Introduction

Swinging is a key component of all supporting and hanging gymnastics exercises. The focus of this presentation will be on vertical circling. Four exercises in competitive artistic gymnastics fall into this category; rings, parallel bars, asymmetric bars and high bar. Swinging in the vertical plane is used for example to link strength and balance positions with smooth circling movements as seen in rings and parallel bars routines. Swinging is also used by gymnasts to increase angular momentum often in preparation for release and regrasp movements or dismounts as seen in asymmetric bars and high bar routines. The first of these will be referred to as a linking swing and the second as an accelerating swing. In this presentation, a gymnast swinging on a single bar (Figure 1) will be used to outline the mechanics of swinging and then two examples of skills will be featured to highlight 'linking' and 'accelerating' swings.

Figure 1. Highbar long-swing

Mechanics of Swinging

The mechanics of all swinging in gymnastics can be summarised simply - to increase rotation a turning force is needed. The larger the turning force and the longer that the turning force acts the greater the increase in the gymnast's capacity to rotate. The special term in mechanics which is used to describe this capacity to rotate is angular momentum and the special term for turning force is torque or turning moment of force.

Figure 2. Gymnast in (a) straight extended, (b) piked and (c) arched body shapes showing the location of the mass centre (CM) in relation to the gymnast's body.

To aid in explaining the mechanics of swinging three basic terms from mechanics need to be established:

1. The mass centre (CM) is an imaginary point at which the weight of the gymnast can be considered to act. In a stretched body configuration the CM is the maximum distance from the hands (Figure 2a). If the gymnast adopts a piked body shape the CM moves beyond the body into the space between the thighs and the trunk, and closer to the hands (Figure 2b). Similarly if the gymnast arches, his CM moves behind the body and closer to the hands (Figure 2c). The CM is a particularly useful concept in gymnastics because it enables the whole body of the gymnast, irrespective of the body configuration, to be represented by a single point and in so doing simplifies the mechanics.
2. The weight of the gymnast is a force acting downwards which is equal to the mass (m) of the gymnast multiplied by gravitational acceleration (g). Gravity always acts downwards. The weight (mg) of the gymnast is shown as a downward force at the CM, (Figure 3).
3. The moment arm is the perpendicular distance between the axis at the bar and the weight force. The moment arm for the weight force will always be horizontal since the weight always acts vertically downwards. In Figure 3 the moment arm is shown as a dashed horizontal line.

The Backward Giant Circle

The torque acting on a gymnast is shown at a single instant during the downswing in a backward giant circle (Figure 3). Strictly speaking there are other forces acting, including the frictional forces at the hands and air resistance, both of which are opposing the motion of the gymnast. However, in relation to the weight force, these forces are small and can be regarded as negligible at present. The bar also bends and applies forces which will be considered in more detail later.

The torque or turning moment of force in Figure 3 is equal to the weight force (mg) multiplied by the moment arm length (d). This torque is acting to turn the gymnast in an anti-clockwise direction and so is tending to increase the backward rotation of the gymnast.

Figure 3 -A gymnast in a straight body position on the downswing. The small white circle is located at the gymnast's mass centre (CM), the weight (mg) of the gymnast is the only force acting downwards at a distance (d) from the axis at the bar.

If the gymnast's body position in the giant circle is considered to be viewed on a clockface, at 12 o'clock he would be in a handstand position (Figure 4a) with a moment arm length of zero. There would therefore be no torque acting on the gymnast. At 9 o'clock (Figure 4b) the moment arm would be at its maximum length and hence the torque acting on the gymnast would also be at a maximum. By 6 o'clock (Figure 4c) the torque would again have returned to zero.

Figure 4 -Gymnast in a straight body position at three locations during the downswing around the high bar. (a) at 12 o'clock with zero torque, (b) at 9 o'clock with maximum torque and (c) at 6 o'clock with zero torque.

