**1. Introduction**

The title of the chapter refers to the research work that the author has been doing into the application of the knowledge of biomechanics in the methodology of teaching motor activities in sports disciplines involving a complex rotational movement of a human body. The author, who previously worked as a PE and physics teacher in a secondary school and an aikido instructor, now teaches biomechanics at university. Basing on his earlier work results, the author found out that some notions in mechanics are better acquired if explained using sports performance examples. According to the author, motor activities of a particular technique practised in PE and aikido classes were mastered best if their dynamics were explained to students using the principles of physics. This method also accelerated the process of understanding the rules of mechanics by the students executing a particular technique. The feelings of the students were similar - in the questionnaire made with 273 randomly chosen [1,2] secondary grammar and technical school pupils, 85% of the subjects supported explaining the rules of mechanics using sports performance examples, whereas 76% of them also supported the method of explaining techniques of the performance of certain exercises involving the rules of physics. The present chapter illustrates the experiments that verified the above-mentioned findings. The tests mainly showed the use of the knowledge of biomechanics in teaching aikido. Some of the groups of adolescents were involved in the experiments at a time interval. The first experiments carried out also checked if the effect of the knowledge of biomechanics on a shot put was increased range. The objectives of the paper are: 1. Presenting the knowledge of the biomechanics of aikido techniques. 2. Verifying whether teaching mechanics by explaining its rules using examples from aikido and various sports disciplines increases the efficiency of teaching. 3. Checking how the knowledge of biomechanics related to the rules of mechanics used in aikido techniques and shot put can improve their performance correctness. 4. Checking how a method of teaching aikido can affect the efficiency of learning aikido techniques by children.

© 2012 Mroczkowski, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

### **2. Biomechanics of aikido techniques**

### **2.1. The principles of mechanics used for executing aikido techniques**

Using the Knowledge of Biomechanics in Teaching Aikido 39

(1)

(2)

of the attack changes the direction of the attacker's motion from rectilinear to curvilinear. He tries to move on the smallest possible curve. If the attacker moves in the same direction as the defender, then he additionally gains centrifugal force. If the practitioners' weights are combined by, for example, doing a grip by only one of them, then the second principle of

> *M I*

The defender, along with decreasing the curvilinear motion radius, is decreasing the moment of inertia I of the practitioners. He tries to move in such a way as to ensure that at the end of performing the technique, the axis of motion rotation is possibly the closest to his body. When executing a certain technique, aikido practitioners are acting with certain forces, and since it is a curvilinear movement, a resultant moment of force M is produced. This moment of force, with decreasing the moment of inertia of the subjects, results in an increase in the angular acceleration ε in this motion (1). However, this analysis is of rather an approximate character. A human body is not a single solid and in a close study a biomechanical segment model of human body structure should be assumed. It is advised to

**Figure 2.** Analysis of distribution of the practitioners' masses around the common axis of rotation O' in

' 2 ' '' ' 2 ' 2 *c*

as well as the distances dA and dB from their centres of mass mA and mB (Fig. 2), must be

*I I md I I I I I md I I md* 

*A B A CA A A B CB B B*

is a sum of the moments of inertia of the subjects, namely the

. For this purpose, their central moments of inertia ICA and ICB,

apply Steiner's theorem (2) for determining the moment of inertia.

dynamics is present here.

the final stage of the technique

The moment of inertia I'

attacker IA' and the defender IB'

The term "aikido technique" must be precisely defined. There are multiple definitions of "sports technique" in professional literature. Bober [3] in his analysis of definitions of sports technique follows Zatsiorsky [4] who thinks that a sports technique is a term which can be described rather than defined. In the author's opinion [2], the term aikido technique refers to a way of neutralizing a specific attack and simultaneous execution of a specific motor task. Neutralizing can be made [5] by (1) locking, (2) throwing or (3) a combination of both. The neutralizing technique differs with regard to the type of attack. Aikido characteristically has a great number of techniques depending on the combination of the means of neutralization and the type of attack. Aikido is a martial art of a defensive character using the power of the attacker. In the self-defence process the following rules are applied [2,6,7]: "give in to win", "turn around if you are pushed", "move forward if you are pulled". In principle, aikido techniques should be elaborated in such a way as to make it possible for even a physically weaker person to execute them against a stronger person [8]. Simplifying the mechanical analysis, this can be confirmed by the principles of mechanics [6]. Aikido is practised mainly as a form of self-defence and it most frequently lacks sports competition. There is a clear division onto the defender executing certain techniques and the attacker against whom this technique is performed. The rules mentioned lead to a conclusion that the defender tries not to stop the attacker's move, especially with his smaller power and weight when it is impossible. If the attacker pulls with a certain force FA (Fig.1a), then with a smaller strength of the defender FB the result of these forces is directed at the attacker, a good solution is a sudden change of the defender's force direction into the one consistent with the force of the attacker. The resultant force being a sum of the vector values can surprise the attacker and make him lose balance. If, on the other hand, the attacker pushes with a greater force than the defender can resist, the resultant force will also have the direction of the attacker's force. In this case, a good solution would be to step out of the line of the attack.

