The Humongous Mecha isn't so much a speculation of practical weapon design as a convenient visual metaphor for the character(s) who pilot it. Steed, sword, and shining armor in one unified package. Extending that metaphor, it may be more satisfying if the hero's final blow for justice is dealt with "his" own right hand across the villain's jaw.
Problem: Said villain is half a mile away, and flying.
Solution: Fire your forearm like a missile!
Problem solved. Don't forget to tell everyone what you're doing, though. And be sure you don't miss; large-scale Rocket Punches tend not to have retrieval mechanisms.
THE most famous Super Robot weapon, even more so than drills. So much so that many old Super Robot toys would include a firing-fist gimmick even if the actual show never used it.
Sub-Trope of Rocket-Powered Weapon.
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Mazinger Z is, of course, the Trope Maker here, including it in almost all the incarnations of the Mazinger franchise. Depending on the iteration, the arm would come back on its own, or he'd have to pick it up. The standard rocket punch is eventually upgraded to the Kyoukagata Rocket Punch ("Reinforced Rocket Punch"), consisting of identical fists with stronger armor. Mazinger Z possess a technique called Daisharin Rocket Punch ("Giant Swing Rocket Punch") in which it spins its arms rapidly, building up momentum before firing off both fists in standard Rocket Punch fashion. Mazinger Z also once used a technique called "Boomerang Fist", in which the rocket punch was attached to the upper arm with a retractable chain, and the "Iron Cutter", a Rocket Punch with blades extended on the sides of the forearms.
A Mechanical Beast -Dian N4- was equipped with a Rocket Punch variant. Dian used its oversized, flying hands to grab, crush and lift things, or to deflect enemy fire. Another Beast, Genocyder F9, invoked the trope when it ripped its own arm off and hurled it at its target.
Unbuilt Trope: The Mazinger's design also kept in mind several things later shows neglected: the mechanisms of launching AND retrieval were clearly visible, Mazinger was built to be able to use all of its other weapons even if it was missing its arms (hence, Kouji was not hindered when a Robeast picked up, disabled or shattered Mazinger's fists, which happened very often like you would expect), and Prof. Yumi ensured there always was at least a pair of Mazinger's spare fists in the Institute to launch at Mazinger in case Kouji needed them urgently.
Deconstructed Trope: Ironically, the Trope Maker series also deconstructed the trope. In one episode, Boss cajoles Prof. Yumi's assistants to build him his own Humongous Mecha (Boss Borot)... using junk. When he eagerly asked if Boss Borot will have a Rocket Punch, Prof. Morimori's answer was: "Are you out of your mind? Your robot is made of SCRAP METAL. The fist would shatter upon impact."
Mazinger Angels: The Fem Bots of Sayaka and her team combine their traditional Torpedo Tits attacks with the Rocket Punch of the series where the characters piloting them were introduced (Sayaka's Aphrodite A combines its Photon Missiles with Iron Cutter, and so on). Minerva X is the exception, wielding a regular Rocket Punch.
Kouji himself does the same thing in the Shin Mazinger Zero manga, ripping his arm off and throwing it as a projectile.
As if the Big Bang Punch wasn't awesome enough, they manage to top themselves again in the final episode. "Rocket Punch 100 Rapid Shots" is all that needs to be said. We're not sure whether that falls under Rapid-Fire Fisticuffs or Macross Missile Massacre.
Ken Kaido: Yeah, it looks impressive, but I freaking hate having to wait for the damn things to come back!
Panda Z (or Robonimal Panda Z: The Robonimation): This 2004 series of super robot parody shorts features Panda-Z, a cute, teddy-bear-proportioned pastiche of Mazinger's design elements. It pushes the Rocket Punch into a massive case of Awesome, but Impractical: The mecha has rocket fists that don't return on their own, leaving the question of how to reattach them to its pilot Pan-Taron, who, utterly mystified, stands there in his armless robot staring down at the fists on the ground as the sun sets. Day turns into night, and we find the robot and its pilot still incapable to resolve the situation. One can only assume that the Photonic Research Laboratories sent someone out to get him when he didn't come home.
