In Taekwondo, a reverse punch is a punch that is performed with the fist on the non-dominant side, based on the stance.
A lot of stances are asymmetrical, and can be described as being left-handed or right-handed. The most basic example of this is a walking stance (or a forward stance). A walking stance can either be a left walking stance – where the left foot is forward – or a right walking stance – where the right foot is forward.
For an asymmetric stance, a punch using one hand may be slightly more powerful and balanced than using the other. This establishes a dominant side for that stance. Techniques performed with the corresponding hand on this side are called obverse techniques. Techniques performed with the opposite hand are called reverse techniques.
Often, the dominant side to a stance is the same side as the foot that’s furthest forward. This is true of a walking stance: whichever foot is forward in a walking stance determines the obverse side, and the opposite side is the reverse side. Thus, for a left walking stance, a punch with the left hand is an obverse punch, and a punch with the right hand is a reverse punch.
For some stances, however, the forward foot does not establish the dominant side. Often, in stances where the weight distribution is not even, it is the leg that carries the most weight that determines the dominant side. This is true of an ‘l’ stance (or a back stance). In an ‘l’ stance, most of the weight is on the back foot, and thus it is the back foot that determines the obverse side. For an ‘l’ stance where the left foot is forward, and the right foot is back, a punch with the right hand is an obverse punch, and a punch with the left hand is a reverse punch.
Many stances in Taekwondo are symmetrical, and thus have no obverse or reverse side at all. The most basic example is a sitting stance. In a sitting stance, neither a punch with the left hand or the right hand is called an obverse or reverse punch. Furthermore, the majority of asymmetric stances are evenly-weighted, and so it is the forward foot and the forward hand that are the obverse side. In fact, it is usually only ‘l’ stances that students find confusing, because ‘l’ stances appear to break the pattern.
The notions of obverse and reverse techniques are not standardised across Taekwondo. Thus, you may find instructors who have different ways of defining and understanding obverse and reverse techniques, and one instructor may call a given technique a reverse technique while another calls it obverse.
Similarly, in textbooks and online, sometimes movements will be described in terms of obverse and reverse techniques, and other times just in terms of left and right, with notions like obverse and reverse left out.
It’s worth noting at this point that the term ‘reverse’ is used differently when describing kicks. A reverse kick does not just mean a kick using the rear leg or a kick using the non-dominant side of the stance you started in. A reverse kick is normally a kick with a spin performed before it. For example, a reverse side kick involves a turn to the rear first, followed by a normal side kick forwards off the rear leg.
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If you'd like to learn more about the Korean terminology used in Taekwondo, consider buying this book: Taekwondo Terminology. It contains an extensive dictionary of terms used in Taekwondo, as well as explanations on how to pronounce Korean words, and aspects of Korean grammar.