You will need a way to rotate these parts if you want any kind of reliability.
It is much faster make small adjustments while we have part prepared to PnP, I mean very close to perfect fit, than do all this job in the fly, so yep small adjustment might be needed for final placement, but time needed for those tiny adjustment can be much smaller when very small angle need to be chamged, which can lead to huge speed improvements in the case fast PnP assembly head is used like those 3axis ultra fast pick & place robots:
Ultra Fast Pick & Place Robot - FANUC's New Three-Axis Delta Robot Packs Small BatteriesBTW: It weights less than your PnP machine, but for sure costs much more, I guess.
Anyway, I've ordered steell balls today from reliable local bearings supplier, to create axis similar to those used in this ultra fast robot and we'll spot weld them on friday, I hope, to see how it works and if it coulbe usable, so theres is some time to create 3D njumeric model of this thing to simulate complex 3D space positioning, based on dimensions of ordered steel balls and robot arms axis dimensions
It is a lot of fun trying to create such fast robot in DIY project
Good luck, I want hit another PnP market with much cheaper PnP available for more electronics and CNC hobbysts from my neighbourhood and without any Kick(off)starter and similar company which earns close to 10% or more on someones ideas, instead people donate us from time to time via Bitcoin (cheap and safe moneys transfers quickly exchanged to real $es), so we are very motivated to deliver as fast as possible something usable and everybody are happy- we can save those 10% which had to else benefit doggy Indiegogo, etc, promoting sometimes stupid, useless ideas, which owners claims they are smarter than... Nobel price winners scientists