Anime and Manga
Lampshaded in Ah! My Goddess, where Sigel's rocket punch is thwarted by a pair of scissors. Those fists might be tough, but the strings used to reel them back in aren't.
In a gloriously hilarious Deconstruction, it doesn't come back, forcing the poor kid to call his target and beg for its return.
The Big O: Big Fau uses its entire forearms as missiles in the Grand Finale. Since the Mega Deus robots in Big O have forearms that are about as big as their torsos, this would seem like a more formidable attack than the typical super robots'. Fortunately, since it's piloted by the Big Bad, it fails, resulting in Big Fau being literally disarmed. The Big O itself averts this with its "Sudden Impact" punch, though, which is as Rocket Punch-y as you can get without actually being a Rocket Punch.
In Bleach, the science master Captain Mayuri has an internal mechanism in his arm that allowed him to launch it in an attempt to grab the fleeing Orihime.
When it fails to return (on account of getting shot by Uryu), he cuts it off and regrows the arm.
In the second season of Code Geass, Kallen's new and improved Guren SEITEN is upgraded to fire its radiation wave arm at enemies while still remaining connected to the mecha through a cable.
In the first episode, Kallen's Glasgow takes critical damage to one of its arms and she attempts a Rocket Punch by weaponizing the system that automatically purges useless limbs. Sadly, it doesn't work, but Jeremiah was impressed by the ingenuity of it.
There are also slash harkens, bladed projectiles on wires that are equipped on practically every Knightmare Frame. The ones that get closest to being Rocket Punches are all incarnations of the Lancelot (mounted in its arm shields), Gawain and Galahad (all ten fingers) and the Shen-Hu (mounted in the forearms and explicitly based on the rope dart).
Dai-Guard pays homage to the idea in the first episode by having its robot team pick up and hurl their robots' disconnected arm like a javelin. Since Akagi is an Ascended Fanboy that has wanted to pilot a Humongous Mecha his entire life (to the point of taking an otherwise useless college course to learn how to do it and spending years in a dead-end job just to be around the only one in existence), it is unsurprising he came up with the idea.
Dangaioh's Boost Knuckle is a PILOTED Rocket Punch. The Token Mini-Moe of the group really hates this maneuver.
Dragon Ball: In the anime version of Goku's fight with the giantandroid Major Metallitron, the latter uses one of these to attack the former..., who takes the full brunt of it. Ouch!
Likewise, Android 16 in Dragon Ball Z has this ability, and uses it against Cell. The trope isn't played quite straight, as the arm doesn't explode, and he has to grab it and reattach it after using the attack.
Nana from Elfen Lied is capable of doing this without any sort of machinery. She uses her diclonius abilities to literally launch her prosthetic arm at her opponent for a long range punch that is capable of covering about 4 meters in a fraction of a second.
In one Fullmetal Alchemistomake, Winry installs a "rocket punch" function on Ed's Automail, and he accidentally shoots his arm off into the distance, resulting in her beating him up for losing her work.
Gaiking: The original 1976 series had Gaiking equipped with a typical rocket punch titled the "Counter Punch".
Gaiking: Legend of Daiku Maryu discusses this trope: Daiya uses the "Puncher Grind" in his second fight only to find the fist isn't equipped to return on its own, and he has to recover it manually or by using Gaiking's Zector Hooks. In Super Robot Wars K, Daiya only uses the Hooks for a Dynamic Kill where he retrieves the fist, then punches the enemy with it and immediately fires it again.
And one of the greatest upgrades the super-powered combined form Gaiking the Great gets? Rockets built into the arm to bring it back. He of course uses this to beat up and embarrass Proist during the initial fight.
Genesic GaoGaiGar is an unusual case, in that only the hand from the wrist down detaches from the rest of the arm.
Kedo from Gash Bell has a couple of variants of this, including a rocket fist the size of a train.
Getter Robo: Neo Getter Robo has the "Chain Knuckle", which as the name suggests, is a Rocket Punch on a chain; inspired by Getter Robo Go, which had a normal Rocket Punch.
One of the Tachikoma Omake episodes from the first Ghost in the Shell TV series has one firing off a fist like a rocket, whilst saying the name of the trope, a second one beside him tries...and everything but his fist goes flying, the first one claims the second one is 'skillful'.
