing degree of difficulty were investigated. The analysis was based upon 49 dives (42 in pike and 7 in tuck) executed by male and female medalists in the 1996 Olympics. Videotapes were digitized to determine competitors’ vertical velocities and angular momenta at the beginning of dive flight. Centripetal force and resultant joint torque models were used to estimate the effort needed to perform multiple somersaulting dives. Increasing degree of difficulty by spinning in a pike rather than a tuck position for the same number of somersaults was associated with decreased vertical velocity at the start of dive flight, decreased angular velocity while somersaulting in a quasi-rigid position, and little change in centripetal force or related muscular effort. Increasing degree of difficulty by adding a somersault while rotating in a tuck rather than a pike position involved increases in vertical and angular velocities, a smaller increase in angular momentum, and notable increases in resultant joint torque and centripetal force. Sufficient muscular torque to maintain a compact spinning position was considered to be the major additional challenge facing divers making the transition from a 21/2 pike to a 31/2 tuck.

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.

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.

Controlling the Ground Reaction Force During Lifting

The control of the ground reaction force vector relative to the center of gravity (CoG) was examined while subjects performed a back-lifting task. Six male subjects (aged 24.0 +/- 2.5 years) repeatedly lifted a barbell. A biomechanical analysis that used a linked segment model revealed that the summed rotations of body segments during lifting yielded a specific rate of change of the angular momentum of the entire body. This equaled the external moment provided by Fsubg; relative to CoG. This implies that multisegment movements involve control of the angular momentum of the entire body through an appropriately directed Fsubg;. Thus, in dynamic tasks Fsubg; is pointed away from rather than lined up with the CoG, as is the case in static tasks.

Moment of inertia of whole body using an oscillating table in adolescent boys

This study measured the moment of inertia of the body using the oscillating table method, and saw how it is affected by age and body size. One hundred and seventeen subjects of junior and senior high school boys of ages 13-18 participated in this study. Moment of inertia was measured in two postures of supine (Imx) and recumbent (Imy) positions. Both Imx and Imy account for the range from 5.6 to 14.0 kg m2 and 4.2 to 13.5 kg m2, respectively, and correlate linearly to body height (Ht) and body weight (W). The values of Imy/Imx becomes 93.6 and 95.2% independent of age and body size. The difference between Imx and Imy might be affected by projection areas on the frontal from the sagittal area of the body. The multiple regression analysis of Ht2 and W with regard to Im was performed to obtain the following multiple regression equations: Imx = 3.44 Ht2 + 0.144 W - 8.04 (R = 0.973), Imy = 3.52 Ht2 + 0.125 W - 7.78 (R = 0.972). When Imx and Imy were estimated using these equations, the standard deviation of error which calculates the percent differences between the estimated and measured values amounted to +/- 5% in Imx and Imy. The results suggest that, with Japanese boys, there is a relationship between the postures and body size (height or weight), independent of age.

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.

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 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.

Body Configuration in Multiple Somersault High Bar Dismounts

An 11-segment three-dimensional simulation model was used to modify the body configurations of eight gymnasts performing multiple somersault dismounts during the Men’s High Bar competition in the 1988 Seoul Olympic Games. Four layout double somersault performances were modified to change a characteristic backward arch to a straight body position. This modification reduced the somersault rotation by 0.03 to 0.10 somersaults. Four tucked triple somersault performances were modified so that the thigh abduction angle was reduced to zero. This modification resulted in underrotations ranging from 0.01 to 0.34 somersaults depending on the amount of thigh abduction in the original movement. The additional angular momentum needed for successful completion of the modified movements was small in general and in no case greater than 13%.

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

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

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

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

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

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