**Figure 1.** Generating the resultant force when the attacker (published in [6]) a) pulls the defender b) pushes the defender

The resultant force of two convergent vectors that is then produced makes it possible to change the direction of the attacker's move (Fig.1b) The defender, by stepping out of the line of the attack changes the direction of the attacker's motion from rectilinear to curvilinear. He tries to move on the smallest possible curve. If the attacker moves in the same direction as the defender, then he additionally gains centrifugal force. If the practitioners' weights are combined by, for example, doing a grip by only one of them, then the second principle of dynamics is present here.

38 Injury and Skeletal Biomechanics

**2. Biomechanics of aikido techniques** 

**2.1. The principles of mechanics used for executing aikido techniques** 

In this case, a good solution would be to step out of the line of the attack.

**Figure 1.** Generating the resultant force when the attacker (published in [6])

The resultant force of two convergent vectors that is then produced makes it possible to change the direction of the attacker's move (Fig.1b) The defender, by stepping out of the line

(a) (b)

a) pulls the defender b) pushes the defender

The term "aikido technique" must be precisely defined. There are multiple definitions of "sports technique" in professional literature. Bober [3] in his analysis of definitions of sports technique follows Zatsiorsky [4] who thinks that a sports technique is a term which can be described rather than defined. In the author's opinion [2], the term aikido technique refers to a way of neutralizing a specific attack and simultaneous execution of a specific motor task. Neutralizing can be made [5] by (1) locking, (2) throwing or (3) a combination of both. The neutralizing technique differs with regard to the type of attack. Aikido characteristically has a great number of techniques depending on the combination of the means of neutralization and the type of attack. Aikido is a martial art of a defensive character using the power of the attacker. In the self-defence process the following rules are applied [2,6,7]: "give in to win", "turn around if you are pushed", "move forward if you are pulled". In principle, aikido techniques should be elaborated in such a way as to make it possible for even a physically weaker person to execute them against a stronger person [8]. Simplifying the mechanical analysis, this can be confirmed by the principles of mechanics [6]. Aikido is practised mainly as a form of self-defence and it most frequently lacks sports competition. There is a clear division onto the defender executing certain techniques and the attacker against whom this technique is performed. The rules mentioned lead to a conclusion that the defender tries not to stop the attacker's move, especially with his smaller power and weight when it is impossible. If the attacker pulls with a certain force FA (Fig.1a), then with a smaller strength of the defender FB the result of these forces is directed at the attacker, a good solution is a sudden change of the defender's force direction into the one consistent with the force of the attacker. The resultant force being a sum of the vector values can surprise the attacker and make him lose balance. If, on the other hand, the attacker pushes with a greater force than the defender can resist, the resultant force will also have the direction of the attacker's force.

$$
\varepsilon\_{\perp} = \frac{M}{I} \tag{1}
$$

The defender, along with decreasing the curvilinear motion radius, is decreasing the moment of inertia I of the practitioners. He tries to move in such a way as to ensure that at the end of performing the technique, the axis of motion rotation is possibly the closest to his body. When executing a certain technique, aikido practitioners are acting with certain forces, and since it is a curvilinear movement, a resultant moment of force M is produced. This moment of force, with decreasing the moment of inertia of the subjects, results in an increase in the angular acceleration ε in this motion (1). However, this analysis is of rather an approximate character. A human body is not a single solid and in a close study a biomechanical segment model of human body structure should be assumed. It is advised to apply Steiner's theorem (2) for determining the moment of inertia.

**Figure 2.** Analysis of distribution of the practitioners' masses around the common axis of rotation O' in the final stage of the technique

$$\begin{aligned} \text{I}' &= \text{I}\_c + md^2\\ \text{I}' &= \text{I}\_A \text{I}' + \text{I}\_B \text{I}' & \text{I}\_A \text{I}' = \text{I}\_{CA} + m\_A \text{d}\_A \text{I}^2 & \text{I}\_B \text{I}' = \text{I}\_{CB} + m\_B \text{d}\_B \text{I}^2 \end{aligned} \tag{2}$$