An antagonistic version in Giant Robo The Day the Earth Stood Still with GR-2.
Okita does his version of this to Hijikata in Gintama.
Gundam SEED Destiny's Destroy has these in the form of two "Detachable Arms", which can either be used as Attack Drones, or to invoke this trope. Judging by their size, they probably weigh more than the mobile suits they're launched at.
∀ Gundam apparently couldn't resist including this either: Corin Nander equips his Kapool with one, as a one-shot custom weapon. It doesn't manage to accomplish much, though, since the one time it was used was against the Nigh Invulnerable Turn-X.
In the Houshin Engi manga, Taikoubou loses an arm in battle and it gets replaced by an artificial one with multiple abilities, the Rocket Punch being one of them.
Kotetsu Jeeg -another Go Nagai series- has two different versions: Dynamite Punch -the normal version- and Knuckle Bomber -the two-handed one-.
Chachamaru does this to her creator in the Mahou Sensei Negima! manga after getting particularly flustered. As does the robot Tanaka in the Tournament Arc. Both are attached to cables that can be used to quickly reel their arms back in.
She also does it to Negi after he recover from his initial fight with Kagetaro.
Earlier, during the battle with Evangeline, She Rocket Nose-flicks Asuna, who Cross Counters with a flick of her own.
And now Negi's gotten into the act with a lightning-based version.
And now Dynamis too, with a shadow-based one. Kind of. He teleports his shadow hand and impales Negi with it. And later in that fight, he spams it.
Similarly, the Tetsujin used by the Jovians even bigger Ascended Fanboys than Akito have Rocket Punch-like attacks.
Medabots. In the final battle against the Big Bad, who is in a giant robot, Dr. Aki reveals a giant version of Metabee(complete with a Medawatch that is the size of a belt) that Metabeee and several other Medabots hop in to pilot. One of the Giant Metabee's attacks? Rocket Punch. Gets lampshaded by Ikki, asking if Aki has a spare arm. Aki responds, moderately angrily, by saying "Reduce, Reuse, Recycle!" before the giant arm rocket propells itself back to the Giant Metabee.
The Asura Path body of Pain in Naruto can detach his fist and fire it with great force at enemies, with it partially fortified with chakra.
Franky (a cyborg), whose rocket-punch include a chain;
Buggy has a somewhat similar move due to his Devil Fruit powers, that extend to every part of his body less feet;
Both Akainu and Ace have a similar move - made of lava and fire respectively.
In a mail, a reader suggested a new move for the protagonist: when he throws one of his elongated super-punch, the swordman Zoro cuts the arm. As the reader noted, "It works only twice". The author was not enthusiast of this idea.
Patlabor: In the first episode of the OVA, the villain knocks the right arm off Noa's beloved Labor Alphonse. Her partner urges her to turn her grief into rage and strike back with the "fist of justice". She catches up with the crooks and flings her Labor's severed arm at them. Of course, since Noa IS an Ascended Fangirl loves Humongous Mecha shows she shouts, "ROCKETTOPUNCH!!" while doing this.
Pokémon: Parodied in one episode where Pikachu seems to do this (shocking the onlookers)... until the cloud of smoke coming from the fist's wrist end is revealed to be Pikachu in a cloud of dust, having thrown itself bodily at the opponent.
Pikachu did hit its opponent...trouble was, said opponent was a Hitmonchan, who received little more than a bruise on its face and proceeded to KO the mouse when its own trainer showed up.
Combattler V is equipped with Battle Guleggar (Combattler releases a chain with metal collar from the arms, used for grabbing opponents by the neck) and Magne Claw (Combattler's hands withdraw into its arms and its wrists shot a spiked, square projectile).
In a different variation, we have unrestrained Zetsui's "Vigorous Fists", which are more like missiles.
Sousei No Aquarion: Mugen Punch. Not quite a Rocket Punch as Solar Aquarion's arm telescopically extends instead of detaching but it's capable of Roboteching and can extend all the way up to the Moon in around fifty seconds, meaning that it covers around 7688 kilometers per second (over 2.5% the speed of light).
