A BIOMECHANICAL STUDY ON TOMOE-NAGE

OF JUDO TECHNIQUES

Matthew EXTON* (Heps Engineering Ltd.)

Yoshihiko IURA (Kanazawa University)

I Introduction

There are few papers concerning to the investigation on the biomechanics of Judo techniques

published in English, and most Judo textbooks only consider the topic superficially. Kudo '(1967)2)

explained the breaking of balance with the use of geometry. An analogy between the human body and

an isosceles triangle was proposed. The varying points of stability were discussed, but the author stressed

that the human body is a three dimensional form and movement of body weight complicates this simple

theory.

Further qualitative investigations of the Judo technique have been conducted by Miura et al. (1970)3),

(1971)4), which correlated electrogoniometric power outputs with electromyographic data during

progressive static positioning. But dynamic competitive situations were not investigated and no

quantitative values were obtained with these studies. Walker (1981)6) conducted a qualitative analysis of Judo in his paper, "The physics of Judo and Aikido". He emphasized the importance in the positioning

the centre of gravity of the Tori and Uke, and the use of torque in breaking the balance and throwing

the opponent.

One of the papers written in English to investigate Judo techniques in a quantitative manner is "Kinetic Analysis of Judo Technique" by Tezuka (1983) .5) The investigation combined the use of

cinematography and dynamography to determine the consistency of performance of skilled Judoists and

the differences in throwing technique. This involved filming a number of Judo throws and comparing

the filmed motions with the dynamographic traces. From the result, author found allied peaks and

troughs of the traces with fundamental points of the analysed throws and concluded that different Judoists

may use different styles of performance for the same throwing techniques.

The objective of this study was to obtain further information on a Judo throw and its mechanical

principles, analyzing normal and competitive throws of Tomoe-nage with quantitative manner.

II Experimentation

The experimentation was held at South Glamorgan Institute of Higher Education in Cardiff, United

Kingdom on January 21st, 1987. The physical characteristics and the experimental apparatus of subjects

are shown in Table 1 and Figure 1 respectively.

Gymnastic tumbling mats were used in conjunction with a "crash" mat to break the Uke's fall. A

grid was placed on the central tumbling mat to ensure the subjects to be placed in the same initial position

before filming. The camera speed was set at filmed 64 frames per second to analyse the throwing motion

sufficiently.

*Heps Engineering Ltd ., Ipswich Road, Cardiff, CF3 7XL, United Kingdom

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Piezoelectric accelerometers were placed on rubber arm and leg bands . A harness was worn by all three Ukes and the Tori wore both the harness and the accelerometer bands on his left ankle and right

wrist. The wiring ran along his left leg and right arm respectively to his right hip and was fixed to the

harness. The excess wiring ran from the Tori's right hip and was plugged to the boom connections . The boom operator followed the motion of the Tori, thus preventing entanglement of the wire with the

subjects. The wiring from the boom was connected to the recorder , receiving the three accelerometers and Signalgenerator outputs.

Three piezoelectric accelerometers were used , two recording changes in the x and y accelerations of the hand motion and one accelerometer measuring the acceleration of the leg motion . All subjects wore swimming trunks and white tape was placed on six joint positions for film analysis . Tori performed the different types of Tomoe-nage with three Ukes of differing mass as follows and he was advised to try the

throws without twisting motion to avoid three dimensional problem for analysis .

(a) Normal Throw : The orthodox technique of placing the foot on the stomach of the Uke as the

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Tori falls onto his back, forcing the Uke over him by straightening his leg and causing the Uke

to rotate about his shoulders.

(b) Competitive Throw : A similar throw to the above with the addition of a sudden pull with the Tori's arm as the Uke rotates about his shoulders.

Synchronization of the recorded and cinematographic data was overcome by using Signalgenerator

producing pulses at 64Hz, the same frequency as the camera speed. The Signalgenerator attached to the boom, a channel of the recorder, and also to a light bulb. This light bulb was placed within view of the

camera to interlink the two sets of data by visually marking the point on the film at which the

synchronizing of the data may be taken.

