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Measurement repeatability is measurement precision under a declared set of repeatability conditions. The VIM's repeatability condition of measurement includes the same procedure, operators, measuring system, operating conditions and location, with repeated measurements over a short time.^[ref] The complete measurement cycle must be specified before its repeatability can be assessed.

For an original length-comparator study, one operator measures the same reference block using the same differential length comparator over a short session. Three readings without disturbing the setup happen to be $20.000,20.000,20.000\mathrm{mm}$. Their sample spread is zero. In a separate series, the operator removes and reseats the block for every trial, obtaining $19.980,20.000,20.020\mathrm{mm}$. That series givesThe two procedures repeat different parts of the experiment. The first data cannot establish the repeatability of the full remove-and-reseat procedure, nor does its zero observed spread prove an absence of readout noise or finite measurement resolution.

A repeatability experiment keeps the declared conditions stable and records each completed trial, including placement and settling when those belong to the procedure. Positioning repeatability applies this reasoning to repeated returns of a moving stage. Repeating a study over longer periods with selected changes can instead assess intermediate measurement precision; studies changing locations, operators and measuring systems concern measurement reproducibility.^[ref] Report those changes rather than describing every repeated experiment as the same repeatability test.

A microtome is an instrument for microtomy: a supported specimen and a knife move relative to one another to separate a thin physical section. The apparatus combines a specimen holder, a knife holder, a cutting motion and a controlled feed that presents new material for the next cut. An ultramicrotome is specialized for very thin sections, including sections for transmission electron microscopy.

A concrete materials-research installation at Yale uses a Leica Ultra UC7, with a trimming mill and glass knife maker. Its listed specimen materials include polymers, material fibres and soft metals.^[ref] For the thin-section cutting cycle, JEOL describes advancing the specimen by a preset feed and moving it against a diamond knife.^[ref] The supports must hold the specimen and knife securely enough that commanded motion is meaningfully related to the material removed.

An original ideal feed-drive calculation illustrates the distinction between mechanism and outcome. Suppose a hypothetical drive advances a lead screw by pitch $p$ per revolution, has reduction ratio $G$ motor revolutions per screw revolution, and receives $N$ equally spaced command steps per motor revolution. Its nominal advance per step isFor chosen $p=0.50\mathrm{mm}$, $G=100$ and $N=200$, this gives $\delta =25\mathrm{nm}$. Four steps command a nominal section feed of $100\mathrm{nm}$. This is an illustrative mechanism, not a claim about the UC7's internal drive. Motor motion does not independently establish the physical section thickness: backlash, elastic motion, thermal expansion and section compression can intervene.

A bounded apparatus experiment would cut a stable polymer reference at several feed settings, measure the recovered physical section thickness independently, and retain the cutting order and operating conditions. Agreement of motor counts with the command tests the drive readout; agreement of measured sections with the intended thickness tests more of the complete process. The distinction parallels the need for an independent readout when testing positioning repeatability.

Minimum incremental motion is the smallest displacement increment that a positioning system can execute repeatedly for the specified input and test conditions. It is an operational motion property, whereas design resolution is derived from the drive geometry and electronic increments. Friction, stiction, elasticity and backlash can make them differ.^[ref]

For an original illustrative test, independently measure the displacement produced by repeated commands from equivalent starting conditions. A nominal 10 nm command gives moves $0,20,0,20\mathrm{nm}$. Their mean is 10 nm, but that mean does not show repeatable 10 nm increments. A nominal 40 nm command instead gives $39,41,40,40\mathrm{nm}$.

Define an example acceptance rule before testing: every measured move must lie within 5 nm of the command, and the readout must have sufficiently smaller uncertainty, stipulated here as 1 nm standard uncertainty. The 10 nm trials fail this rule; the 40 nm trials pass. Among these two candidate increments, 40 nm is the smallest accepted one. It is not a proof of the globally smallest achievable increment because intermediate candidates and other conditions were not tested.

Report the command convention, load, motion direction, starting procedure, displacement sensor, measurement uncertainty and acceptance rule. A rotary encoder on the motor does not automatically measure the final load motion. Independent readout, for example with an interferometer, tests the assembled stage rather than only the commanded count. Positioning repeatability at a target and the ability to make a small move are related but distinct properties.