Mechanics of a Stick-Slip Piezo Motor: Printed Rail, Calibrated Preload (0.099 N per Tick), Flexure, Friction Pair

The rail I retired

The slider needs to move along one axis and no others, so I first bought an MGN12H miniature linear rail with its matching bearing block. However, a caged-ball block is built for machines that push it with real force, and its precision comes with drag, since seals, retainers, and preloaded balls all add friction before the payload contributes anything.

Drag works directly against this motor, because the only forward force available is friction at the foot, at most µN, with N counted in single newtons here (that week's notes put the entire available budget at roughly 0.3–0.5 N [design_notes §18, 2026-07-09]). The block's breakaway force, the static friction that must be overcome before it moves at all, turned out to be more than the drive could supply [project CLAUDE.md §2].

Before giving up on the block, I tried Krytox grease and bearing oil in it, and I bent the ball-retainer wires outward so the balls could recirculate more freely. The notes from that week add that the first setup ran two blocks on one rail, and they flag the two-block over-constraint itself as a prime roughness suspect [builder, 2026-08-06; design_notes §18, user report 2026-07-09].

Each attempt was checked with a tilt test, which measures the breakaway force with gravity (one end of the rail is raised until the loaded slider first slips, and F_break = m·g·sinθ). Even after the modifications, the block only broke loose at a steep tilt, around twenty-something degrees, by my recollection [builder, 2026-08-06; design_notes checked 2026-08-10: §18's 2026-07-09 entry prescribes the tilt test and a ≤0.13 N pass bar, but no measured angle was ever logged, so the recollection is the only record]. A motor whose entire drive force is a fraction of a newton cannot afford a rail that needs that kind of push to start moving, so the MGN12H was retired.

At the time I treated the rail's friction as the main problem, and in hindsight it wasn't. The drive electronics weren't delivering what I believed they were (half the voltage the documents claimed, and later a suspect channel) [builder, 2026-08-06; §M7]. But retiring the rail was still the right call, for a reason that §M10 makes precise. Since the motion I was hunting was invisible to the eye, I couldn't tell which suspect was guilty, so the approach was to remove every suspect I could afford to remove, and the high-drag rail was one of them.

Rail v2

The replacement came off my own printers, a custom rail whose slider rides on bearing bolts, rolling in V-grooves printed directly into the rail body. Of its two groove sets, the bottom set carries gravity and the side set takes the preload reaction, the lateral force the actuator pushes back with (§M2's diagram shows both). I got the idea by asking which forces the rail had to resist, and then I aimed one angled V-groove at each. I sketched it before I modeled it, and once it existed on paper it just made sense [builder, 2026-08-06].

The design keeps only what the physics requires: rolling contact instead of sliding contact, point-ish contacts on hard bearing surfaces, and no seals or retainers, or anything else that adds drag without adding function at these loads. And because rail and slider are printed, every dimension is adjustable in CAD (groove angle, bolt spacing, running clearance), all of it in hours per iteration. The fits on this machine follow the fit-tolerance method from §M4c's resin work, which is to measure the real clearances and design to them.

My recollection is that the new rail breaks away at roughly a one-degree tilt, which would be an enormous improvement, but that number comes from an unrecorded conversation and appears in no project file, so it is officially unverified. The re-measurement is specified (tilt test, five repeats, slider mass measured by water-displacement balance, F_break = m·g·sinθ) and has still not been done. The bench day it was booked for went to the motion diagnosis instead (§M11). The rail also gets leveled until the slider shows no self-creep in either direction before any data run counts, because a rail with this little drag will follow any tilt the bench gives it.

For replication, the rail body and slider carriage are FDM prints off the A1 mini, while the preload bracket prints in resin as part of the flexure body (§M5's ledger has the printer-by-part list) [builder, 2026-08-07, correcting an earlier draft line that called these SLA parts]. The only other parts are off-the-shelf bearing bolts. Model files ship with the release.

The preload screw as a measuring instrument

Both inequalities above contain N, so it cannot be "hand-tight" and has to be a number that can be set, repeated, and swept. All of the preload mechanism is printed into the flexure body that holds the stack. A circular seat holds a coil spring, and a screw bears on the spring's far end. Turning the screw inward compresses the spring, which pushes the flexure, and with it the stack, so that the foot presses against the alumina track.

The spring force follows Hooke's law, and design_notes §18 holds the numbers. The spring in service (≈Ø9.4 mm, from the parts assortment) measured k = 0.79 N/mm on the digital scale with calipers, and the screw advances 1.0 mm per turn. The arithmetic (0.79 N/mm × 1.0 mm ÷ 8) gives 0.0988 N per ⅛-turn tick, which is where the 0.099 N figure below comes from [design_notes §18].

