KEY WORDS: Biomechanics, impulse, kinematics, martial art, momentum, collision.

where F∆t = mv₂ - mv₁ or F∆t = ∆mv

Four highly advanced (black belt) participants served as the tori for this study. A single highly advanced participant (black belt) was used as the uke and accepted the throws for all participants. All participants used in this study had at least 5 years of national competition experience. Information including age, weight, and height were collected for all participants (Table 1). All participants signed informed consent, consistent with University guidelines concerning the testing of human participants. Each participant performed three different types of throwing techniques: seoi-nage (hand throw), harai-goshi (hip throw), and osoto-gari (leg throw). To ensure an adequate combination of maximal effort and proper technique, the participants were required to perform the throws with maximal effort while maintaining their balance (staying on at least one foot and no more than one hand touching the ground) after the throw was executed. This procedure was designed to simulate throwing under ideal conditions, where uke began each throw in a stationary position and elicited no conscious resistance to tori's efforts. The procedure is similar to typical throwing practice, referred to as nage-komi.

Two video cameras (JVC 60 Hz) synchronized by LED were used to collect the data. The cameras were positioned approximately 90 degrees apart facing one side of uke and tori so that a sagittal view of the action was seen. Directions for the harai-goshi and seoi-nage throws were set such that uke always began each trial facing the positive x (anteroposterior) direction and his right shoulder facing the positive z (mediolateral) direction. For the osoto-gari throw the z orientation was changed such that uke's right shoulder was facing the positive z direction and the front of the body facing the negative x direction at the start of the throw. This process was to insure that uke was always thrown predominantly towards the positive x direction with his right shoulder initially facing the positive z direction. The upward direction was designated as positive y (vertical) for all throws. Power spectrum analysis consistent with the Nyquist Theorem indicated that 60 Hz was an adequate collection frequency for judo movements.

A three dimensional motion analysis system (Peak Performance Technologies, Inc., Englewood, CO) and the DLT (Direct Linear Transformation) procedure were used to analyze three-dimensional kinematic data. As judo requires that all participants wear a judo uniform (judo gi), joint markers could not be used. Therefore, manual digitization of 18 body points for both tori and uke were performed for all trials by a single digitizer who was experienced with the sport of judo. The digitized data were smoothed using a 4^th order zero lag Butterworth filter with a cut-off frequency of 5 Hz based on power spectrum analysis.

COM calculations were based on anatomical parameters from Clauser et al., 1969 and computed by the motion analysis software into a virtual point. COM momentum values were calculated using three-dimensional COM linear velocity measurements and participant mass. These values were averaged for each phase. Impulse values were calculated as the difference between average momenta of tsukuri and kake phases or the phases in which collision between the two bodies occur. Both descriptive and inferential statistics were used to interpret the data. Differences in momenta between phases, directions, and throws were statistically analyzed with a three-way repeated measures analysis of variance (p < 0.05). Differences in impulse between different throws were analyzed with a one-way repeated analysis of variance (p < 0.05). Tukey post hoc tests were used to analyze significant interactions. Only measurements based on the average COM momentum values of uke were reported in this study, since uke's motion is considered the product of tori's throw.

Since throwing phases have yet to be defined in biomechanical terms, they were set according to popular opinion in instructional literature (Kano, 1986; Kim and Shin, 1983; Koizumi, 1960; Harrison, 1952). The harai-goshi and seoi-nage phases were broken down in similar fashion. The kuzushi phase begins with the first movement towards the entrance of the throw by tori and ends with the placement of tori's supporting (left) foot to the ground so that both feet are planted on the ground. Tsukuri immediately follows kuzushi and begins with tori's feet pushing off the ground and ends with uke's heels beginning to rise from the ground. Kake immediately follows tsukuri and begins with uke's toes and feet rising from the ground, the body being thrown into the air, and ending when uke's body and any part of both legs hitting the ground (Figure 1). For the osoto-gari throw, kuzushi begins with the onset of tori's leg drive from the sweeping (right) leg allowing the supporting (left) leg to move towards uke and ends with tori's sweeping leg moving up to uke's body. Tsukuri immediately follows kuzushi and begins with tori's sweeping leg passing uke's body and ends with tori's sweeping leg making sweep contact. Kake immediately follows and begins with sweep contact to uke's body and any part of both legs striking the ground (Figure 1).

