the muay thai roundhouse kick is a littel different. where taekwondo is more of a snappy kick, the muay thai is more of a push. It comes from lifting and chambering your knee and the all important pivot on your base leg. the pivot allows you to turn your hips over which is where the power of your kick comes from. and yes you do strike with your shin, not your foot. so basically it goes step, lift knee, chamber, pivot, turn hips over and drive through. here are some examples
The Taekwondo method is to plant the foot, lift the kicking leg and snap it around from the knee. The Muay Thai Te Tut (cut kick) doesn't come from the knee, but directly from the hip with the leg relaxed like a whip and the foot on the ground is not planted but up on the ball and twisting on the ground to follow through. The Te Tut takes a fraction of a second longer to connect but hits with a lot more power. Some Muay Thai guts like to throw some kicks snappy to set up harder ones, like an inside leg kick from the lead leg followed by a harder right Te Tut. In essence, there are actually quite a few variations of the Muay Thai roundhouse. Cut kicks, diagonal kicks, downward kicks, half-knee kicks, and so on. They each have their subtleties.
The object in Muay Thai is to hurt the guy. If your kick hurts the guy, then it's about as "right" as anything else that accomplishes that goal. Although if you're talking about a kick that snaps from the knee, chances are it won't hurt as much as the blasting follow-through of the classic Muay Thai round kick. On the other hand, there's less of a chance of it getting caught.
You can, but it would be pointless. In Muay Thai you pivot your hips and put your whole body into the kick which generates a ton of power. TWD 'snap' there kicks using only the quads. It sounds hard but all bark and no bite. You have everything to gain and nothing to lose by using the Muay Thai method.
most martial arts go with the lift leg, chamber and kick principle.
there's different sorts of round kicks in muay thai but generally you're standing pretty close to your opponent, typically much closer than taekwondo, so it's more appropriate to use your shin, or even knee
Muay thai roundhouse is more powerful though... Taekwondo does have really powerful spin kicks though
Not much of a difference anyways.
Is it right to kick like taekwondo way in muay thai but you use the shin only the technique?