Resolution Resolved

July 24, 2008
Surprise! There’s no guarantee a stage can make moves on the order of its resolution specs.

Scott Schmidt
Senior Applications Engineer
Positioning Systems Div.
Aerotech Inc.
Pittsburgh, Pa .

Edited by Robert Repas

Modern motion-control applications are typically defined by a broad set of specifications. Typical specs detail accuracy, repeatability, velocity regulation, and many other qualities. Most of these performance metrics are well defined, intuitive, or both. But others are occasionally misinterpreted or incorrectly specified. Resolution is one such benchmark.

System or stage resolution is often spelled out for motion controls as well as in vendor catalogs and Web site specifications. However, many misinterpret what the term truly means. Most assume this value represents the smallest move the overall system of stage mechanics, controls, and drive electronics can reliably provide. That value, however, is more commonly defined as the minimum incremental move. The minimum incremental move is often far different than system resolution.

To define both terms more precisely, resolution is the smallest value that a motion system can be commanded to move or is capable of detecting, as determined by the feedback device and controller. It is the theoretical minimum incremental move. The true minimum incremental move is the smallest move the stage can consistently and reliably deliver. It is often defined by some value of uniformity in step size.

As an example, say a complete electromechanical system uses a 2-mm/rev ball screw along with a 1,000-line sinusoidal output rotary encoder and appropriate encoder interpolation. Such a system could have a theoretical resolution of 10 nm that the controller can detect from the encoder. But while you can command a 10-nm move, the system almost certainly won’t be able to achieve it. The reason: stage mechanics. Backlash, windup, and other compliance factors in the mechanical drivetrain block most if not all motor rotation in such a small move from producing linear motion. Clearly, a firm understanding of true system resolution, as well as what contributes to the limits of minimum incremental motion, is crucial to understanding performance of precision positioning systems.

Drive and bearing Effects
The source of the most obvious differences between resolution and incremental motion comes from the mechanical system that converts the rotary motion of the motor to the linear motion of the stage. Errors in coupling compliance, along with backlash in the screw and in other mechanical linkages, accumulate to steal some motorshaft rotation before completely engaging and turning the ball or leadscrew.

While most of the above motion sinks are present in screwdriven stages, direct-drive systems also may have nonidealities that corrupt their motion. Errors form when a feedback device, such as a linear encoder, is not exactly at the point of work, i.e., the carriage. While the motor might have accomplished some small incremental move, the tabletop may not have followed the same motion profile. Parasitic angular motion from pitch, roll, and yaw along with offsets between the encoder and work point create Abbe errors. Linear-encoder misalignment with the direction of travel also degrades fine-stepping ability in linear-motor axes.

Nonideal bearings can degrade motion performance and impact the stage minimum step-size in both rotary-motor-driven and direct-drive stages. Such nonidealities can take the form of skidding, stiction, and bearing-induced overshoot.

Lightly loaded ball bearings have a tendency to skid rather than roll during the initial moments of a newly commanded move. The rotary motor and drive screw see a different type of motion compared to traditional rolling-ball bearings. This also causes wear on the balls, which degrades bearing performance.

Stiction, also known as static friction or breakaway friction, is a slightly higher resistance to the start of motion than that seen after motion begins. It can exacerbate screw backlash with a possible pitching, rather than linear, motion.

Because mechanical bearings always have some stiction to overcome, such systems often need a higher force to start motion than to maintain it. Applying too large a force can make the stage overshoot its move by an amount less than the minimum achievable distance. Because stiction must now be overcome in the opposite direction, the end effect is the same, although the error has changed signs.

Many stage designs suffer from some or all of the effects mentioned. There are certain types, such as air-bearing linear stages, that exhibit none of these problems. As the bearing surface is virtually frictionless, stiction is a nonissue. Furthermore, overshoot is rarely a factor as an air-bearing stage will respond to all but the smallest corrective force commands. Skidding errors are impossible because there are no rolling elements present that can skid.

Screw-Driven Stages
As noted above, ball-screw and leadscrew-driven systems have some inherent nonideal attributes such as screw backlash and coupling compliance. One attempt to quantify these errors used a precision ball-screw-driven stage with a screw pitch of 2 mm/rev commanded to make a series of small moves. The stage’s rotary-motor encoder was used for position feedback. The encoder generated an amplified sine-wave signal that was interpolated using quadrature encoder multiplication technology. The final linear resolution was 10 nm per interpolated machine count. The controller faithfully commanded and plotted each move based on the feedback from the rotary encoder. However, independent verification of the move was with a capacitive gage mounted close to a target carried by the stage.

