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Design resolution is the theoretical smallest commanded movement implied by a positioning mechanism's drive components. For a screw drive, it can be calculated from screw pitch, reduction gearing and motor or encoder increments. It is not automatically the minimum incremental motion that the final load executes repeatedly.^[ref]

For an original ideal drive, let a lead screw advance $p=0.50\mathrm{mm}$ per revolution, with 50 motor revolutions per screw revolution and 2000 resolved counts per motor revolution. One count corresponds toDoubling the count resolution to 4000 per motor revolution gives theoretical $q=2.5\mathrm{nm}$ without changing the screw. That calculation does not halve friction or remove backlash. A controller may display both increments even if the load moves only after several such commands have accumulated.

Keep the location and counting convention of the feedback sensor explicit. Counts at a motor shaft, counts at a screw and directly measured load position are different observations. A gearbox can introduce compliance between them. Pair the design calculation with an independent motion test to establish operational performance. A smaller theoretical increment also does not by itself establish absolute positioning accuracy or a smaller measurement uncertainty.

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.

Physik Instrumente makes precision motion equipment used in scientific apparatus. Its archived M-222–M-226 motorized micrometer family illustrates a concrete measurement issue: motor-shaft encoder counts and screw geometry give a design resolution, while actual motion also depends on mechanics and loading.^[ref]

For a worked reconstruction from the manufacturer's M-222.20 specifications, use screw pitch $p=0.5\mathrm{mm}$ per revolution, gear reduction $G=(31/9{)}^4$ and 60 encoder counts per motor revolution. The nominal linear increment isThis agrees with the listed design resolution of $0.059\mu \mathrm{m}$. The same table separately lists minimum incremental motion of $0.1\mu \mathrm{m}$ and backlash of $5\mu \mathrm{m}$ for that model.^[ref]

Thus a command corresponding to one encoder count is not evidence for an independently resolved 59 nm movement of the load. The listed backlash corresponds to roughly 84 nominal counts, illustrating why reversing direction is a different test from continuing in one direction. These are calculations from a legacy specification, not new performance measurements. In an assembled instrument, compare commanded and independently measured displacement, including reversals, to establish the usable response and its measurement uncertainty.

Positioning repeatability describes the scatter of positions reached when a motion system repeatedly returns to the same commanded position under specified conditions. It is an application of measurement repeatability, a form of measurement precision. A system may return to almost the same wrong position each time, so small scatter does not establish measurement accuracy.^[ref]

The approach direction belongs in the test description. Unidirectional positioning repeatability keeps it fixed; bidirectional positioning repeatability includes returns from both directions. To measure the assembled stage, independently observe its final position rather than only the motor's rotary encoder count. Physik Instrumente describes a static test that lets the platform stop before reading it, using an interferometer for displacement and an autocollimator for angular error, with two reflecting mirrors on the stage.^[ref]

For an original numerical example, repeatedly command $x_{\ast }=10.000\mathrm{mm}$. Suppose an independent position readout with known measurement calibration gives the errors $e_j=x_j-x_{\ast }$, in micrometres,Each direction has the same sample standard deviation,Yet their arithmetic means are 0 and $2.0\mu \mathrm{m}$. The magnitude of their mean difference, a positioning reversal error at this target, is 2.0 micrometres, far larger than the within-direction scatter. Pooling all eight values gives a sample standard deviation of $\sqrt{8.04/7}\approx 1.149\mu \mathrm{m}$; that statistic mixes the directional shift with the smaller return-to-return variation.

The calculation uses a declared sample standard deviation, not an unspecified manufacturer's tolerance or a universal repeatability convention. A positioning specification must state its approach directions, target positions, settling/readout procedure, load, environmental conditions, statistic and measurement uncertainty. A single target does not establish performance over the travel range. The manufacturer's method explicitly separates directional means from scatter and combines information from multiple targets when forming axis-level specifications.^[ref]

Backlash is one possible cause of direction-dependent behavior, while thermal expansion and instrumental drift can move the apparent target over time. A repeatability experiment must distinguish those effects from random scatter. Measuring small returns to one target also answers a different question from minimum incremental motion, which asks whether a small commanded change can actually be executed.

Unidirectional positioning repeatability describes the scatter of repeated returns to one commanded position when the final approach direction is held fixed. Specify the complete reset-and-return procedure so that each trial approaches under comparable conditions. PI distinguishes this directional scatter from its summaries that include reversal effects.^[ref]

For an original example, always approach from below. At a 2 mm target, suppose the position errors are $-0.4,-0.2,0.0\mu \mathrm{m}$; at an 8 mm target they are $1.6,1.8,2.0\mu \mathrm{m}$. The means are $-0.2$ and $1.8\mu \mathrm{m}$, respectively, while both sample standard deviations areThe same repeatability statistic accompanies quite different mean errors along the travel. A common shift of every reading at a target changes its mean but not its within-target spread.

For illustration, an explicitly declared specification taking the largest tested directional sample deviation would report $0.2\mu \mathrm{m}$ for these two data sets. A specification using a full width or a multiple of that deviation would have a different numerical value. PI's own published convention states which directional spreads and target aggregation it uses; compare like definitions rather than only their units.^[ref]

Observe final platform motion with an independent position readout, not just the motor's rotary encoder. Allow the chosen settling time and keep load and environment controlled. Consistently approaching from one side does not establish bidirectional positioning repeatability, and a small return scatter does not show that a small incremental command can be executed: that is the separate question of minimum incremental motion.