Analysis of the cinematographic result was carried out on a film motion analyser. The segmental

mass and centre of gravity values were taken from Dempster's (1955a)1) data, the segmental moment of

inertia was taken from that of Whitsett (l963)7). To obtain cinematographic data in conjunction with the

piezoelectric data, the sequence was analysed from the first frame in which the light from the

Signalgenerator was seen to be lit.

Analysis of the piezoelectric accelerometer results'; was carried out with the use of the recorder

connected to a graph plotter via a signal analyser. The results were recorded from the point at which the

first signal from the fourth channel as the Signalgenerator recording was received when it was triggered.

The above was repeated for all three channels and for each required throw.

III Results and Discussion

Figure 2 shows the centre of gravity displacement of the three Ukes during the normal throw. The

traces are very similar in both shape and phase. As the Tori drops to the floor, the Uke's centre of gravity

in turn lowers as he is pulled forwards/downwards by the Tori's arms. The centre of gravity displacement

reaches its lowest value in the vertical axis (Y-axis), when the Tori positions his leg on the Uke's stomach.

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EXTON : A Biomechanical Study on Tomoe-Nage of Judo Techniques

With the pull of the Tori's arm and the straightening of the leg , the Uke is elevated to a maximum height just after the Tori's leg is straightened . It can be seen that the centre of gravity displacement in the vertical axis never attains as high a displacement as the centre of gravity of the Uke standing . The centre of gravity displacement then decreases in the vertical axis as the Uke falls to the floor . The shape of the trace, as the Uke is thrown, is due to the combination of the forces exerted by the Tori throwing

the Uke upwards/forwards and gravity acting down . Figure 3 presents the moment of inertia plotted against the frame number for the three Ukes during

the normal throw. The traces may be explained by considering the trace on Middle -Weight Uke as follows : The moment of inertia decreases in magnitude from frames 0 to 15. This decrease in magnitude

is due to the movement of the Tori falling and placing his leg on the Uke's stomach . As the Tori falls he pulls the Uke downwards/forwards and this in turn lowers his radius of rotation about his ankles . From the above equation, if the radius of rotation decreased then so will the moment of inertia .

Once the foot is placed on the Uke, the Tori begins to pull with his arms and straighten his leg and

the Uke rises off the floor. Then the Uke is no longer rotating about his ankles, but about the Tori's

shoulders. The Uke is initially in a crouched position and his radius of rotation about the Tori's

shoulders is small. As the Tori's leg is straightened and arms pulled, the Uke's body "opens-up" due to

the centrifugal forces caused by rotating. The radius of rotation ,therefore increases and produces a

corresponding increase in the moment of inertia, reaching a maximum at the point of impact on reaching

the floor.

Figure 4 shows the angular velocity plotted against the frame number for the three Ukes during the

normal throw. The three traces are similar in shape but differ in phase and magnitude during the throw .

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The peak angular velocity of the three Ukes is at the same frame number and approximately the same

angular velocity differing within 0.5 radians per second.

All traces consist of an initial increase in angular velocity, but varying gradients. The curve of traces

showed several peaks and troughs with differing phases and magnitudes. The traces, with reference to

the Middle-Weight Uke, may be explained as follows : As the Tori drops to the floor, he exerts a pull.

This pull produces a large change in angular velocity, frames 0 to 6. The angular velocity reaches a peak

at frame 8 as the Tori is about to position his foot on the Uke. During the placement of the Tori's leg

on the Uke's stomach, the angular velocity decreases slightly. This is due to the change in direction of

the Tori's drop, from falling towards the Uke, frames 0 to 15, to falling away from the Uke, frame 15

onwards.

When the Tori's foot is positioned, the angular velocity increases up to frame 21 as the Uke's

direction of motion is changed from moving downwards/forwards to upwards/forwards. The angular

velocity from frames 21 to 31 decreases to a minimum at frame 30 as the Uke reaches his highest vertical

position. From frame 31 onwards, the angular velocity increases considerably as the Uke rotates due to the pulling of the Tori's arms and gravity acting downwards. The Uke lands on the floor at his maximum

angular velocity, frame 58.