Similar to the Shin Mazinger example above, Kamina snaps Simon out of a Heroic BSOD by throwing Gurren's severed forearm at Lagann. Not quite a "Rocket" punch, but the HUD on Lagann adds a starburst graphic as an allusion.
One of Vash's opponents in an early episode of Trigun has a rocket punch attack: Gofsef Nebraska, a 23 feels-tall cyborg mutant whose dad rides on his shoulder. His fist has a retractable cord, enabling him to bring it back and shoot it repeatedly. Vash takes it all in stride, though. He taunts the brute after one attack by scrawling graffiti onto the fist. He then proves his dominance by deflecting the fist in mid-flight by firing five precise shots at it.
The OVA Z-Mind had a variation where the title mecha created a wormhole which it punched through. Ion-shooting arm at the enemy, while still connected to the Guren through a cable.
Go Lion has the Four Lion Attack (or 100-Ton Punch), which launches the lion heads that form its hands and feet at the enemy.
Let's not forget, Rusty's "Hypersonic Kicks". Although the feet stay on, they are given really high momentum by the feet jets.
Not rocket-powered, but DC Comics has a couple of characters that use the same basic principle. Green Lantern Hal Jordan is famous for using his ring to create a giant boxing glove, and Green Arrow often uses boxing glove arrows. Cyborg has a for-some-reason detachable arm with a rocket in it, but never used it as such (only using the rocket to retrieve/move he arm for surveillance) in the Teen Titans animated series, but not in the original comics. (Yet.)
S.T.R.I.P.E. in Justice League Unlimited uses this in the episode "Chaos at the Earth's Core.''
He uses it in his own book as well.
Spiderman had a villain who later turned hero named "Rocket Racer" who had this via rocket powered gloves. They didn't detach though; he had mini missiles for ranged attacks.
In an issue of Hellboy, he briefly fights a cyborg Nazi with robotic fists linked ot his forearms by chains. This character is soon killed off but probably inspired Mr. Wink in the second film (see below).
Ultraman-ripoff Inframan in The Super Inframan receives a new weapon called "Thunderball Fists" before the final confrontation in his self-titled film. Two guesses what they do. Strangely, the original Ultraman didn't have a rocket punch, and isn't exactly a robot either.
In the Arnold Schwarzenegger film Jingle All the Way there is a parade based on a show themed after a Sentai show, where both the protagonist and antagonist steal (for some reason fully functional) outfits of the corresponding characters. The antagonist gets a rocket punch amongst his abilities, which surprises both of them when he uses it.
"TA TA, Turtleman!"
What about Robot Jox? Especially the climactic fight scene after our hero is ejected from his Humongous Mecha. He proceeds on foot to hotwire the rocket fist from a fallen piece of his opponent, defeating the enemy mech with its own severed arm.
And let's not forget the fist bazooka in Hot Shots!: Part Deux.
A troll called Mister Wink in Guillermo del Toro's Hellboy II: The Golden Army has a prosthetic metal hand that he can fire and call back using a chain and the hand's ability to crawl with its fingers.
The Korean rock band W And Whale had a song called Rocket Punch Generation Shine (or RPG Shine), which invokes this trope in both the lyrics and video. And it's catchy as hell.
The Japanese pop singer T.M. Revolution has a song called Madan -der freischutz- (Magic Bullets) has this trope in the video.
The 4th edition of the Dungeons & Dragons setting Eberron has this. A Paragon Path for Artificers called the Self-Forged starts by replacing a hand with a Magitek replacement called a Battlefist. The ultimate "spell" for the Path allows the Artificer to shoot the Battlefist away on a chain of energy, allowing them to continue to control it even while it's detached from their body.
3.5 Warforged (or in theory anyone with access to the Kensai Prestige Class) a +1 throwing returning fist.
The Blood Wind spell from 3.5 lets a creature throw its natural weapons, which return by magic. Monks treat their unarmed strikes as natural weapons, and can make unarmed strikes with any part of their body.
4e Barbarians can get the feat "Hurl Weapon", which lets them use any off-hand weapon as a thrown weapon. The Monk's unarmed attack counts as an off-hand weapon...