Between positions a and b in Figure 4 the gymnast's torque would increase and then between b and c it would decrease. The gymnast's weight is a fixed value since his mass and gravitational acceleration (go = o 9.81 m.s-2) are both constant. Therefore the only factor influencing torque is the length of the moment arm. By remaining straight throughout the downswing, the moment arm length is controlled by the angle that the gymnast's CM makes as it circles around the bar. Similarly, once the gymnast passes under the bar, if he remained straight, the moment arm would again be controlled only by the angle that the gymnast's CM made with respect to the bar. If the gymnast did nothing else he would circle back to the handstand position on top of the bar. However, this would only be true whilst there were no frictional forces at the hands or air resistance opposing the motion. In the gymnasium both these resistances are present and so the gymnast would not complete the circle but would 'stall' somewhere around 2 o'clock in Figure 4. In the overgrasp grip as shown in Figure 5, the gymnast is performing the backward giant circle and the frictional forces between his hands and the bar act at a tangent to the bar in the opposite direction to his motion. The frictional forces are therefore producing a torque throughout the giant circle which is slowing him down. Air resistance against his body will also be slowing him down throughout the movement.

Figure 5 -Frictional forces opposing the direction of motion in the giant circle. Ref: Hiley (1998a) adapted from Hay (1994)

Fortunately for the sport, gymnasts are not inanimate and can vary the configuration of body segments to alter motion. As shown in Figure 2b, when the gymnast altered his body configuration from extended to piked, the CM moved slightly closer to his hands. That is the radial distance between the CM and the bar decreased slightly and hence with it the moment arm was also reduced. It is the latter distance that determines the torque and so piking would reduce torque. If a gymnast wishes to maximise the torque, he needs to maximise the moment arm length. This means keeping the mass centre as far away from the bar as possible. The straight body shape is the best configuration to achieve this objective.

In summary, on the downswing, keeping the body straight increases the moment arm length and therefore increases the torque.

Once the gymnast passes under the bar, the body weight force will act to oppose the gymnast's motion. In other words, the weight force, which always acts downwards, is now producing a torque in a clockwise direction whilst the gymnast wishes to continue circling in the anti-clockwise direction. If the gymnast were to remain perfectly straight the circle could not be completed. All that is needed is for the gymnast to reduce the torque slightly by shortening the moment arm between the weight force and the bar to achieve the desired effect.

Keeping the body straight also increases a gymnast's resistance to rotate. Moment of inertia is the special term in mechanics used to describe a body's resistance to change its angular motion. The higher the moment of inertia the greater the resistance and so the longer it would take for a gymnast to fall from a handstand position above the bar to a hanging position below the bar. By remaining extended on the downswing a gymnast therefore takes advantage of two factors: the moment arm and the swing-down time are maximised.

To maximise his rotation a gymnast should stay 'as long for as long as possible'.

When a torque acts over a time period, angular impulse is created. Angular impulse quantifies the gymnast's change in angular momentum, or his capacity to rotate. The greater the angular impulse the greater the change in angular momentum. To gain the greatest increase in angular momentum a gymnast should aim to keep both the torque and the swing-time high. Conversely when the gymnast passes under the bar, he now needs to reduce both the torque and the swing-time. By shortening his body he can achieve both since his CM moves closer to the bar reducing his moment arm and his moment of inertia. To achieve a reduction in the moment arm and the moment of inertia, the gymnast can adopt a shallow 'dished' body position by slightly altering the angles at the hips and shoulders (Figure 1). To achieve this slight change in the body's configuration the gymnast uses muscular contractions to 'close' the hip and shoulder angles. In so doing the gymnast is taking some of the energy stored in a chemical form in his muscles and converting it into mechanical energy of movement. If the amount of energy transferred from his muscles exactly balances the energy lost due to friction at the bar and from the air, the gymnast would return to a stationary handstand position above the bar. If the energy transferred from the gymnast's muscles is greater than that lost due to friction, the excess energy would be seen as extra rotational energy. In other words the gymnast would have increased his speed of rotation through the handstand position above with the bar.

A gymnast's circling motion around a bar is controlled by the timing of small changes in the joint angles at the hips and shoulders.

Elastic Energy

There is another form of energy in bar circling and that is elastic energy stored in the bar. FIG 'Code of Points' states that a high bar should deflect 100 mm when loaded with a force of 2200o N (approximately equivalent to the weight of three and a half male gymnasts) and return to its original horizontal position when the load is removed. The bar is therefore a spring. As the gymnast swings the bar will deflect from its resting neutral position. (Look at Figure 1 to see that a gymnast's hands move around the central neutral bar position throughout the circle). The greatest force occurs when the gymnast is travelling fastest at the bottom of the circle and so the bar will be bent most at this point. The force at this time will exceed the weight of 4 gymnasts in a standard giant circle and be as much as the weight of 6 gymnasts in an accelerated giant circle. As the gymnast rises on the upswing the bar will begin to return to its original position and in so doing return some energy to the gymnast. The amount of energy stored in the bar is proportional to the deflection of the bar. Not all the energy stored in the bar will be returned and so the gymnast needs to input some extra energy from his muscles to compensate for this loss. A 'springy' bar is beneficial in a number if ways and later in the section on the accelerated giant circle the motion of the bar will be considered in more detail.