The gradient of the angular velocity traces represent the angular acceleration. Since torque is

proportional to the angular acceleration, then the gradient also represents the resulting torque acting on the Uke at a point during the throw. From Figure 4, it can be seen that there is a large resultant torque

exerted during the initial stage of the throw, as the Tori breaks the balance of the Uke (Kuzushi). There

is a momentary decrease in torque during the positioning of the leg and body of the Tori (Tsukuri). This

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EXTON : A Biomechanical Study on Tomoe-Nage of Judo Techniques

is followed by two torque, frames 16 to 21 and 31 to 58, as the Tori throws the Uke (Kake). The phase differences between the three Ukes may be due to the initial speed of the Tori positioning

himself in the throwing position. Since the initial gradient is larger the earlier curve with peaks and

troughs is produced. It can be seen that the gradient in Middle-Weight Uke is greater than the one in

Light or Heavy-Weight Ukes and so the peak comes sooner .

Figure 5 presents Tori's angular momentum plottoed against frame number in the Middle-Weight

Uke during the normal throw. From frames 0 to 7, the angular momentum increases as the Tori lowers

and positions his body to throw the Uke. The angular momentum decreases from frame 7 reaching a

minimum value at frame 17. This is the point at which the Tori's direction of fall changes from towards

the Uke to away, producing a corresponding decrease in the Uke's angular velocity .

From frames 17 to 41, the angular momentum increases as the Tori falls to the floor, straightens his

leg and exerts a pull with his arms. The angular momentum attains a maximum value at frame 41 , the

point at which his leg has parted from the Uke's stomach and is about to fall to the ground. The decrease

in angular momentum from frame 41 onwards corresponds to the Tori's leg falling to the floor and Tori

rolling flat onto his back.

Figure 6 shows the angular velocity plotted against frame number for the Middle-Weight Uke

comparing the normal with the competitive throw.

The purpose of this comparison was to assess whether, by use of the Conservation of Angular

Momentum, the Uke could be made to rotate faster during the final stage of the throw. The underlying

theory is that as the Uke leaves the Tori's leg he has imparted to him an angular momentum .

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i *A, 23 —(3) , 1991

Angular Momentum = I • co

I= Moment of Inertia

=m• r2

co = Angular Velocity

As the Uke rotates about the Tori's shoulders, the angular momentum will remain constant. If the

Tori pulls suddenly, pulling inwards towards himself, the radius of rotation is decreased proportionally.

The angular momentum must remain constant according to the Law of Conservation of Angular

Momentum and so that angular velocity increases proportionally as below.

Angular Velocity (0))= Change in Angle Time Taken

The Uke rotates through the same angle in both the normal and competitive throws. Therefore, since

the angle is constant, then an increase in angular velocity produces a corresponding decrease in the time

taken to throw the Uke as can be seen in Figure 6.

The gradient of angular velocity change during the competitive throw is greater than that of the

normal throw. Since the gradient is the total angular acceleration exerted on the Uke, then this is

proportional to the torque as below.

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It may therefore be concluded that a greater overall torque is exerted during the competitive throw

at the pulling phase to produce a greater angular velocity during the rotating stage .

Figure 7 shows the piezoelectric traces for the Middle-Weight Uke in the both normal and

competitive throw. The traces were sampled at a 99dB range and 50Hz frequency .

The traces are plotted as decibel versus frame number. The gradient of the traces represents the

change in acceleration. According to the Newton's Second Law , force is proportional to acceleration,

then the change in acceleration at a given point is also representative of the change in force . The

magnitude of these forces is comparative and cannot be taken as absolute values since the proportionality

between the acceleration and force is not known.

It may be noted that a negative gradient represents a force directed towards the Tori as a pull . A

positive gradient therefore represents a force directed away from the Tori as a push.

An explanation of the traces 1 to 3 during the normal throw is as follows : Trace 1 is that of the leg

accelerometer. The traces show that there is an acceleration within the first frames, as the Tori steps off

the ground with his throwing leg. This acceleration decreases up to frame 16, the point at which the leg

contacts the Uke's stomach. At this point a number of accelerations occur, between frames 16 to 21, as

the Uke changes his direction of motion and the Tori pulls back his leg ready to extend it. Between

frames 21 and 22 the Tori rapidly retracts his leg force against the Uke's stomach, following with a large

acceleration from frames 22 to 27 against the Uke's stomach . The Tori's leg straightens as he exerts this

force, the maximum force occurring at frame 27 , before the Uke's body begins to lift off the Tori's foot.