Statistical analysis revealed significant differences in average COM momentum for each phase and each direction (p < 0.001). Thus, each throw demonstrated different momenta in the x, y, and z directions during kuzushi, tsukuri, and kake phases. The seoi-nage depicted significantly different momenta from the harai-goshi and osoto-gari throws (p = 0.008), while the latter two were not significantly different from one another (p = 0.069). Resultant impulse values were not significantly different between throws (p = 0.096). Nonetheless, impulse as well as force and time components for each throw are reported to describe collision characteristics between tori and uke (Table 2). Comparing the three different types of throws, harai- goshi created the greatest force onto uke with a force value of 158.9N averaged over a period of 0. 63s (time period of tsukuri and kake), followed by osoto-gari (156.3N; 0.73s), and seoi-nage (120. 4N; 0.74s), respectively. The seoi-nage demonstrated the smallest impulse and force values indicating a relative weak collision between tori and uke.

In this study, it was assumed that uke's movement was the product of tori's effort to throw uke. Since all throws were considered "perfect throws" (no conscious resistance by uke), analyzing uke's movement would conceivably offer explanations as to what factors determine a perfect throw, a throw which competitors refer to as an ippon (full point) throw. Statistical analysis revealed that COM momenta in each direction for each phase of the throw were different. The following discusses COM momentum and impulse characteristics for each throw separately.

Harai-goshi (hip throw)
During the kuzushi phase uke's COM depicted momentum forward along the anteroposterior (x) direction, upward along the vertical direction (y), and moving away from tori's pulling hand (left hand for a right handed throw) along the mediolateral (z) direction. The tsukuri phase indicated a continuation of forward momentum, a change from an upward to a downward momentum, and a change in mediolateral momentum towards tori's pulling hand. The kake phase indicated a continuation of momentum forward, downward, and towards tori's pulling hand (Figure 2).

The harai-goshi throw in general terms is a hip toss with uke being thrown in the forward direction. The study indicated as such with uke's momentum increasing from kuzushi to tsukuri phases at 20.6 to 52.6 (kg·m)/s respectively. This can be considered a skilled trait by tori considering that they must continually pull uke forward while simultaneously shifting their feet and turning their body 180 degrees. The momentum is generated by the force created by tori's arms, most notably from the pulling arm (left arm), but ultimately originating from the pushing force of the feet or ground reaction force (Tezuka et al., 1983; Harter and Bates, 1985; Serra, 1997). Thus, the harai-goshi and judo throws in general incorporate a kinetic link between segments, where momentum is progressively increased from the feet, legs, trunk, to the arms (Morehouse and Cooper, 1950). Further analysis did indicate that peak momentum in the forward direction typically occurred just after right foot touch. Therefore, judo players should strive to create the greatest forward momentum on the body of uke just after right foot touch.

From tsukuri to kake phases, momentum in the forward direction sharply decreased from 52.6 to 4.6 (kgom)/s respectively. This was representative of uke and tori colliding and likely explaining the sudden drop in uke's momentum. This observation is very consistent with the definition of tsukuri, in that, there is an attempt to fit into uke with close body contact through collision. From this perspective the harai- goshi throw requires the ability for the thrower to create large momentum either through high velocity, large mass, or both. Two of the heaviest players in this study created the greatest resultant impulse and force onto uke. Therefore, from a practical standpoint this throw may be better suited for heavy players with enough mobility skills to turn their body 180 degrees fairly quickly and create a plastic collision such that uke and tori's bodies become one.

Momentum of uke in the vertical direction for the kuzushi and tsukuri phases displayed a trend in the upward direction but was considered weak due to high standard deviation values. It is possible that the relative height of tori compared to uke affected these measurements. It is also possible that momentum generated in this particular direction, while important to the success of throw, is quite small. A study by Sannohe, 1986 indicated that pulling upwards and forward with tori's pulling hand at 10 degrees from above horizontal elicited the strongest angle of pull. The present study demonstrated a weak trend to substantiate this concept, since uke's body was moved upward by all participants during the kuzushi phase. However, it should be mentioned that the recommended angle of pull in the Sannohe, 1986 study was determined through a pulley device and not under real throwing conditions.

Momentum in the mediolateral direction indicated a movement of uke's body away from tori's pulling hand during the kuzushi phase (-8.9 (kg·m)/s). Unlike the forward direction there was an opposite movement to the direction of the throw or what seemed to be a light resistance by uke in the mediolateral direction (Figure 3). By current definitions kuzushi is the phase in which uke's balance is broken in preparation for a throw, however, in this case kuzushi is not used to break balance but perhaps to elicit a slight resistance. This resistance in turn would allow tori to shift their feet, turn their body, and execute tsukuri. Thus, one can offer another definition of kuzushi in that it is a phase that allows the fit-in or tsukuri to occur.