The same section records why the preload goes through a spring at all. Since the leg is roughly 1 MN/m stiff, a rigid position-set screw would turn 2 µm of print or assembly error into 2 N of preload error, one hundred percent of the working target. The rule is force-controlled preload, never position-controlled. To keep the number accurate, a setting is always approached from the tightening direction, because thread backlash makes the loosening direction read wrong [design_notes §18].

One ⅛-turn tick of the screw changes N by 0.099 N (Measured, design_notes §18, calibrated 2026-07-10). N = 0 is defined by a paper-strip touch-point procedure (the preload where a paper strip at the contact just stops sliding free), so every preload in this project is counted in ticks from a repeatable reference rather than from feel [project CLAUDE.md §2]. §M12's planned speed-versus-N curve (N = 0.2 → 2.5 N swept in 2-tick steps) is only meaningful because a tick is a calibrated 0.099 N.

Every travel this machine has produced, the provisional July run and the confirmed reversal pair in §M11 alike, happened with the foot barely touching, at or near N = 0. As §M11 notes, the July setting was not one I could put a number on at the time.

The flexure, version one

The part I call the flexure holds the stack (a printed pocket and a clamping screw, no adhesive [builder, 2026-08-06]), carries the preload hardware just described, and ends in a printed foot that couples the stack's motion into the track. It is printed in resin (§M4's printers) and deliberately simple, and it is not yet a flexure in the textbook sense of an optimized compliant mechanism.

Version one had one requirement, transmitting the stack's ~2 µm stroke faithfully enough to produce motion. It did (§M11), and it was never cleverer than that [builder, 2026-08-06; model files: flexure_leg_v1.scad / flexure_leg_v1.stl / flexure_leg_v1_sketch.svg]. When this chapter was written, the next version was on paper. A lever-amplification study (amplifier_leg_v2_report.md) worked through printed-lever geometries against resin's real stiffness and fatigue behavior and ended with a GO recommendation at an amplification of A ≈ 3.5, roughly three and a half times the stroke at the foot for the same stack.

The lever has been the hardware since 2026-08-11 (the postscript covers it). Resin-specific optimization (compliance tuned to the material's modulus and creep, with §M4's tolerance data as design inputs) falls inside the "3D-printed SSPA" gap that §M1 describes. Phase 1's job was to make version one move before starting that work.

The contact surfaces

The track is an alumina plate, hard, flat, and cheap in small pieces. The committed sliding partner is a 2 mm silicon-nitride (Si₃N₄) ball seated in the foot, a bearing-grade ceramic pair chosen for wear behavior. Silicon carbide was considered and rejected because it abrades the alumina track. The goal is a contact that survives rather than one that machines its own groove [design_notes §16 via project CLAUDE.md §2].

Throughout the first-motion hunt, the ball stayed in the drawer. The foot was bare printed resin, a dome tip on alumina, because I didn't want to spend the ball's pristine surface (or risk galling transfer) on the messy trial-and-error phase. Resin galls within minutes of macroscopic sliding, which is why the ball was bought, but at micrometer slip distances the resin foot seemed an acceptable stand-in.

But in August, a freshly printed dome moved the slider twice and then went dead within the same session, and neither flipping the alumina plate nor installing a factory-clean one brought it back [run log 2026-08-11]. Two plate changes with no effect point at the foot, and design_notes §16 had already named galling as the mechanism.

The ball went into its socket in mid-August and has been the contact since [run log 2026-08-20]. The one leftover is the µ_s tilt-coupon test, which was written for the resin contact (three printed bumps standing in for three balls) and needs rewriting for the ball before it runs.

Budget

That table is the state of the mechanics, with one calibrated number, four quantities I have not measured, and a plan for measuring each of them. A month ago I would have been embarrassed by it. §M10 explains why I no longer am, because in this regime, knowing which numbers are missing is what makes the work an experiment.

Postscript (2026-08-20)

This chapter describes the July configuration, and August promptly renovated it. Three updates, kept here as a dated postscript rather than a rewrite. The A ≈ 3.5 lever left the paper and has been the hardware since August 11. The Si₃N₄ ball left the drawer and has been the contact since mid-August, after the resin dome proved to be a consumable exactly as §16's galling note predicted.

And the section above about clamping the stack in a printed pocket gained a hard lesson. The stack seat must be rigid, and printed tolerance decides whether it is. The Korea-printed Sunlu flexure gripped the stack tightly and moved. But the gray reprints ran a looser fit, the stack wiggled in its seat, and the whole stroke died in that lash, a failure §M4's tolerance chapters describe in the abstract and this motor demonstrated in hardware. The original board's author, told of the symptoms, put it in one line. Printed parts are soft and absorb the stack's motion. The follow-up design work (rigid magnetic stack coupling, steel contact track) is §M11–M12's story.