If Ancient Gear Wyvern is Normal or Special Summoned, it allows you to add an “Ancient Gear” card from your Deck to your hand. You can only activate this effect once per turn and, if you do activate it, you can't Set Spell/Trap Cards for the rest of the turn, but don't worry: you can Set Pulse Mines before you Summon Wyvern to get around this minor drawback.
You can't add Geartown to your hand via Wyvern's effect, but you can add Ancient Gear Golem or, even better, Ancient Gear Box. If Ancient Gear Box is added to your hand outside of your Draw Phase, it will allow you to add another EARTH Machine monster with 500 ATK or DEF to your hand, meaning primarily Ancient Gear Frame and Ancient Gear Knight. Fusion Summoning Ultimate Ancient Gear Golem takes a great amount of resources, which is exactly what makes this particular combination so good.
By discarding a card, Ancient Gear Frame allows you to add to your hand an Ancient Gear Golem or a Spell/Trap Card that specifically lists “Ancient Gear Golem” in its text.
The only card in Duel Links that Ancient Gear Frame can search that Wyvern can't is Spell Gear, so most of the times you will Summon the latter, but being able to thin your Deck is always nice and you won't always start with Wyvern in your hand.
Since Ancient Gear Knight has to be Summoned twice in order to gain its “Ancient Gear” effect, Ancient Gear Frame is arguably the best card you can add to your hand via Ancient Gear Box.
If Ancient Gear Frame leaves the field because of an opponent's card effect, you can Summon up to three copies of Ancient Gear Golem or Ancient Gear Golem - Ultimate Pound from your hand ignoring their Summoning conditions.
The card has to be face-up on the field for its effect to trigger, which means you can't just Set it, wait for a Koa'ki Meiru Maximus to destroy it and then swarm the field with multiple 3000 ATK monsters. With 1600 ATK, there is really no need for your opponent to destroy Ancient Gear Frame with Treacherous Trap Hole or Offerings to the Doomed, especially if they know about its effect.
You can only Special Summon Ancient Gear Golem from your hand, so getting three of them on the field via this effect will not be that easy. Now, I’m not saying Ancient Gear Frame is a bad card: it works extremely well against Spellbook, but most of the times the crazy floating effect won't come into play.
King of the Swamp can be discarded to search Polymerization or even used as Fusion Material for Ultimate Ancient Gear Golem, substituting Ancient Gear Golem. You can't use King of the Swamp to Summon Pair Cycroid.
Ultimate Ancient Gear Golem is a 4400 ATK monster that can inflict piercing damage, shut down your opponent’s backrow on attack declaration and, if destroyed, even Special Summon Ancient Gear Golem from your Graveyard, ignoring its Summoning conditions.
There are only two problems with this card: it’s a Fusion Monster that requires 3 Materials and Polymerization and nothing stops your opponent from taking control of it and simply swinging into your Life Points.
After testing out the deck, I can safely say that the first issue doesn’t come up that often: the deck has notably improved when it comes to consistency and certainly has a lot of potential. As for the second issue, Enemy Controller will mainly be a problem if you Summon Ultimate Ancient Gear Golem on Turn 1.
Pair Cycroid is a 1600 ATK monster that can attack your opponent directly. Thanks to Wyvern and Ancient Gear Box, getting the Fusion Materials for this card is really not that hard and there are certainly going to be situations in which you will want to Summon it to pick off an already weakened opponent.
Ancient Gear Castle will provide your monsters with a 300 ATK boost, which will put your Ancient Gear Frame on par with a Koa'ki Meiru Sandman and above any Level 4 Destiny HERO. If Ultimate Ancient Gear Golem is destroyed by Koa'ki Meiru Maximus, thanks to the Continuous Spell, your Ancient Gear Golem will still be too big for it to run over.
As always, Restart can provide more consistency and avoid potential unplayable hands, but skipping a Draw Phase can be particularly hard for this deck.
As I explained, Middle Age Mechs can make a huge difference in this matchup, bringing Ancient Gear Golem to 3300 ATK, above Koa'ki Meiru Maximus, but your opponent still has a way to deal with both Ultimate Ancient Gear Golem and Ancient Gear Golem: Koa'ki Meiru Ice.
Going 2nd against Vampire can lead into a really quick match: after activating Vampire Familiar and/or Vampire Retainer’s effect, Ultimate Ancient Gear Golem will likely be able to finish off the opponent with a single attack. Going 1st and Summoning Ultimate Ancient Gear Golem leaves you open against Vampire Vamp, which can get rid of it without triggering its floating effect while also creating something that none of your monsters can deal with, but leaving the field open would also likely translate into a loss.
Pulse Mines can be used to stall and Offerings to the Doomed to destroy Ultimate Ancient Gear Golem, but your opponent will need at least two of the latter, which I’m not saying it’s impossible (Karakuri Anatomy), to get rid of the Ancient Gear Golem that will be Summoned afterward.
Masked HERO will likely struggle against this deck and will resort to attacking you directly with Masked HERO Anki, which Sphere Kuriboh and Pulse Mines can easily prevent. Even if Ultimate Ancient Gear Golem is flipped face-down by a Paleozoic Canadia or a Floodgate Trap Hole, it will still be too big for Anki.
Since you have no way of dealing with Yubel, your best bet is to Summon Ultimate Ancient Gear Golem on Turn 2 or 3 and swing into a face-down Fire King Avatar Yaksha. If Yubel becomes more relevant, you might want to try running Forbidden Chalice: this Quick-Play Spell, if activated during the Damage Step to prevent Sphere Kuriboh, can easily win you the game.
Silent Magician (and Silent Swordsman) are able to negate Polymerization, which makes this one of the worst possible matchups for this deck. Even if you go 1st and Summon Ultimate Ancient Gear Golem, Spellbook of Fate can still banish it, which means its floating effect won’t even trigger. Your best bet is to use Ancient Gear Frame as a deterrent and/or use Sphere Kuriboh/Pulse Mines to put Silent Magician and SSilent Magician LV8 in Defense Position.