The Tori's leg decelerates from frame 27 onwards .

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Trace 2 is that of the arm accelerometer placed in the vertical axis (Y-axis) relative to the Tori's arm.

From frames 0 to 8 there is a change in acceleration corresponding to the pulling action of the Tori as

he falls towards the floor. Between frames 8 to 9 there is a large acceleration producing a large pulling

force corresponding to the point at which the Tori begins to change his direction of movement. There

is a pushing force from frame 9 onwards, this is the Tori pushing up against the Uke as he falls to the

floor, preventing the Uke from falling on him. This force assists the change in direction of the Uke's

movement from downwards/forwards to upwards/forwards, and its maximum is at frame 13.

There is little change in acceleration until frame 36, when there is a large pulling force followed by

a large pushing force. This is the force exerted by the Tori in causing the Uke to rotate about his

shoulders.

Trace 3 is that of the arm accelerometer placed in the horizontal axis (X-axis) relative to the Tori's

arm. The trace is very similar to that of trace with the exception of large accelerations at frames 2, 30

and 31. The acceleration at frame 2 is due to an initial pushing action by the Tori as he steps off the

floor ; a smaller acceleration may be seen on Trace 2 at the same point. The accelerations at frame 30

and 31 are due to the Tori pushing the Uke before pulling to cause rotation.

It should be noted that the final acceleration of the arms occur after that of the leg, implying that the

leg force helps project the Uke, but the arm forces produce the final rotating motion.

The traces 4 to 6 for all three piezoelectric accelerometers of the competitive throw are similar to

those of the normal throw, except for a slight phase difference which corresponds to the angular velocity

traces.

Trace 4 is that of the leg motion, and is similar to the trace obtained from the normal throw. There

is a phase difference of 6 frames between the normal and competitive traces at the point at which the leg

accelerates to lift the Uke. This phase difference corresponds well with the same point on Figure 6, in

which the competitive and normal throws are approximately 8 frames phase difference. The peak

magnitudes of the two traces are very similar implying that the same force is exerted for the competitive

and normal throw.

Trace 5 is that of the arm accelerometer placed in the vertical axis (Y-axis) relative to the Tori's arm.

The trace is again similar to the normal throw except for a slight phase difference during the pulling

action. At frame 39 there is a sudden acceleration which is absent in the normal throw. This sharp push

and pull motion of the arm is the tugging movement causing the Uke to rotate sooner than the normal

throw.

Trace 6 is that of the arm accelerometer placed in the horizontal axis (X-axis) relative to the arm.

The trace is similar to that of the normal throw except during the pulling stage. It may be noted that the

competitive throw has one very large acceleration at frame 36 comparing with the normal throw which

has two sharp accelerations at frames 30 and 31 and there is a phase difference of 6 frames. This large

force exerted is due to the pulling action by the Tori. From Figure 6, it can be seen that the large torque

to produce the Uke's rotation is initiated at approximately the beginning of the final acceleration gradient.

This corresponds to the above large acceleration.

It should be noted that the phase difference obtained between the trace appears to increase as the

throw progresses. This may indicate that since the traces are similar, then the phase difference achieved

with previous figures is not due to inconsistent performance by the Tori but to the reaction of the Uke's

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EXTON : A Biomechanical Study on Tomoe-Nage of Judo Techniques

body to the forces exerted.

IV Summary

Tomoe-nage of Judo throw and its mechanical principles was investigated in this study comparing

the normal with competitive throw with 3 Ukes differing mass. And analysis of centre of gravity , moment of inertia, angular velocity, and angular momentum during the motion of Tomoe-nage with piezoelectric

accelerometer resulted as follows.