Several of the original Takara Diaclone robot toys that were used when Hasbro originated the Transformers line had spring-launched fists, but this ability was never incorporated into the original cartoon.
For a more recent example, Reveal The Shield Lugnut's forearms are both spring loaded for double-fisted P.O.K.E goodness.
The Playskool Transformers Go-Bots (aka "1-2-3 Transformers" and "Go-Go-Go-Bots!") toy line featured a character called Aero-Bot, whose toy had launching fists (attached by strings, so they don't get lost) which hung under his wings in jet mode. There was also a slightly redesigned version in different colors named Silverbolt. This was a forerunner of Lugnut's more fully realized equipment.
Parodied in BlazBlue. In the segment of Teach Me, Miss Litchi!, Kokonoe installed a Rocket Punch in Iron Tager (it's not part of his actual moveset). However, she's not satisfied with the result and was thinking to move it somewhere else. Maybe on his chest... or his — GIGANTIC TAGER!!!!
Robo from Chrono Trigger had a Rocket Punch as his weakest special ability, where he would throw his fist at the enemy; it was hooked to a chain so he could reel it back in. A stronger attack, named "Uzzi [sic] Punch", had him do this multiple times in rapid succession.
Some of Geno's weapons in Super Mario RPG do this. Then again, he's an animated doll.
Darkstalkers: Jedah, everyone's favorite self-harming vampire, not only fires his arms off in bloody geysers, but also his fingers and his goddamned head.
In the Dragon Ball Z games, Android 16 has the Rocket Punch as a basic ki attack. And yes, he does yell his attack.
Kurtis, whether in human (cyborg) or Prinny form, has at least one variant of this as an attack in each of his appearances throughout the Disgaea series. He also yells it out in 3 and 4, though only with the Japanese audio on.
His Final Arm attack (Used in 2, 3, and 4) seems to pay homage to the rocket punch's origins, as it drills though the target, then inexplicably causes them to explode after they crackle with electricity in a fashion you'd expect from a damaged Humongous Mecha.
In 3, and the remake of 2, his robot clones can magichange into a fist weapon (With two rocket punch special attacks), while his true Prinny self magichanges into a gun that can shoot rocket punches.
Lady X uses this as a Finishing Move in Rumble Roses, but it doesn't look nearly as cool as one might expect, knocking her opponents across the ring despite being so slow-moving that they should be able to stop it cold with just one fingertip.
Robot Alchemic Drive: Vavel's a big remote-controlled homage to Mazinger Z, so it stands to reason it would have its own version of the Rocket Punch, called "Assault Knuckle"
Persona 3's Aigis has this as one of her weapons. By the time you get it, however, it's usually outclassed.
Labrys, from Persona 4 Arena, has a Rocket Punch of her own, connected to her body with a chain. This ability is shared amongst the other 5th Generation Anti-Shadow Weapons.
G. Kaiser, from Tech Romancer, has Rocket Punches as a standard special attack. Considering it's a blatant Expy of Mazinger...
Area, a Mad Scientist (even though she looks more like the daughter) from the Street Fighter EX games has something similar. Instead of launching her arm, she wields a huge mechanical gauntlet (named 'Cancer' for some reason). Some of her attacks feature it launching in various manners. Her most powerful attack fires it off and then detonates it; while the move does excellent damage, you then lose the gauntlet for the rest of the match, which basically kills her offense.
Mega Man V (Game Boy) replaced the usual Mega Buster with this as its charged attack. Megs can also do this in Mega Man 6 with the Rush Power Adapter.
In Mega Man Battle Network, by using an arrow combination as he activates the Guts Punch chip, Rock can transform it into the Rocket Guts Punch. The combination, of course, is down, down-right, right. Gutsman himself enjoys using the Rocket Guts Punch at higher versions. In the anime, Rock uses the Rocket Guts Punch as his primary weapon when in Guts Soul (in Battle Network 4, he can only do the Guts Punch). Also possible a Program Advance consisting of selecting Guts Punch, Ice Fist and Dash Attack, (in that order) to fire a stream of fists straight ahead, while time is frozen.
