You might find this information useful, this one sure did.

Precursor locations (personally confirmed, but some are real hard to get - there are videos on youtube that can help with specifics). You can collect these parts without the quest.

******* begin copy pasta*******

1 - Left arm - Yldzuun (Alik'r)
2 - Right arm - Klathzgar (Bangkorai)
3 - Left leg - Avanchnzel (The Rift)
4 - Right leg - Santaki (Alik'r)
5 - Pelvis - Lower Bthanual (Deshaan)
6 - Chestpiece - Aldunz (Alik'r)
7 - Spine - Mzulft (Eastmarch)
8 - Left hand - Inner Sea Armature (Stonefalls)
9 - Right hand - Mzithumz (Deshaan)
10 - Dynamo core - Bthzark (Stros M'kai) - Requires "Buried Secrets" quest, which is acquireable both outside and inside the delve
11 - Integral of calculus - Mechanical Fundament (Clockwork City)
12 - Integral of introspection - Near the Ventral Terminus (Clockwork City)
13 - Integral of reason - Machine District (Clockwork City) - Requires "Lost in the Gloam" quest, which is the 5th main story quest
14 - Nullification staff - Bthanual (Deshaan)
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