With the exception of some Martial Art Styles such as Xinyi quan that focuses on the palm as the root of its striking philosophy, almost all martial arts and fighting sports in the world use punches for upper body striking, so you should practice your push ups according to this golden principle. Of course hand push ups are good, but they should not be your primary choice when comes to Martial Arts for the above reason.
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Another reason why you should choose knuckle push ups rather than hand push ups is that in hand pushups your wrist works in 90° position, which can reduce blood-flow to your hand if you decide to have a set of as many push ups as you can in a row, while knuckle push ups have the advantage that your wrist works in line with your forearm, making the exercise more impact-like.
Not only knuckle push ups should be your daily exercise for achieving your martial goals, but they will help train your mind too: when you begin knuckle push ups training, the first thing you will notice is pain: our recommendation is to focus on your posture, breathing and precision, as overcoming such a light pain is just the beginning of the process of controlling your Mind, a process that will take you to higher and higher goals if you are resilient.
So, to answer the question “Are knuckle push ups good for you?” – yes, of course they are, and there’s no reason why you should prefer the traditional way. There are no side effects to your knuckles in practicing this kind of push ups, as the compression that will be applied to them during your workouts will just make it easier for your body to switch to advanced B.M.C.© exercises. It’s just like everytime you practice knuckle push ups you are training twice: one the one hand your arms and core, and on the other hand you are hardening your skin and mind.