As written - no. You must sacrifice one artifact at a time, and their triggers go on the stack before you next get priority, which means they're not all in the graveyard at once, which prevents you from forming a loop.
However, if you have something like Bog Initiate on the board (or any similar "filter" mana ability), you can do this. The reason is that, when activating an ability with a mana cost, you are given special permission to activate mana abilities (which Krark-Clan Ironworks has) and the triggers will only go on the stack once you get priority, by which point all the artifacts are in your graveyard and thus valid targets.
Specifically you do this:
1) Declare activation of Bog Initiate's ability.
2) Declare that in the "paying costs" part of activating the ability, you are activating Krark-Clan three times, in the following order: Terrarion, Myr Retriever, Scrap Trawler. (Scrap Trawler must be last in order to properly trigger abilities.) This gives 6 mana.
3) Pay the cost. You now have 5 mana.
4) Complete activation of the ability. Since it's also a mana ability, it resolves immediately. You know have 5B.
5) All the triggers go on the stack. Place them on the stack with the following targets (order is irrelevant):
Terrarion's draw (no target)
Myr Retriever's own ability, targeting Scrap Trawler
Scrap Trawler's triggered ability for itself dying, targeting Myr Retriever
Scrap Trawler's triggered ability for Myr Retriever dying, targeting Terrarion
Scrap Trawler's triggered ability for Terrarion dying (no valid target, fails to go on the stack)
When the abilities all resolve, you will draw a card and put the three artifacts back in your hand, with 5B floating - enough to recast the artifacts. Finally, recast the artifacts and you are back to the original board state, but up one card draw.
Edit: clarification
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URStormRU
GRTitanshift[mana]RG/mana]
However, if you have something like Bog Initiate on the board (or any similar "filter" mana ability), you can do this. The reason is that, when activating an ability with a mana cost, you are given special permission to activate mana abilities (which Krark-Clan Ironworks has) and the triggers will only go on the stack once you get priority, by which point all the artifacts are in your graveyard and thus valid targets.
Specifically you do this:
1) Declare activation of Bog Initiate's ability.
2) Declare that in the "paying costs" part of activating the ability, you are activating Krark-Clan three times, in the following order: Terrarion, Myr Retriever, Scrap Trawler. (Scrap Trawler must be last in order to properly trigger abilities.) This gives 6 mana.
3) Pay the cost. You now have 5 mana.
4) Complete activation of the ability. Since it's also a mana ability, it resolves immediately. You know have 5B.
5) All the triggers go on the stack. Place them on the stack with the following targets (order is irrelevant):
Terrarion's draw (no target)
Myr Retriever's own ability, targeting Scrap Trawler
Scrap Trawler's triggered ability for itself dying, targeting Myr Retriever
Scrap Trawler's triggered ability for Myr Retriever dying, targeting Terrarion
Scrap Trawler's triggered ability for Terrarion dying (no valid target, fails to go on the stack)
When the abilities all resolve, you will draw a card and put the three artifacts back in your hand, with 5B floating - enough to recast the artifacts. Finally, recast the artifacts and you are back to the original board state, but up one card draw.
Edit: clarification