The moment of inertia I' is a sum of the moments of inertia of the subjects, namely the attacker IA' and the defender IB' . For this purpose, their central moments of inertia ICA and ICB, as well as the distances dA and dB from their centres of mass mA and mB (Fig. 2), must be determined. When the radius on which the attacker is moving decreases, the moment of inertia of the position of the practitioners' bodies gets smaller and their angular velocity rises. If we neglect the motion resistance, we can talk about the principle of the conservation of the moment of momentum

$$Io = \text{const} \tag{3}$$

Using the Knowledge of Biomechanics in Teaching Aikido 41

(5)

defender is even likely to do a one leg jump. When performed correctly it facilitates the shift of the defender's weight down. Then all his P=mg is used in the technique. Most frequently the force enabling an aikido throw is a result of the centrifugal force of the attacker and the weight of the defender (Fig. 4). A good example illustrating the conduct of the defender would be a spinning top that apart from a rotational motion would do an up movement, such as jumps. An approximate formula for a resultant force producing a throw can be

> 2 2 2 1

*m V F m <sup>g</sup> r* 

**Figure 4.** Resultant force acting on the attacker in the final stage of the technique (published in [6])

The figure does not show all the vectors of the force, which can be obtained by means of, for example, pelvis turns, characteristic for aikido performed by the defender along with the body turns around in a horizontal plane, or by means of a force coming from the use of particular muscles of the attacker. Many authors explain the dynamics of the defence techniques (in martial arts) quoting the principles of biomechanics [6-11]. Of special interest here are the lectures of Jigoro Kano explicating the "give in to win" principle. The father of judo was familiar with the biomechanical aspects of judo. The interplay of centrifugal and centripetal forces or movements resembling a spinning top involved in the execution of aikido techniques was understood by the son of the aikido founder Kishomaru Ueshiba [12]. Koichi Tohei [13], the only one who was awarded by the founder of aikido when he was still alive with the 10th Dan, claimed that the secret of Morihei Ueschiba was his ability to relax when executing the techniques which was also due to a low position of the centre of mass. However, it is not a complete loosening of muscles, but rather straining the muscles which, for example, causes a child to have such a power that another person cannot snatch the

determined as follows:

m1 – the defender's mass m2 – the attacker's mass

The subjects behave similarly to figure skaters when performing a pirouette. In this figure they move their lower limbs close to the axis of rotation and by doing this they increase their angular velocity . In some moment of the motion, the centre of mass of the defender should be at the closest possible distance from the axis of rotation of the performers' bodies' arrangement. His hands should be as close to this axis as possible. This leads to a decrease in the moment of inertia of the performers and to an increase in the value of the centrifugal force F acting on the attacker.

$$F = \frac{mV^2}{r} \tag{4}$$

As the formula (4) shows, the centrifugal force gets bigger when the velocity the attacker attacks with goes up, his weight increases and the radius he follows gets smaller. The behaviour of the attacker can be compared with the behaviour of a car on a road bend. The sharper the bend and the smaller the radius r, the bigger the car speed V and the bigger force acting on the car, increasing the risk of falling off the track. The behaviour of the defender resembles the motion of a spinning top (Fig. 3). The external force acting on the spinner cannot disturb its rotational movement. The defender makes a move causing the attacker and not the defender to gain the centrifugal force. Therefore, he performs stepping out of the line of the attack in such a way so as the whole motion is done around the axis of rotation going most desirably through his body.

**Figure 3.** Spinning top (published in [6])

The centrifugal force may allow neutralizing the attack. However, it is usually too small to knock the attacker over. In order to do a throw, the defender uses his weight, which when adequately transferred may exceed the centrifugal force gained by the attacker [6]. Therefore, in a great number of techniques, the defender suddenly lowers his centre of mass in order to increase the technique dynamics. In the final stage of the throw, provided the attacker's body is inclined enough, in order not to meet his unexpected counter-punch, the defender is even likely to do a one leg jump. When performed correctly it facilitates the shift of the defender's weight down. Then all his P=mg is used in the technique. Most frequently the force enabling an aikido throw is a result of the centrifugal force of the attacker and the weight of the defender (Fig. 4). A good example illustrating the conduct of the defender would be a spinning top that apart from a rotational motion would do an up movement, such as jumps. An approximate formula for a resultant force producing a throw can be determined as follows:

40 Injury and Skeletal Biomechanics

of the moment of momentum

force F acting on the attacker.

rotation going most desirably through his body.

