The biomechanics of twisting somersaults. Part IV: Partitioning performances using the tilt angle

Optimal Control as a Tool for Innovation in Aerial Twisting on a Trampoline

Aerial twisting techniques are preferred by trampoline coaches for their balanced landings. As these techniques are not intuitive, computer simulation has been a relevant tool to explore a variety of techniques. Up to now, twisting somersaults were mainly simulated using arm abduction/adduction only (2D). Our objective was to explore more complex (3D) but still anatomically feasible arm techniques to find innovative and robust twisting techniques. The twist rotation was maximized in a straight backward somersault performed by a model including arm abduction/adduction with and without changes in the plane of elevation. A multi-start approach was used to find a series of locally optimal performances. Six of them were retained and their robustness was assessed by adding noise to the first half of the arm kinematics and then reoptimizing the second half of the skill. We found that aerial twist performance linearly correlates with the complexity of arm trajectory. Optimal techniques share a common strategy consisting of moving the arm in a plane formed by the twisting and angular momentum axes, termed as the best tilting plane. Overall, 3D techniques are simpler and require less effort than 2D techniques for similar twist performances. Three techniques which generate ∼3 aerial twists could be used by athletes because kinematic perturbations do not compromise the performance and the landing.

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.

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.

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.

Effect of Ability on Twisting Techniques in Forward Somersaults on the Trampoline

This study was designed to investigate the effect of ability on technique in the forward somersault with half twist (Barani) and the forward somersault with one and one half twists (Rudi) on the trampoline. Eleven trampolinists ranging in ability from elite (national representative) to early intermediate (regional representative) were analyzed using three-dimensional analysis techniques. Cumulative twist angle, rate of twist, angle of tilt of the twist axis, chest rotation, hip angle, and hip lateral flexion angle were measured. Characteristics of the arm actions were also assessed using an internal frame of reference. To generate twist in the Baranis, trampolinists tilted the axis between 5° and 14°; the amount of tilt was inversely related to ability (p < .05). In the Rudis, subjects tilted the axis between 15° and 23° using more asymmetrical arm actions and larger and more rapid hip extensions, hip lateral flexions, and chest rotations than in the Baranis. The timing and magnitude of the actions differed among the subjects and were related to ability.

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.