[iiJDSii]

I've done similar projects in the past (robot arms pushing performance limits in the few thousand $ range), and I found pretty good results with stepper motors, and gearboxes with sufficiently low backlash. For reference, these designs got to approx 1mm repeatability with 2.5kg payload at ~80cm reach, meant to model a human arm somewhat.

Here's some specifics if you're interested. Depending on the end effector payload requirements, a mix of NEMA34,24,17 can do this (bigger ones for earlier joints). You can go cycloidal/harmonic gears if you have the budget, otherwise each actuator (motor + driver + gearbox + shaft coupling) would run you something like $100-$200 depending heavily on supplier and exact requirements (+$50 or so for closed-loop systems). So not terrible on the price front. Then for the base joint you'd want some wider cylindrical gearbox that distributes the load across better.

If you're able to work with a machine shop I think you can put together something really high quality. Here's some example design inspirations, some of them even better than what I described I was able to put together as a hobbyist:

https://www.youtube.com/watch?v=7z6rZdYHYfc (this one is fantastic; a smaller and lighter version operated more slowly would have even less wiggle from the base) https://www.youtube.com/shorts/II8gdIXPgaE (this is more comparable to the OP) https://www.youtube.com/shorts/_x7P9eZCkVM https://www.youtube.com/watch?v=g9AfhqOd-_I (most professional one I've seen, and almost certainly this BOM would be under $3k, probably under $1k in China. In fact I'll go ahead and email these guys since this is so cool and I wonder if they sell smaller models) https://www.youtube.com/watch?v=iB2NAgfVjIs (definitely check out Chris Annin, American roboticist who imo makes some of the best open source low cost stepper motor robots)