Two examples of circling in gymnastics will be used to illustrate these mechanical relationships in action. First a long-swing with full pirouette on parallel bars or Long-swing Diamidov will be used to examine a linking swing and secondly an accelerated giant circle will be used to examine ways of increasing angular momentum in preparation for a dismount.

Long-swing Diamidov: The longswing Diamidov was first seen in competition during the Friendship Games in 1984. Two techniques have been regularly used to execute this skill on parallel bars. One method demonstrated by Li Jing of China, and the second, based on the technique introduced by Yuri Balabanov (formerly of the USSR), and more recently developed by Misutin of the Ukraine. Both gymnasts have enjoyed World and Olympic success using different techniques, but which is the preferred method and why? There are two parts to the action of interest, the swing and the pirouette. The pirouette is partially determined by the angular momentum developed during the swing. Observation of the two performers shows Misutin raising his free arm to the side of his body during the pirouette. Li adopts a very narrow body shape during the pirouette. Earlier information on moment of inertia clearly showed that reducing moment of inertia reduces a body's resistance to rotate and so in the pirouette a narrow shape should enable the twist to be performed more readily. An earlier study of Li's technique (Liu and Liu, 1989) reported that Li experienced some difficulty in regrasping the second bar as he ended his pirouette and that his CM was slightly off centre. Conversely, observation of Misutin in action suggests that he has ample time to pirouette and regrasp the bar. However, Misutin appears to contravene the idea that a narrow shape is preferable when twisting. It is well documented that tilting the body during a somersault produces twist (Yeadon et al., 1990) and so perhaps the arm raising action by Misutin towards the end of the 'somersault' rotation aided the twist as a result of tilting the body. Video analysis (Kerwin et al., 1993) however, showed that the somersault angular momentum was insufficient to generate enough twist to be of any value. The answer lies in the alternative explanation that the arm raising tilted the body and shifted the CM towards the supporting bar and aided the balance of the gymnast giving him time to spot and place the second hand on the bar at his 'leisure'. Both techniques require sufficient angular momentum about the somersault axis to complete the rotation and since the gymnast begins in a stationary handstand position, this angular momentum can only be created during the downswing phase of the skill. By placing digitised images of the two gymnasts body configurations next to each other it is possible to highlight small but important differences between the two techniques.

Figure 6 -Li and Misutin during the downswing phase of the Diamidov on parallel bars

Li is slightly dished on the downswing whilst Misutin is completely extended. Misutin's technique is therefore more effective in producing angular momentum since his moment arm is greater and his total downswing time is slightly longer. Under the bar, both gymnasts adopt a slightly hocked shape to clear the floor before extending on the upswing into the pirouette position. Misutin however, has more angular momentum to 'play with' and so can afford to be more leisurely in his execution. He can remain fully extended and although his arm is raised sideways and his actions appear slower, he has more time and hence more control of the fine adjustments in the pirouette. Li on the other hand is slightly short of angular momentum and has to adopt a more flexed body shape to complete the somersault rotation and at the same time fit in the pirouette. Thus although the side arm action is clearly beneficial for control it is only possible as a result of the very effective downswing technique creating the required angular momentum.

The Giant Circle

The giant circle on high bar and asymmetric bars is the most important element in swinging gymnastics routines. This skill forms the basis of the whole exercise and with slight variations becomes a range of skills. The accelerated giant circle will be used to illustrate the accelerating swing and will highlight the subtlety of timing in the angle changes at the hips and shoulders which elite gymnasts have mastered. The aim of accelerating a giant circle is to increase angular momentum in preparation for either a release and regrasp movement or for a dismount. To perform a double straight backward somersault dismount for example, the angular momentum needed is substantial (Kerwin et al, 1990).

