What are the differences between open-palm and knuckle push-up forms in terms of benefits, risks, and muscle development?
There's an aspect not covered yet. Knuckle pushups place more stress on the bones of the hand compared to the open palm pushup. Martial artists take advantage of that fact as a way to toughen the bones in the hand so that when they punch something hard, the hand doesn't break. Essentially, the body responds by increasing calcium deposits at the knuckle and along the phalanges.
As to the muscles involved, there isn't much of a difference between them. The forearms will be more engaged with the knuckles because it is needed for balance. A similar effect can be had by fingertip pushups. This variation strengthens the muscles in the fingers as well, which is useful to prevent them from getting jammed when playing basketball.
There are two risks with improper use of the knuckle pushup over the open hand:
All that said, there is no way to declare one of them as superior. Knuckle pushups have their use, as do open hand pushups. There is no reason not to do them both. Just don't do knuckle pushups every day of your life for the next decade or so. Also explore fingertip pushups as well.
I like to add a summary of my personal experience with open-palm and knuckle push-ups. I have done at least 100 push-ups a day since 1983, even when travelling (in airports and hotels). In 1999 I developed wrist pain and changed to knuckle push-ups, first on hard surfaces (until 2003) and subsequently on a towel or on carpet as a preventive measure for possible knuckle or wrist injuries. Switching from open-palm to knuckle push-ups completely eliminated the wrist pain within about two weeks. Between 2001 and 2006 I did, on average, 155 push-ups a day (alternating daily between 130 and 180, in two sets). I resumed the 100 push-up routine when I developed pain in the both shoulders in 2006. The reduction to 100 a day and keeping my left shoulder (where I had broken the rotator cuff ten year earlier) close to my torso liminated that pain. The knuckle push-ups have not significantly impaired the flexibility of my hands or wrists (as indicated by my work on the computer) and built up significant amounts of callus on the central knuckle of each hand and smaller amounts on the index finger knuckles. Doing push-ups on soft surfaces has reduced the amount of callus during the last few years.
In conclusion, I am glad I switched from open-palm to knuckle push-ups because this permitted me to continue this exercise without pain. I recommend that knuckle push-ups be done on carpets or other soft surfaces rather than on hard surfaces. I would like to hear the experiences of other long-term 'push-uppers'. I am now 72 years old and started doing daily push-ups at 44 but had done them periodically (a few times a month or less) since about agout 16.
Two benefits of doing push ups off your knuckles:
For these reasons I prefer doing push ups this way. Although extending your range of motion is not always a good thing. If you have shoulder problems, for example, then you could be doing more harm than good. So I'd do what feels right for you.
Another thing to keep in mind is the distance between your hands. Keeping your hands far apart will put more demand on your chest and shoulders while keeping your hands close together will be harder on the triceps.
I tried google'ing which muscles are used with the two pushup variations mentioned, but, besides the obvious focus on the knuckle and wrist for the knuckle pushup, I think there's more focus on the forearms and lats, where the palm seems more focus on the chest and shoulders. This is based on the hand position (similar to pull ups - from a full palm out pull up to a neutral hand position). Even doing pushups with your hands in the two positions you can easily feel the difference. There's about 12 pushup variations, including how wide you have your hands, so, for the best results try them all.
Here's a link to some of the variations: http://www.muscle-workouts.com/pushups.html
I did knuckle pushups as my only pushup for many years, close to thirty. Not every day, but at least 50 pushups three maybe four days out of the week. I've also done them virtually every time on soft surfaces. I've experienced no ill effects. But then I'm an IT professional and maybe that daily keyboarding has balanced things out.
Recently just for the variation I've started including deficit open-palm pushups in my routine.
In my experience, it is good to do pushups on the palms in the beginning. Palms provide a larger base of support (especially with the fingers spreaded). For some reason I also find it a little bit easier to focus on keeping the trunk active (which I think is very important), when doing it on the palms. Also, one thing that is useful for me in protecting the wrist is to spread the fingers and push them into the ground - which is just like trying to make a fist. Then, as others have already said, it is beneficial to switch gradually to knuckles, if you'd like to do large numbers of pushups, not to overuse the wrists. But I would also suggest to switch back sometimes to the palms, it can provide larger variety (eg you can move your hands further back, which makes the pushup much harder - on your knuckles you would fall on your face). To summarize, I think it is "better" to do them on your palms, unless you plan to do large numbers on a regular basis - but remember more is not always better.
No worries with your hands. If you want to make your wrists stronger then knuckle push-ups are the way to do it. My training is karate/taekwondo/kali-escrima/kick-boxing and lately bujinkan. But take your time to do it right - you don't have to do 100 at once, take care that you have your wrist in the wright angle. You know - as you would push your hand throug stone.
Sorry - i realized i'm late with this comment - sorry.
I used to do many open palm push ups. Due to an injury unrelated to push ups, I had to have wrist surgery to repair a TFCC (forgot what that acronym means). I was unable to do open palm pushups for about 1 year after surgery, so substituted knuckle pushups instead. They are great, especially if you are predisposed to wrist problems. I wear MMA gloves when I do them to protect my knuckles. Been doing them for almost 3 years now. No callouses or other issues.
As a very recent convert to knuckle push ups so I can't really comment on them yet. One thing about push ups in general is too keep a good form- body perfectly straight and rigid, head slightly raised and upper arms kept in close to the body for less stress on shoulders and elbows. Did push ups for years and at my peak I would bust out over 500 daily but didn't realise my technique was for sh#t, which led to shoulder problems. Also got long term hand injuries from turning my hands too far inwards (fingers pointing toward each other - a BIG no no) when doing push ups so knuckles really appeal to me. As has been said already, do them on carpet or an exercise mat.