Seoi-nage (Shoulder Throw)
The kuzushi phase indicated momentum of uke's COM in the forward direction and away from tori's pulling hand in the mediolateral direction. There was a tendency for the COM to have upward momentum with only one participant creating a momentum downward. During the tsukuri phase there was a continuation of forward momentum. There was a tendency for upward momentum to occur with all but one participant creating a momentum downward. For the mediolateral direction two participants created momentum towards tori's pulling hand, while the other two created momentum away. During the kake phase there was a continuation of momentum in the forward direction, downward direction, and towards tori's pulling hand (Figure 4).

The seoi-nage throw is also considered a forward throwing technique with uke being tossed over the shoulder. Likewise, the results also indicated increasing forward momentum from kuzushi (24.5 (kg·m)/s) to tsukuri (50.2 (kg·m)/s) phases. There was also an indication of leg and trunk contribution through kinetic chain since the peak momentum during this phase was created just after right foot contact. Unlike the harai-goshi, however, the seio-nage throw maintained uke's forward momentum through the kake phase (44.6 (kg·m)/s) as well. This can also be considered a skilled trait by tori considering that they must also shift their feet and turn 180 degrees during the kuzushi phase of this throw. Since there was not a great change in uke's momentum from tsukuri to kake phases, collision may not be considered an important aspect of this throw. Likewise, the seoi-nage depicted the lowest resultant impulse and force values. Though impulse was not significantly different between throws, momenta generated by this throw were significantly different from the other two. The time period over which impulse occurred was surprisingly large considering that this throw is preferred by lighter and faster players. It is conceivable that collision force is actually larger than what was measured in this study, since the kake phase for seoi-nage tends to be longer than other throws due to uke being thrown over the shoulder and staying in the air longer.

Uke's movement pattern in the vertical direction was also considered statistically weak as depicted through the large standard deviation values. Only one participant was shown to create a downward movement onto uke. This participant was also the lightest and one of the shortest participants. It is possible that pulling uke upward is not intended to be used for breaking uke's balance for this throw, rather, it is used to open uke's armpit so tori can position their arm underneath. The short participant was likely able to do this without pulling uke's body upward to a large degree. In addition, it would explain how a person of short stature may be able to reach a desired angle of pull to generate and maintain forward momentum which seems to be the main premise of seoi-nage. This also may lend credence to the common opinion that seoi-nage is well suited for players of shorter stature.

Uke demonstrated a resistance in the mediolateral direction during kuzushi (-11.3 (kg·m)/s). Thus, kuzushi is once again used to allow tsukuri to occur. Many instructors have taught throws conducive to this theory knowingly or not. They will tell students to "snap pull" during kuzushi which is considered a non-maximal quick and discrete pull. The shifting of tori's feet during kuzushi does not allow a maximal pull since the feet are often in the air. It is likely that the "snap pull" is used to create an instantaneous resistance by uke or freeze uke while tori regains foot position and obtains a tighter fit during the tsukuri phase. From a practical standpoint a judo player can use this resistance to their advantage by timing the execution of kuzushi when uke shifts their COM towards their left leg (for a right-handed throw). Some instructors will tell judo players to execute seoi-nage when uke's right foot begins to move forward. Considering this theoretical concept of resistance it would make sense, leaving uke with little alternative but to defend the throw by pushing-off with their right foot and shifting their COM towards the left. This application is conceivable for both the seoi- nage and harai-goshi throws.

Osoto-gari (leg throw)
Uke's COM had a tendency to move with forward momentum during the kuzushi phase with only one participant demonstrating momentum backwards. All participants demonstrated a momentum upward and toward tori's pulling hand during kuzushi. The tsukuri phase indicated forward momentum and a continuation of momentum upward and towards the pulling hand. Kake depicted momentum backwards, downwards, and away from tori's pulling hand (Figure 5).