**Figure 3.** Spinning top (published in [6])

angular velocity

determined. When the radius on which the attacker is moving decreases, the moment of inertia of the position of the practitioners' bodies gets smaller and their angular velocity rises. If we neglect the motion resistance, we can talk about the principle of the conservation

The subjects behave similarly to figure skaters when performing a pirouette. In this figure they move their lower limbs close to the axis of rotation and by doing this they increase their

should be at the closest possible distance from the axis of rotation of the performers' bodies' arrangement. His hands should be as close to this axis as possible. This leads to a decrease in the moment of inertia of the performers and to an increase in the value of the centrifugal

<sup>2</sup> *mV <sup>F</sup>*

As the formula (4) shows, the centrifugal force gets bigger when the velocity the attacker attacks with goes up, his weight increases and the radius he follows gets smaller. The behaviour of the attacker can be compared with the behaviour of a car on a road bend. The sharper the bend and the smaller the radius r, the bigger the car speed V and the bigger force acting on the car, increasing the risk of falling off the track. The behaviour of the defender resembles the motion of a spinning top (Fig. 3). The external force acting on the spinner cannot disturb its rotational movement. The defender makes a move causing the attacker and not the defender to gain the centrifugal force. Therefore, he performs stepping out of the line of the attack in such a way so as the whole motion is done around the axis of

The centrifugal force may allow neutralizing the attack. However, it is usually too small to knock the attacker over. In order to do a throw, the defender uses his weight, which when adequately transferred may exceed the centrifugal force gained by the attacker [6]. Therefore, in a great number of techniques, the defender suddenly lowers his centre of mass in order to increase the technique dynamics. In the final stage of the throw, provided the attacker's body is inclined enough, in order not to meet his unexpected counter-punch, the

. In some moment of the motion, the centre of mass of the defender

const (3)

*<sup>r</sup>* (4)

*I*

$$F = \sqrt{\left(\frac{m\_2 V^2}{r} + \left(m\_1 g\right)^2\right)}\tag{5}$$

$$\frac{V^2}{r} = \frac{1}{2}\tag{6}$$

$$\frac{V^2}{r} = \frac{1}{2}\tag{7}$$

**Figure 4.** Resultant force acting on the attacker in the final stage of the technique (published in [6]) m1 – the defender's mass m2 – the attacker's mass

The figure does not show all the vectors of the force, which can be obtained by means of, for example, pelvis turns, characteristic for aikido performed by the defender along with the body turns around in a horizontal plane, or by means of a force coming from the use of particular muscles of the attacker. Many authors explain the dynamics of the defence techniques (in martial arts) quoting the principles of biomechanics [6-11]. Of special interest here are the lectures of Jigoro Kano explicating the "give in to win" principle. The father of judo was familiar with the biomechanical aspects of judo. The interplay of centrifugal and centripetal forces or movements resembling a spinning top involved in the execution of aikido techniques was understood by the son of the aikido founder Kishomaru Ueshiba [12]. Koichi Tohei [13], the only one who was awarded by the founder of aikido when he was still alive with the 10th Dan, claimed that the secret of Morihei Ueschiba was his ability to relax when executing the techniques which was also due to a low position of the centre of mass. However, it is not a complete loosening of muscles, but rather straining the muscles which, for example, causes a child to have such a power that another person cannot snatch the

### 42 Injury and Skeletal Biomechanics

child's favourite toy out of his hands. This ability of relaxing or loosening referred to above, is related to the concept of "ki". The idea of "ki" has rather a wide meaning in the Japanese culture and it is difficult to translate it into a European meaning. Generally, it is understood as life energy possessed by every man. However, an explicit explanation of "ki" in terms of mechanics is at the current level of research limited and thus goes beyond the subject matter of this presentation. The breathing techniques generally applied in some aikido schools understood as developing "ki" make it possible to master the ability to relax/loosen when doing a throw. In terms of throw dynamics in aikido it gives a greater possibility to shift the force coming from the weight of the defender P=mg.

Using the Knowledge of Biomechanics in Teaching Aikido 43

attacker is acted on with the moment of force equal to the product of the *FW* resultant and the

The moment of the force produced causes the attacker to lean forward and lose his balance.

**Figure 6.** Defence against an arm attack following a circle at the head level – analysis of forces in a

**Figure 7.** A form of a defence - grasping the attacker's arm with both hands (published in [14])

The above-mentioned aikido technique can be performed by a disabled person using only one upper limb. Force G is the most important as far as the dynamics of this technique execution is concerned. For applying this force, only one upper limb is needed, because only one point of the force application is enough. The application point of force G is supposed to be like "the eye of a cyclone". It is a central place where movement is the smallest. Force Fb changes the direction of the attacker's move (its value does not have to be big). Only one hand is needed for this change of direction, whereas the other can, for example, shield the body. With adequate speed of the defender, this technique can be executed with one hand neglecting shielding of the body. As previously mentioned, the movement of the defender in aikido often resembles the motion of a spinning top [Fig. 3], which apart from rotating also executes an upward movement. At the end of the technique the arms are in most cases

radius on which the attacker is moving.

vertical plane (published in [14])

placed close to the axis of the body rotation.
