Linear motion (R-FLEX) for minature 6.2 mm pitch optical fiber position robots with polar (R-theta) kinematics
R-FLEX is a compact, low-part-count flexure-based radial positioning mechanism designed for the next generation of massively parallel fiber-fed spectroscopic telescope instruments. Current instruments such as the Dark Energy Spectroscopic Instrument (DESI) employ 5,000 robotic fiber positioners at 10.4 mm pitch, whereas future surveys require 2.5-3x higher packing density, necessitating new positioning technologies. The R-FLEX mechanism converts small rotations at the flexure base into large, nearly tilt-free radial motion at the fiber tip, achieving naturally low-backlash linear motion within a compact 5.8 mm diameter package. Coupled with a rotating theta-stage, this enables overlapping circular patrol areas at 6.2 mm pitch, as envisioned for projects like Spec-S5. Development proceeded through parametric modeling and optimization, finite element analysis, fabrication, and prototype testing. Prototype units characterized by optical centroiding achieved a corrected radial accuracy consistently better than 4 um RMS over a 3.9 mm travel range, with maximum fiber tilt 0.092 deg, defocus 42 um over the required range, and durability over more than 400,000 targets per robot across operating and survival temperature extremes. Preliminary Spec-S5 accuracy, defocus, and fiber tilt requirements are specified for the complete R-theta robot, and these radial-stage results exceed those requirements, leaving margin for the companion theta-stage. A parametric optimization pipeline makes R-FLEX a versatile, mass-producible platform that can be re-optimized for precision-positioning applications beyond Spec-S5. This offers the precision, compactness, and reliability needed to collect hundreds of millions of spectra for new studies of the large-scale structure of the universe.