In the second game of the series, there are three successive powered-up versions of Guts Punch that have increasingly complicated Rocket Punch commands - Bronze Fist fires a single rocket punch, Silver Fist (this troper's favorite for its ease of use) fires an individual Rocket Punch down every row, and Gold Fist fires three punches down each row.
Spring Man from 7 has the retractable-arm variety of rocket punch in the same vein as Robo.
The Rush Super Adapter of 7 shoots powerful rocket punches on a full buster charge. After picking up a certain upgrade, they become homing punches.
In the same game Bass has a rocket punch in the second Dr. Wily stage when he's merged with Treble.
The General in Mega Man X 4 has a rocket punch attack, though the most dangerous thing about this attack are that 2 laser cannon weapons that appear where his wrists used to be. The fists themselves are pretty harmless, and can be used by X/Zero to get a better shot at General's weak spot, his head.
In Maverick Hunter X, Vile can obtain an entire set of weapons which launch his fist forward with differing amounts of speed, damage, range and power usage. They're used in place of arm-mounted vulcans or missile launchers, and are usually stronger on average but harder to work with since Vile can't fire more than one of his arm at a time.
In Cyborg Justice, the Launch arm works like this, but it requires you to walk over to where it landed and pick it up to reattach before it blows up.
ZHP: Comes in two flavors, depending on which arm you equip the Rocket Punch to: the left arm uses Rapid-Fire Fisticuffs, while the right arm launches its target in the air and smacks him around a few dozen times.
Annihilator Droids in Champions Online regularly use rocket punches. Somehow, they leave them with their arms intact.
Blitzcrank from League of Legends, much like Robo, also has a rocket punch. However, the arm is retractable, and its main purpose isn't to punch enemies out but grab them and drag them away from their allies to Blitzcrank and his allies, where they'll be promptly slaughtered.
Vi has a pair of gigantic Hextech gauntlets that are rocket-propelled. She uses them to charge at people fist-first and smack them in the face, or uppercut them into the sky.
The Defenders in Final Fantasy X can fire one of their fists to halve a character's HP. Another one instantly locks into place afterwards.
One of Barret's weapons in Final Fantasy VII has the appearance of a boxing glove instead of the usual gun-arm and is actually named "Rocket Punch", but it subverts the trope as a close-range melee weapon instead of a ranged attack.
Falcon of Power Stone uses this as his main method of attack in his super form.
Byrne from The Legend of Zelda: Spirit Tracks has a huge-ass power glove that he can fire to grab or punch his opponents. It's attached to a chain, making it retrievable.
Unzan from Touhou shoots giant pink fist-shaped bullets. He's also a giant pink living cloud.
Demolitions expert Araym from Septerra Core blew his arms off in the last war, and had them replaced with, essentially, big rocket arms. He gets very few attacks that aren't some form of Rocket Punch.
In X-Men: Children of the Atom and Marvel vs. Capcom 2: New Age Of Heroes, Sentinel can fire its arm at a foe. It even says "Rocket Punch" when doing so. In the words of Yipes- "PLAYING BLOODY KNUCKLES"
Cyber-Akuma, the modified clone of Akuma made by Apocalypse in Marvel Super Heroes vs. Street Fighter also has one of these as one of his attacks.
In Ultimate Marvel vs. Capcom 3, Nova does a variation where he fires his entire body at the enemy at full speed to deliver a powerful punch. Considering his nickname is the Human Rocket.
Spyborg in Star Fox 64 likes to fire both of its fists in succession.
In Makai Kingdom, the Bonus BossRobosuit uses this as one of its attacks. The Robosuit is obviously intended as an homage to the classic Giant Robot school of mecha design.
The AI usually only uses it when you've placed it in critical or when you've blown off certain parts as well. It's also pretty cool in the amount of variations of rocket punches it can do as well.
The Grungust series of mechs in Super Robot Wars Original Generation have the BOOST KNUCKLE ability, which launches their entire forearm at an enemy like a missile. It returns afterwards. The Type-3 Grungusts combine tropes with This Is a Drill in the form of the Drill Boost Knuckle, as does the Thrudgelmir.
