Tegatana before, during and after executing a technique

This post is inspired by the question of one of our users who has watched our instructional video about tegatana.
Find the question below, and also, what I answered. Now I'm attempting to explain my view about tegatana further.
The question:
It feels natural to hold the arms close to the body; extending them so far forward feels strange. What does tegatana gain from positioning the arms like that as it transitions into other aikido maneuvers?
The answer:
Importance of tegatana
The purpose of tegatana is to keep an appropriate distance from the attacker. If the arm is bent we can get too close to the attacker and he can use this against us. When taking on the guard position, tegatana ensures to take a proper base-distance from the attacker (maii). When you have a proper distance between tori (defender, who does the technique) and uke (attacker), tori will have space and time to execute certain movements.
If your arm is close to your body then you don't have the sufficient distance. Also, connecting to the attack(er) and initiating physical contact when a forceful attack is coming will become harder and controlling the attacker will also become harder. We need to connect to the opponent when his attacking energy is not expressed fully because then it will be easier to connect with their movements. Tegatana helps you with this. If you are a beginner, I think it is advisable to have your arms in front of you in tegatana because then, as defender, you are much safer and you can always keep a safe distance from the opponent when doing a technique. Later, at a higher level, you might not need to hold your arms in front of you in tegatana, but you will still need tegatana when doing the technique.
Extending the above paragraphs:
If you bend your arms during the execution of a technique then on one hand, you will lose the distance from the attacker. On the other hand, if the attacker comes with great attacking force (and why wouldn't he do that as this is his task, role) he might easily bend your arm further so you will need to use all your muscles to keep some distance. This way it's very hard to control an attacker. If you are strong, or at least stronger than your attacker, you might afford not holding propertegatana but we should not assume this but that the attacker is stronger. Accordingly, you need to work so that you will need to use as little of your own energy (force, muscles) as possible. You can do so by keeping a propertegatana.
Obviously, there are some techniques in which you need to bend your arm otherwise you can't grab and lead your attacker. However, these situations occur only when the attacker is already in an unstable position (off balance) and you (as defender, tori) are positioned safely fromuke (the attacker). These situations are created using tegatana first. You use tegatana to make contact with the attacker's body (arm, usually), and so you have a safe distance from the attacker before getting so close that you can control his movements completely.
I don't want to contradict my mechanical engineer nature so here's a bit of illustration:
Tegatana may be viewed using the following example. From top view, we can see the defender's centre of gravity as the centre of a circle, and tegatana can be viewed as the radius of that circle. With this radius, we can draw a circle around tori's centre. The attacker's movement is usually (well, almost always) is along a straight line pointing towards the centre of the above circle. The defender needs to move in a way that he has to make the attacker's straight line into the tangent of the circle. If this manoeuvre does not succeed a breakpoint will occur in the movements and the defender can't lead the attacker from one movement to the other smoothly. To keep the tangent-based situation, the defender needs to move because if he doesn't, he won't have a chance to adjust to the straight line of the attack. During a technique, until you have total control you need to keep adjusting your circle.
If tegatana always changes, i.e. the arm is bent or completely extended until straight, there is no defined circle. It is not possible to determine a straightforward tangent and thus, the attacker can't be lead in a similarly well defined way. There will be breaks in the direction of the attack which naturally breaks the harmonious movements.
Tegatana helps to keep your circle and, through this, you will be able to keep a safe distance from the attacker.
I hope I managed to discuss importance and purpose of tegatana better in this longer post, but if you still have questions please post them.
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