1. The displacement of centre of gravity for 3 Ukes during the normal throw showed similar tendency . 2. The moment of inertia for Light and Middle-Weight Ukes showed similar tendency but those in

Heavy-Weight Uke showed difference during the normal throw . And its maximum values supported

the theory that the moment of inertia is proportion to the mass.

3. The angular velocity for 3 Ukes during the normal throw showed similar curve consist of several

peaks and troughs but the phase and magnitude of each curve showed difference. 4. The value of the angular momentum for Tori during the normal throw showed the minimum at the

stage of "Tukuri" and the maximum at the stage of "Kake" . 5. In the comparison of the angular velocity for Middle-Weight Uke during the normal and competitive

throw the latter showed greater change of gradient and decrease in the time taken to throw the Uke . 6. In the comparison of the piezoelectric traces for Middle-Weight Uke during the normal and

competitive throw a similar tendency was shown. But the difference in the time between pulling Uke

and bend leg for lifting Uke was observed.

References

1) Dempster, W.T., Space Requirements of the Seated Operator, Wright Patterson Air Force Base, 1955

2) Kudo, K., Dynamic Judo, Japan Publications Trading Co. Ltd., 1967

3) Miura, S. et al., A Study on Uchi-mata of Judo Throwing Techniques , Judo ; 41-10, Kodokan, 1970 4) Miura, S. et al., A Study on Osoto-gari of Judo Throwing Techniques , Judo ; 42-12, Kodokan, 1971 5) Tezuka, M., Kinetic Analysis of Judo Technique , Biomechanics VIII-B, 1983 6) Walker, J., The Physics of Judo and Aikido, Leitungssport, 1981

7) Whitsett, C.E., Some Dynamic Response Characteristics of Weightless Man, Wright-Patterson Air

Force Base ; Ohio, 1963

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武 道 学 研 究23-{3},1991

柔道投技の巴投に関する運動力学的研究

マテ ユー ・エクス トン(ヘ ップスエ学社)

井 浦 吉 彦(金 沢大学)

本研究 は,柔 道の投技 の うち巴投 を採 り上 げ,基 本的施技方法 と応用 的施 技方法 で体重 の異な る3名 の相手

を投 げた場合 の動作 を,映 像 と圧電式加速度計 を用いて分析 し,柔 道 の投 技 のメカニズムを明 らか にす ること

を 目的 とした。

実験 は1987年1月,イ ギ リスにおいて行 い,映 像 と圧電式加速度計 か ら異 な る方 法で施技 され る巴投 の動作

中の重心位置,慣 性 モーメ ン ト,角 変位,角 速度,角 運動量 を求 め,比 較検 討 した。得 られた結果 は下 記の通

りである。

1.基 本的 巴投 の施技 中における3名 の受 の重心移動は,ほ ぼ同様 の傾 向を示 した。

2.基 本的 巴投の施技 中における3名 の受の慣性 モーメ ン トにお いて,軽 量 及び中量 の受 は同 じ傾 向を示 した

が,重 量 の受 は,異 な る傾 向を示 した。 また,最 高値は重量,中 量,軽 量の1順であ り,慣 性 モーメ ン トが

体重 に比例す ることを裏付 けた。

3.基 本的 巴投の施技 中における3名 の受の角速度で は,何 れ も2層 曲線 を形成 する とい う点で は一致 したが,

時間的変化 及び値 に違 いがみ られた。

4.基 本的 巴投の施技 中における取の角運動量 は,い わゆる 「つ くり」の局面 で最小を示 し,「 掛 け」 の局面

の直後で最大 を示 した。

5.中 量の受 における角速度 の比較で は,基 本的 巴投 に比べ,相 手 を急 激に引 く動 作を伴 う応用 的巴投 に著 し

い角速度変化及 び角速度 の増加 による施技時間の短縮がみ られた。

6.圧 電式加速度計 による比較 では,基 本 的巴投及び応用的巴投 と もほぼ同様な傾向を示 した ものの,取 の動

作 中の 「つ くり」 の局面 において,基 本 的巴投では相手 を引 くと同時に脚の屈曲がみ られるが,応 用的巴

投で は相手 を引いた後暫 くしてか ら脚 の屈 曲がみ られた。

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