KoRyuOh, having been made from Kusuha and Bullet's Type-3, also sports a Rocket Punch in the form of the Tiger Knuckle.
Despite being a human-sized Robot Girl, Aschen Brodel of Endless Frontier can launch her fists at enemies and pull them back with wires.
Asgard in Wild ARMs 5 uses one as a sort of ejection seat to get Avril out of harm's way before the start of the game. He uses it again near the end of the game, this time in the traditional manner, when his missing arm returns during his time of need and Rocket Punches Volsung's Humongous Mecha in the face.
Metal Gear Solid: Peace Walker has a tongue-firmly-in-cheek variation performed by Zadornov, where he makes a peace sign and shoots it while shouting "Rocket peace!" The theme of the game is nuclear deterrence (peace gained through rockets), so this is either symbolic or just one of Kojima's references to the anime he watched as a kid. Or both.
"Rocket Kubochi" and "Double Rocket" In Inazuma Eleven, rocket punches that are used in a soccer match as a goalkeeper's punching techniques.
The Robot costume's main attack in Costume Quest is a Rocket Punch, even called by that name.
In Star Wars: The Old Republic, the Bounty Hunter has an ability called Rocket Punch where they use rocket boots to uppercut an opponent.
Plok is a rare biological example in which the title character is able to shoot out and reattach not only his fists, but his legs as well.
Variation in the Mass Effect 3 multiplayer. The turian Havoc Soldier uses his rocket pack to leap a huge distance and stab his omniblade into a hapless enemy.
The MEC Trooper from the "Enemy Within" expansion to XCOM: Enemy Unknown has a "Kinetic Strike" module as an optional weapon. As a backup melee weapon, it's highly effective, especially against its Alien counterpart, the Mechtoid.
A variation is executed by Space Kid in Episode Two.
Voltron (specifically Go Lion) had its "Lion Head Attack," which fired its "hands" and "feet" at the enemy. Naturally, Voltron was always flying at the time, so it wouldn't fall over from suddenly losing its feet.
Bump In The Night was a series that took place with all the monsters and toys that live in a kids room. One of the Running Gags was a Lawful Stupid toy robot firing its "Fist Missiles" at the titular Mr. Bumpy. Said fists frequently stopped, looked around for Bumpy, and lifted up objects and used tools to better help them find him.
Avatar: The Last Airbender of all places has a variation: members of the Dai Li have gloves made of rocks that can be launched as a punch or to grab someone inconspicuously. In addition, the gloves are segmented, so small sharp pieces can be shot off like bullets, and it can be bent into a claw or fist while flying at enemies.
On episode of the Men In Black TV Series had J shrunk down to the size of a small alien, and forced to use a robot suit built to look just like him. The robot suit in question could actually fire off its fists as Rocket Punch attacks, which unfortunately bit J in the ass when he missed and set the arm way farther than he had the chance to get back to.
J: I like that arm.
A truly bizarre variation occurs in a rare and obscure experimental cartoon called The Little Island. One of the three unnamed characters raises his fist, which suddenly enlarges and pops off his wrist, then comes crashing down on him from the heavens. Several times.It starts at the 3:46 mark of this segment.
Lugnut from Transformers Animated possesses a rather different kind of Rocket Punch, in which jet engines attached to his forearm propel his explosive-tipped (and still attached) fist into the ground at supersonic speed. The result is an enormous explosion of kinetic force that can level a city block. Bulkhead counters this by triggering the explosive prematurely with his wrecking ball. Wreck-Gar just used a high-five.
In the season 2 finale, Lugnut actually uses launches his fists (in both robot and jet mode), to little effect against Omega Supreme.
Lockdown, on the other hand, plays it straight. Since he's made largely of stolen parts, it's no surprise that they can fly off.
And Bulkhead's wrecking ball probably counts too, since it takes the place of his fist and swings out on a cable.
The titular Megas XLR has a set of these, though like Genesic GaoGaiGar, it fires the actual fists at times.
Apparently, a prosthetic arm has been developed using rocket propellant bursts to overcome the strength limitation of more traditional mechanisms like servos and hydraulics. In time, someone's bound to get punched by one.