Unlike the two previous throws, the osoto-gari tosses the uke backwards. Thus, one would expect uke to move backwards in all phases. However, this was not the case as uke's momentum increased from kuzushi to tsukuri in the forward direction at -1.9 (kg·m)/s and -16.7 (kg·m)/s respectively (negative sign depicting the forward direction for uke in this case). It wasn't until kake that uke moved backwards (16.9 (kg·m)/s). From these results, it is likely that tori actually pulls uke towards them while stepping into the throw during both kuzushi and tsukuri. It is also possible that uke once again creates a slight resistance to tori's push so that tori can properly fit into the throw. This is in agreement with Imamura and Johnson, 2003 who found chest to chest contact and tori's upper body angular velocity as an important aspect of osoto-gari. Thus, judo players should strive to create large chest to chest collision onto uke through a combination of pushing momentum created by the right foot push-off via kinetic chain and pulling momentum created by the arms.

Imamura and Johnson, 2003 also indicated very little movement of uke in the vertical direction during osoto-gari. The current study indicated a pattern of upward momentum during the kuzushi and tsukuri phases although the values were small with a large standard deviation. Likewise, this was evident in all three throws analyzed in this study.

In the mediolateral direction there was no indication of a resistance from uke. Rather uke's body moved towards tori's pulling hand with the greatest momentum being created during the tsukuri phase. Thus, tsukuri tends to be a particularly important phase for this throw. Again, these findings agree with Imamura and Johnson, 2003 and the front-to-back findings of the present study, which suggest that chest to chest contact is very important for osoto-gari.

The results also indicated an importance for large momenta being generated for this throw, particularly in the anteroposterior and mediolateral directions. The average resultant impulse for osoto-gari was similar to that of harai-goshi indicating the importance of a strong collision between tori and uke. Since osoto-gari does not require a 180 degree turn of tori's body, it is often considered an easier throw to execute. From this perspective it is well suited for players with limited mobility skills and heavy players who can generate large momentum before contact.

Three different but mainstream judo throwing techniques were used for this study. Likewise, biomechanical similarities and differences were found for each. Judo throws can be viewed as collisions between two bodies, therefore, impulse characteristics of uke's body were considered representative of collision magnitude or, in this case, throwing power. The osoto-gari and harai-goshi throws created the largest impulse onto uke's body, therefore both throws can be considered "power throws" and likely well-suited for large and powerful individuals. The seoi-nage, on the other hand, created the smallest impulse and force onto uke. This throw was unique in that it maintained a large forward momentum on uke's body even after body contact. This indicated that this particular throw does not require size and strength from tori for better collision but rather shorter stature, speed, and skill to fit-in underneath the body of uke and roll them over their shoulder without compromising forward momentum.

A form of resistance by uke was found in the mediolateral direction during the kuzushi phase for both forward throws. This was based on a slight increase in momentum of uke in the opposite direction of tori's pull. This allows the next phase, tsukuri, to occur. If uke does not offer any resistance during kuzushi, tori will not be able to achieve a complete fit-in and will lose upper body contact with uke. Creating this type of resistance can also be described as freezing uke temporarily. Intuitively one can envision fitting into a stationary opponent more easily than one that is moving. Although the osoto-gari did not demonstrate this concept in the mediolateral direction, it did indicate it in the horizontal direction. Consequently, it is possible that a form of this theoretical resistance is present in all throwing techniques. Highly skilled judo players have developed the ability to initiate this resistance whether they are conscious of it or not. Undoubtedly it takes years of training to develop the proper timing necessary to execute it well. While the results of this study do not presume to replace years of judo training, it does offer a pragmatic approach to learning a skill that has long been held mystic in nature.

It would be interesting to quantify the amount of resistance allowed for a successful throw. One can assume that the resistance must be very slight and instantaneous. If the resistance is too large or strong, uke has performed proper defense and the throw will not work. It is also important to clarify whether or not this resistive force is created by uke or merely the consequence of tori's force, for example, uke's limbs moving in the opposite direction of tori's push or pull in the form of an inertial lag. Clearly, more research is needed to study this concept further. Some suggestions include analysis of judo players executing ippon (full point) throws during competition, similar analysis comparing novice and skilled judo players, and studies using kinetic measures via force plates to analyze the motion of uke.

• The degree of collision between the thrower (tori) and person being thrown (uke) may be a reflection of throwing power.
• The hip throw (harai-goshi) and leg throw (osoto-gari) created large collisions onto uke and are considered power throws well-suited for stronger and heavier players.
• The shoulder throw (seio-nage) created small collisions onto uke emphasizing the importance for skill rather than strength.
• A theoretical resistance to tori's pull was found during the kuzushi phase indicating a propensity for uke to freeze and allow tori to better fit into the throw during the tsukuri phase.