Translational (Straight) Movement
Translational movement is simply moving from point A to point B.
This may seem deceptively simple, and that’s because it really is. Translational movement is very intuitive to us, we interact with it all the time. Want the box on the top shelf? Move it translationally up. Just make sure that once you are there you also move it translationally sideways onto the shelf, or you get to experience it coming translationally down.
Rotational (Spinny) Motion
The other fundamental type of movement is rotational. The simplest form of rotation you can imagine is something like a top spinning on a table, or a ferris wheel going around.
The point an object rotates around is called the Center of Rotation. In both of these cases the object is rotating around its Center of Mass, so it’s not going anywhere.
A more interesting case is something that is not rotating around its Center of Mass. This is only possible if there is an outside force acting on it. Consider a bucket of water on a string, twirled around your head. The bucket certainly isn’t spinning around its center, it’s spinning around where you want it to through the force transmitted through the string. This is how we can achieve a speed multiplication effect in swords; the sword rotates about a place of our choosing to increase the velocity of the part we want to hit the opponent.
The Center of Rotation doesn’t have to remain fixed in place; in most cases it actually doesn’t. When you swing you don’t keep the sword in a perfect arc, it changes through the motion.
Interestingly enough, this is also at play in something like a human knee. The knee isn’t actually just a simple hinge joint, which is why it is so difficult to implement braces/prosthetics on it. Due to the shape of the bones, the Center of Rotation moves around as the knee flexes, sometimes even moving outside the knee itself!
In reality, most motions are a combination of both. If you have ever played with a spinning top you will know that the damn things don’t sit still, they wander across the surface off the table. This is a combination of rotational motion (the top spinning) and translational motion (moving across the surface of the table). And if you were a child, like me, who kept trying to see what the maximum speed at which you could spin the top was, you got another vertical translational component when it dashed to the edge of the table and fell off.
You don’t always have to rotate an object around its center of mass. When you swing a sword (if you are doing it right) it should be rotating about the center of your body right before it hits the target.
This leads to another interesting property. From a physics point of view we can take this rotation and consider it the combination of two different motions: a Translational Motion and Rotational Motion about the Center of Mass.
Hilt Velocity vs Tip Velocity
Relating this all back to swords while keeping it all simple: Swing the sword faster, sword does more damage.
That’s part of an intuitive understanding people don’t need explained to them. What most people do not grasp intuitively is the difference between hilt speed and tip speed.
What do I mean by this? Imagine if you just hold the sword and chop straight down. The tip is moving at the same speed as the hilt. If you move your hilt at 1 m/s, the tip moves at 1 m/s.
If instead we rotate about the shoulder, we get a speed multiplication effect at the tip. The part of the sword that meets the target will be moving much faster than the hand.
If we move the Center of Rotation to the center of the body, we get the optimal tip speed. Fairly simple and intuitive to understand intellectually. And like most things, the problem arises when we try to put it into practice.
Sometimes when people fail at cuts, the cause is simply that they were too slow. The key is that they are too slow AT THE TIP. If you have watched a decent amount of cutting, you have probably seen a more advanced practitioner perform a cut that looked quite slow and like it took very little effort. What you saw was the effect of good rotation in action. Though they don’t look to be moving especially fast, they are able to get the sword rotating around the center of the body, which causes the part that actually hits the target to be moving quite quickly.
When an individual learning to cut fails because their sword was too slow, their first reaction is often to try to ‘muscle through’, using strength to force the sword to move faster. The problem is that they end up just moving the hilt faster. This increases the speed of the tip very little, and in fact it can often slow it down — even though they feel that they are swinging faster.
Key takeaway: if you are looking to increase the tip speed, moving the hilt faster can help. But pay more attention to where the sword is rotating around. If you can create a good center of rotation about the body, you can probably increase the speed of your swing while moving slower than you were before.
Stopping the Rotation
Just because you start to rotate the sword, doesn’t mean you keep it rotating. This is an issue that I see a lot with undercuts, but it is by no means isolated to them. Picture having the sword in a low guard, ready to cut up with a true edge undercut. As you begin, the sword moves in an arc — it has to. But then as the sword comes forward, the blade stops rotating and you simply ‘punch’ the sword straight up.
In the above example, while you may feel that you had a good rotation based on how the cut started, when it hit the target it had actually stopped and thus the blade was moving very slowly.
And wrapping up…
I hope this was enlightening for you, and that it also gave you a better grasp of rotational motion and how it can help you start moving the sword a little bit more dangerously.