Figure 7 -Two types of accelerated giant circle (a) traditional, and (b) scooped

Two distinct techniques have evolved in gymnastics to accelerate the giant circle. A 'traditional' technique (Figure 7a) in which the giant circle is performed in a manner similar to the basic swing described earlier, but with the emphasis being placed on increasing the gymnast's rotation on every circle. In addition a second 'scooped' technique has been developed in which a gymnast remains piked whilst passing over the bar (Figure 7b). In the traditional technique the gymnast maintains an extended body configuration from the handstand position. There is then a slight 'arching' of the body prior to the bottom of the circle followed by a 'dishing' as the gymnast passes under the bar. This hip hyper-extension and flexion adds energy into the system and increases the rotation. On the upswing phase the characteristic shallow pike is seen with the gymnast extending into the handstand configuration close to the top of the circle. In contrast the scooped technique is characterised by an extended body position as the gymnast passes through the horizontal on the downswing followed by hyper-extension. The kick through to the dished shape is delayed and appears as a more distinctive piking action late in the upswing which continues over the top of the bar. The gymnast does not extend completely until he is at about 9 o'clock on the downswing. In both these versions of the skill the aim is to increase angular momentum in preparation for bar release. Three questions come to mind:

1. Why have two techniques developed ?
2. Which is the better technique?
3. Is there another technique that would be better than either of these?

Answering these questions is not straightforward. The simple mechanical analysis of the swing described earlier, although acknowledging the importance of the subtle timing of hip and shoulder angle changes, does not enable an ideal sequence and timing of changes to be determined. Also the fact that the bar bends horizontally as well as vertically means that the length from the gymnast's CM to the bar is not defined as simply as appeared earlier. What would be needed to answer these questions experimentally is a gymnast who could perform all the possible variations in hip and shoulder angle changes, at precise times and at prescribed speeds. The gymnast could then be set the task of performing the many thousands of possible combinations of movements whilst being recorded on video tape so that his angular momentum could be calculated. No gymnast could achieve this. A 'model gymnast' who would never get tired, who could do exactly what has been prescribed and who would not introduce any personal variations into the skill would be ideal. What is being described is a 'robot gymnast'. A robot is a physical model but a computer simulation model could be produced to carry out all of these tasks and answer these questions providing that one could be designed and programmed to behave like a real gymnast swinging on a real highbar. This task has been completed by Dr Michael Hiley as part of his PhD research studies (Hiley, 1998a) at Loughborough University. The human body is an extremely complex biomechanical system and to replicate all its features in a computer model is currently impossible. However, a simplified version of the biological and mechanical features of the gymnast and bar which represent the behaviour of a real performance can be produced. The computer model comprises a gymnast and bar, both of which are governed by the laws of mechanics. To construct the model, a gymnast's physical size and strength had to be measured. A member of the Great Britain senior men's national squad acted as the subject. Video recordings of him performing a series of long-swings on an instrumented highbar were recorded so that any predictions from the model gymnast could be compared with reality to ensure that the model was accurate. The physical size of the gymnast was determined using an inertia model (Yeadon, 1990). The output was mass, CM and moment of inertia data for the individual gymnast. The strengths of the muscles around the hips and shoulders were determined using a dynamometer and the deflection of the high bar under a range of loads was determined to establish the 'spring' like characteristics of the apparatus. The computer model produced is represented in Figure 8.

Figure 8 -The computer simulation model, (Hiley,1998a)

The model comprises four body segments; arm, torso, thigh and lower leg and has springs at the end of the arm to represent the bar and at the shoulders to represent the 'stretching' characteristics of the gymnast. The 'gymnast' spring located at the shoulder in the model represents the elastic stretching and recovery of the gymnast and includes shoulder, spine and wrist extensions, which occur under the large loads experienced during the giant circle.

