The concept is fairly straight forward but I will over simplify with a conceptual explanation:
Your gearbox has an output shaft connected to your rear drive wheel and a power input shaft connected to your engine via the clutch. The input shaft can be rotating anything from idle at 1K rpm to redline. The output shaft can be rotating anywhere from stop to the maximum speed of the rear wheel through the tranni equivalent to say 155mph. On each of the 2 shaft are gears of different ratios (diameters and teeth) so when you shift you 'connect' the shaft and a gear rotating at engine speed with the shaft and a gear rotating at rear wheel speed.
If you have two gears on two shafts rotating at different speeds you can understand that the chances of getting the gear teeth to mesh together and join up the two shafts whilst moving at different speeds are going to be pretty slim. The purpose of the clutch is to disconnect power drive from the engine so the power input shaft momentarily stops rotating (actually it's slowing down) so you can connect the gears on the input and output shaft. The occasional 'crunch' you hear is the output gear forcing the freewheeling or stopped input shaft to mesh at the same speed. The gears are made to take these 'knocks' provided they are not powered (clutch is in). When you let the clutch out after shifting, the power is connected from the input shaft and gear to the output shaft and gear with the right ratio.
Engines have higher rpms than the rear wheel, so to reduce the ratio you have a smaller gear on the input than the output shaft. When you shift a gear up or down, you change the relative sizes of the gears so for the same engine and road speed before the shift you will not mesh the two new gears, unless the speed of one is changed.
For each shift there will be a road speed and a corresponding engine speed at which the gears on the input and output shaft can mesh without the use of the clutch. Generally the higher the road speed, and smaller the ratio change e.g 5-6, the easier it is to practice the clutchless change because speed differences in the two shafts going 5-6 are going to be similar. That's where you should start.
How do you know when to do the clutchless shift? You have to watch the tacho. and road speed first. Most riders will put a small amount of pressure on the shift lever whilst just backing off the throttle. If you are clutchless shifting up, you are trying to roll off the rpm just enough so the bike will be going at about the same road speed after the shift (but with lower rpm) as before. Going up is easier than coming down, but harder to get right going from shift 2 than 5-6.
Clutchless down shifting is far more difficult and virtually impossible below shift 3 because the ratios (shaft speed differences) are getting greater and you need practice watching the tacho and road speed with light pressure on the shifter to get it right. You can usually with light pressure on the shifter 'feel' when you hit the sweet spot for the shift.
I clutchless upshift all the time mostly 5-6, but generally not below shift 3 or with loads and a pillion. As long as you've developed a sensitivity at the toe and for any reaction or jolt from the bike, and worked to eliminate it, then I don't think you do damage - but it's down to your skill. You certainly save on clutch and hydraulic wear.
Going 5-6 is quick and lazy so I do it a lot. Lower gears need time to get the right rpm/road speed balance so I'd say it's slower to do if you are really pacing the bike and virtually impossible under hard acceleration without risking damage. The other lazy saving technique is double shifting up or down with clutch, but not under hard acceleration or perhaps fully loaded with pillion. The K has bags of torque and clutchless shifts get better with practice. Most of what I posted is memory and whilst I can do it successfully, getting all the details right when not riding is a tall order. So only practice 5-6 6-5 first, until you get no sharp decel reactions from the bike.
I started by reducing my clutch pull before shifting on higher gears to the extent I'm now hardly separating the clutch at all - that's good for clutches, bearings and you're well on towards clutchless changing.
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