I asked a question? Oh no!

Veracity beats Baerns initiative and rolls as high as he possibly could have on investigation anyway - can I amend his action after the machines act? It seems largely redundant.

A tiefling and a duergar looked on in alarm as two ceiling-mounted cranes careened toward their companion, looking ready to crash into the staircase and/or its occupant.

Baern is a proud Svirfneblin, thank you very much :)

Can the gears be interacted with apart from damaging them? Could a tinkering check disable them?

The dragonborn braced as best he could for the impact but the cargo sling slammed into him with such momentum that his efforts seemed almost laughable.  The impact swung his body out off the twisted stairway, only one taloned hand maintaining contact with a twisted handrail. Vecaal flailed precariously for a moment, his body almost parallel to the ground below, before gravity brought him back into the damaged metal structure.  Banging hard against the stairway, he barely managed to hold on and avoid disaster.  Grunting in pain, he secured his grip and searched the ceiling for whatever Veracity was pointing out.

Spotting the closest cog, the dragonborn reached one hand down by his waist and then flung out his arm with full extension.  A glowing golden dagger flew from his hand toward the mechanism.  Using his momentum he swapped his grip on the stairs, spun, and sent another golden dagger spinning toward the cog.  Then, with what appeared to be a grin or grimace (it was always hard to tell with a dragonborn) his slithered up the stairway, hoping to get ahead of the next crane barreling his way.

OOC:
10:46, Today: Vecaal Alifras rolled 15 using 1d20+3.  Acrobatics.  Just made it to hang on to the stairs!

Attack 1 hits AC16 (augmented by bardic inspiration) for 6 dmg.
11:04, Today: Vecaal Alifras rolled 10 using 1d20+5.  Attack.
11:04, Today: Vecaal Alifras rolled 6 using 1d6.  Bardic Inspiration.
11:11, Today: Vecaal Alifras rolled 6 using 1d6+3.  Damage.

Attack 2 misses.
11:13, Today: Vecaal Alifras rolled 11 using 1d20+5.  Attack.

Climb 30 ft upward with Move action.  Successful roll already provided.

Die roller is toying with me already...

Veracity, in the moments before the crane smashed into the staircase, traced with a keen eye the intricate chain of belts, pulleys, and gears that drove the cranes. There! and there! she was able to point out to the others, including three newcomers who had just burst through the door. She could only hope they were allies. Her pointing purple finger indicated two critical cogs which, if bent or destroyed, should render the cranes inoperable.

Everyone else: Veracity has pointed out two gear trains that could be broken to shut down the cranes (she already failed an Investigation check to look for a way to control the cranes without breaking them, so I didn't include that in the result, but someone else could use an action to Investigate for this if they wanted). The nearer set of gears is 25' from the staircase. The further is 40'.