To address the three questions a series of 'experiments' were conducted. The model gymnast was instructed to make selected movements by specifying the exact times and speeds at which hip and shoulder angle changes should be made. Checks were made to ensure that the muscle strength required to complete the movements was within the previously determined limits. All the movements were therefore biologically possible and in many ways similar to the sorts of instructions that a coach would give to a gymnast, albeit in a more precise manner than is typical in the gymnasium. To address the three questions raised earlier, a scoring system was needed so that each performance could be rated and a particular trial identified as being better or worse than previous attempts. The objective in the accelerated giant circle is to increase rotation and so the amount of angular momentum generated would be an ideal score to use. The last one and three-quarters rotations of the bar prior to release were studied. The model gymnast was given a speed of rotation over the bar at the start of the accelerated giant circle, based on previous video analyses, of just under 130º/second (~1/3 rev/sec). The point of 'release' was set for a theoretical double layout somersault dismount at 8º below the horizontal as reported previously (Brüggemann et al, 1994). It takes thousands of trials to investigate all possible combinations of joint angle changes within a giant circle. After many days of computing a solution was reached which maximised the model gymnast's angular momentum without exceeding his strength limits. Two solutions were arrived at, one with marginally more angular momentum than the other. The graphics sequences representing these solutions are shown in Figures 9 and 10.

Figure 9 -The 'Global' optimum giant circle technique

The global optimum technique is the result of the best of all possible permutations of joint angle changes and depicts a sequence very similar to the 'traditional' circling technique shown in Figure 7a. The graphics sequence begins at position 1 in the left hand figures and shows the first complete circle. The right hand figures show the final three-quarters of the circle leading up to release. Notice the gymnast 'dishing' through the bottom of the circle (4-6) and extending through the handstand over the top of the bar (8-9). The amount of angular momentum generated for this modelled gymnast was 125 units and represents enough to complete two and a half layout backward somersaults in the dismount. This optimum technique therefore produced more angular momentum than would be required for a standard double layout backward somersault dismount. During the computing process, a second optimum solution was found which produced 3% less angular momentum than the technique shown in Figure 9. The graphics sequence for this second technique is shown in Figure 10. The starting position and speed of rotation over the bar are the same as for Figure 9 and the first part of the downswing looks very similar to the global optimum. The dishing under the bar at point 5 is less pronounced although by position 6 the body configurations are very similar in the two techniques. From points 7 to 11 however this second 'local' optimum technique is quite different to the former 'global' optimum technique. The gymnast maintains a piked shape through the top of the circle and does not completely extend until he is approaching the horizontal on the final downswing. This local optimum solution is much closer in appearance to the 'scooped' technique shown in Figure 7b.

Figure 10 -The 'local'optimum giant circle technique

Returning to the three questions presented earlier:

1. Why have two techniques developed ?
2. Which is the better technique?
3. Is there another technique that would be better than either of these?

Question 1: It would appear that two techniques have developed since both are good techniques for producing large amounts of angular momentum and so both serve the desired purpose of accelerating the giant circle. The two techniques arrived at by gymnasts and coaches are remarkably similar to the theoretical optimum solutions arrived at by the modelling process.

Question 2: If only the maximum amount of angular momentum is the criterion, then the global optimum solution is better than the local optimum solution. The global solution is closest to the traditional circling technique. Why then might gymnasts favour the 'scooped' technique? Perhaps more strength was needed, or perhaps the total energy cost for the gymnast was higher for the global technique. Interestingly the gymnast was found always to be working well within his strength limits in the previous calculations and only on the final action leading up to release did the joint torques approach values close to the gymnast's maxima. The simulations were run again with the gymnast's strength reduced by 25%. This time the global optimum solution was found to be the scooped technique rather than the traditional technique. It would therefore appear that both techniques are good and perhaps when a gymnast is tired towards the end of the routine there is a case for using the scooped rather than the traditional technique. It is not obvious from the images why the scooped technique should be as effective at generating angular momentum. For example, the principle of 'staying as long for as long as possible' on the downswing does not appear to have been adhered to. Closer examination of the scooped technique however shows that extra horizontal acceleration by the gymnast as he passes over the bar, bends the bar more in the backwards direction and moves his mass centre further from the neutral bar position than the body shape alone would indicate. Simple mechanics can therefore sometimes be deceptive and highlights the need for more powerful simulation modelling techniques.

Question 3: Is there another technique which is better than either of the two presently in use? The optimum solution for the gymnast in this study was shown in Figure 9. If the real gymnast could mimic these joint angle changes exactly as prescribed by the model this would be the best of all possible techniques for him. However, as shown, changing the gymnast's strength changed the optimum solution. Similarly a precise optimum for any gymnast would depend on his physical size and condition at the time. So whilst it would be possible to determine the best possible technique for an individual gymnast, it is likely that the two techniques already in use are individual interpretations of optimum solutions and the absolute best solution is probably going to remain a theoretical one.