I'm one of those tall, lanky people whose legs are much longer than their arms. While this is often advantageous in Taekwondo, our style attempts to integrate punches and kicks. While leading with a punch and then following up with a kick poses little problem, I find that combinations that start with a kick and then lead to a punch result in swinging into thin air. So my question is this: what are some techniques that can help me close the distance/extend my reach when transitioning from a kick to a punch during a combination?
1 A short good hint that helped me a lot (I am also a 2 m. long guy).
Don't lean backwards when kicking. Many do this to counterweight their legs. From that position it's hard to follow it up by a punch and you are vulnerable for overtakes and even more (if allowed): takedowns and swipes.
It may take some practice.
2 Extend those arms!
I still find so many people who don't fully extend their arms and don't twist their hips enough. This is necessarily to get the speed, reach and power you need.
3 Train with positioning, train with both legs in front (regular and south paw) in other words train footwork a lot!
Taekwondo is a great system, but I believe the essence of martial arts is to develop your own personal art, based on a system. Different body shapes will tend towards different combinations and techniques - it's still Taekwondo, but it's Taekwondo done your way. Be careful though: this is not permission to ignore your instructor. He's there to help you discard the bad, focus on the good, and develop your personal art; he's not there to be ignored because you're "doing it your own way".
Punching and kicking have naturally different ranges for lots of people. Different kicks, and different punches, have their own ranges. One of the key skills you need to develop as a martial artist is the ability to select the right strike for the range, or to control your range to suit your style.
Combination kicks and punches are key to taekwondo - but you need to adjust the combination to suit your opponent's reaction. If you throw a right-leg front-kick and your opponent slides away to your right, you need to discard the plan to follow up with a left-leg roundhouse. Sparring is very dynamic, and you're constantly adjusting.
Kick-punch combinations aren't likely to work well if your opponent is moving back out of range to avoid your kicks. If you commit, in your head, to a kick-punch and your opponent just steps back out of range of the kick, you're gonna have to close the range as you punch - and in my experience trying to close range with a punch is asking for them to have a go at a quick front-kick as you move in.
When K-P Can Work
All that said, I use kick-punch combinations all the time. Whenever my opponent side-steps a kick and I find them in close, it's much faster to follow up with a few punches than to try to gain enough room to throw a kick. For me, punching is a range-gaining technique - you can certainly land effective hand techniques in sparring, but their main utility to me is to keep my opponent occupied and push them back to bring them in range of a kick.
I know people who do use punches differently - I tend to use kicks to close range, punches to gain them, but I've seen people who can close in with punches. If you want to work that into your own style, ask your instructor to help you work on it. I can offer this advice - your biggest risk is that your opponent will see your ribs as a tempting target as you step in without a kick chambered. The best way to combat this, in my opinion, is to either let your opponent close the range for you (move sideways out of the way of their kick) - you can also just watch for an opening when they're off-balance.
As for the original question, regarding the kick-punch, you can throw a quick kick in as you move out of the way - I often find that if someone's wound up a big kick I can step sideways as I throw a prop kick, and then finish in punch range - or you want wait for the right opening, often if they're off-balance after a missed kick, and then throw in a quick kick while stepping in to punch range.
In summary, what you really need to do is to think about range. Kick-punch combinations are all about using a kick as you close in to punching range, and that just isn't going to work if you're both on balance and your opponent tends to step out of range of kicks.
It's worth noting that it can be a great technique on what I think of as bully sparrers - people who rely less on technique and more on throwing their weight around and forcing you to move. These people tend to step in even with no opening, and rely on the tendency of taekwondo students to want to stay in kicking range. Punish them by stepping off the line of their movement, throwing in a quick prop kick, and following up with a few punches.
I find there's not enough time to change hip position after a kick, so if the combo is kick first then punch, I typically can only make use of a punch with the same side I kicked with.
So if I'm lunging in with a right kick, the punch is also with the right. It feels a bit weird if you've never tried it that way before, and you have to set up your upper body for the punch as well... you'll need to practice it to figure out when it's most efficient to punch.
Like, if you're doing a roundhouse kick, when you make the kick, bring your knee in straight away... you're kinda folding up or tucking in your kick as soon as you've past the striking point... and at the same time, cock your right arm in a position from where you can punch out and then punch. It's different from a normal punch and sort of comes out a little sideways, but you can follow up really quickly with your left hand, and then the left leg is ready... turning kick, back kick, sliding side kick, then a fatality.
I think you have to focus about where you want to put down you foot after your kick. Also you have to keep your harm into the fight when kicking and not put back your chest. Did you try to train in other style ? I'm not a big fan of Human Weapon but here is a Savate combo integrating punch and kick by starting with punch Jab-Kick-Hook. Another example of Savate Kick-Kick-Right-Left here. A Samba combo Kick-Punch-Kick here. I think the kick that is executed here are all allowed it TKD.
Getting a good kick-punch combination relies on where you are moving to, and where your feet are.
The most common use is when a kick is blocked.
Either of these are relatively straightforward, and the punch is often the fastest way to get a point.
Don't leave your left out too long after the kick, you will lose balance and won't be able to put your foot where you want it.
If you're too far away to punch, don't punch! Keep kicking if you're too far away, and if you're too far away to kick, don't kick at all.
Practice footwork drills. These differ between martial arts, so you probably need to talk to your instructor about how they do it.
Option 1: Lead with closer range kicks - following a crescent kick or an axe kick with a punch will be a lot easier than following a front or side kick with a punch.
Option 2: Instead of returning your feet to the original position after a kick, them fall where they kicked. So after a kick you'd end up in a lunge position (think Yoga's Warrior poses), from which you could follow with a punch.
Option 3: Make footwork part of your combo. So instead of trying for kick-kick-punch-punch you could do kick-kick-step-punch-punch. There's a pause, but that pause is likely timed with the opponent making a step to the back or to the side.
Option 4: Bait your opponent to come in, your legs are likely longer than your opponent's, so they'll want to close the distance and get inside. Throw a couple of kicks then chamber and have the punch ready for them as they close the distance (if you can do a superman punch this could be a good opportunity to use it).