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 11/2 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 11/2 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. © 2014 Elsevier Ltd

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

Twisting

In a non-twisting dive, the diver must control the somersault rotation in order to enter the water at the correct angle. In a twisting dive both the somersault and twist must be controlled to give the correct amounts of rotation at entry. In addition, the angle of tilt away from the vertical somersault plane should be zero at entry into the water. As a consequence, the diver has a much more complex control task during the aerial phase of a somersaulting movement when twist is present. This chapter describes the ways in which twist can be initiated, controlled and stopped

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

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

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

The Diver with a Rotor

We present and analyse a simple model for the twisting somersault. The model is a rigid body with a rotor attached which can be switched on and off. This makes it simple enough to devise explicit analytical formulas whilst still maintaining sufficient complexity to preserve the shape-changing dynamics essential for twisting somersaults in springboard and platform diving. With `rotor on' and with `rotor off' the corresponding Euler-type equations can be solved, and the essential quantities characterising the dynamics, such as the periods and rotation numbers, can be computed in terms of complete elliptic integrals. Thus we arrive at explicit formulas for how to achieve a dive with m somersaults and n twists in a given total time. This can be thought of as a special case of a geometric phase formula due to Cabrera 2007.Comment: 15 pages, 6 figure

TWIST LIMITS OF LATE TWISTING DOUBLE SOMERSAULTS ON TRAMPOLINE

The aim of this research study was to determine the twist limits for double somersaults on trampoline with the twist in the second somersault. An angle-driven computer simulation model of aerial movement was used to determine the maximum number of half twists that could be produced in a double somersault using asymmetrical movements of the arms and hips. Simulations of 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. It was found that 3½ twists could be produced in the second somersault of a forward piked double somersault with arms abducted 8o from full adduction during the twisting phase and that 3 twists could be produced in the second somersault of a backward straight double somersault with arms fully adducted

Optimal 3D arm strategies for maximizing twist rotation during somersault of a rigid-body model

Looking for new arm strategies for better twisting performances during a backward somersault is of interest for the acrobatic sports community while being a complex mechanical problem due to the nonlinearity of the dynamics involved. As the pursued solutions are not intuitive, computer simulation is a relevant tool to explore a wider variety of techniques. Simulations of twisting somersaults have mainly been realized with planar arm motions. The aim of this study was to explore the outcomes of using 3D techniques, with the demonstration that increasing the fidelity of the model does not increase the level of control complexity on the real system. Optimal control was used to maximize twists in a backward straight somersault with both types of models. A multistart approach was used to find large sets of near-optimal solutions. The robustness of these solutions was then assessed by modeling kinematic noise during motion execution. The possibility of using quaternions for representing orientations in this numerical optimization problem was discussed. Optimized solutions showed that 3D techniques generated about two additional twists compared to 2D techniques. The robustness analysis revealed clusters of highly twisting and stable 3D solutions. This study demonstrates the superiority of 3D solutions for twisting in backward somersault, a result that can help acrobatic sports athletes to improve their twisting performance

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