The stage was commanded to move in a series of ever larger steps. Meanwhile the capacitive gage graphically recorded the actual distance moved. It turned out the stage translated only a small portion of the desired distance initially. In other words, the motor spun an amount commensurate with the commanded distance, but this didn’t result in the desired move. After a few commanded moves, the system overcame its mechanical play and began realizing the desired moves in their entirety. Similarly, there was a notable hysteresis in the motion with a reverse in direction. Larger moves appear somewhat less susceptible to these effects. Stated more accurately, the wasted motion of the motor is simply less significant compared to the magnitude of the commanded move. Conversely, in attempts to move from 10 to 50 nm, the stage showed no appreciable motion. Commands to move resulted in only floor and background noise.

The graphs clearly show hysteresis at each directional change. In the smallest move depicted, the system never fully overcomes the coupling and screw windup and backlash before the test regimen begins commanding reverse motion steps. There is some hysteresis apparent even in the largest commanded moves of 1-micron steps.

The graphs might rule out this family of stages for applications requiring small, bidirectional moves. Nevertheless, large classes of applications are routinely served by this technology. For instance, general positioning with point-to-point moves of tens-of-microns to millimeters can take advantage of the relatively good accuracy and repeatability these stages exhibit, as well as their economical nature. This drive strategy might be practical even for small moves with a suitable “run up” distance prescribed and with moves made in only one direction to eliminate hysteresis effects.

Direct-drive stages
While screw-driven systems display noticeable motion sinks, direct-drive linear stages that use linear motors also have some inherent parasitic effects. A demonstration of this used a test arrangement similar to that for the screw stage testing. The direct-drive stage had a linear encoder that provided a fundamental pitch of 20 μm. Again, the encoder output was an amplified sine signal interpolated using encoder multiplication technology to yield a resolution of 10 nm/machine count. Likewise, capacitive-probe measurements again went into graphs of the actual stage movement.

Although the small step size is outstanding compared to the ballscrew-driven stage, some parasitic motion is still wasted on the return “staircase” of moves. This error is primarily from bearing nonrepeatability. The error distance was also too small for a reliable corrective move or for the controller to detect. Recall that system resolution is 10 nm, compared to a parasitic error distance of 1 to 2 nm. Simple stage-tuning artifacts created the minor positional overshoot seen at the start of some of the plotted moves.

Overall, though, the linear-motor stage could realize the small motions commanded. With a few system changes, such as a finer resolution encoder, the system could likely realize 10 or even 5-nm steps. This ability lets relatively economical, direct-drive, mechanical-bearing stages work in high precision and high-performance applications such as fiber alignment, Bragg grating production, and laser micromachining.

Note that these tests didn’t specifically address some system effects. For instance, environmental effects can substantially impact performance. You need a test chamber with carefully controlled vibration isolation and temperature to truly compare stage motions. Otherwise, thermal expansion and ground-floor vibration could easily corrupt the step size measurements.

In fact, environment is even more important in the context of the final application than as a testing consideration. If temperature causes a 2-μm shift in the stage carriage, the workpiece mounted to the tabletop will shift as well. This could have critical consequences in the final dimensions of a micromachined part. For reference, tests performed during this study used a temperature-controlled room and had the stages mounted on an air-isolated granite test plate.

Similarly, our testing didn’t consider amplifier technology. Linear amplifiers offer smoother motion because they do not display the switching noise seen with pulse-width-modulated (PWM) drives. This noise can appear as greater in-position dithering that could easily “swamp” small step moves. Additionally, PWM drives can exhibit a “dead-band” effect. This arises at direction reversals, where the commanded signal changes signs. A linear drive can smoothly transition to a different direction, while the PWM source will exhibit some finite amount of time without current output. The lack of current will manifest itself as delayed or lost motion in a practical system. Our tests used linear amplifiers to let the data accurately portray stage capability.

Further evaluation
We have not mentioned other design options or we deliberately set them aside for the sake of comparing a few common technologies. For instance, it’s possible the screw-stage performance might improve with the addition of a secondary linear-encoder scale along its travel. It is yet to be determined what, if any, impact the size of the stage has on small moves. For example, it seems logical that small screw-driven stages would perform better than larger versions.

While these tests looked at ball-screw-stages, what about leadscrew-driven slides? Or how would stepper-motor driven stages perform compared to brushlessservomotor stages?

There are a number of encoder choices for both rotary and linear-motor stages. It is natural to assume that a finer pitch, more accurate scale will offer better step-size capability. But the degree of improvement is yet to be determined.

Alternative drives, such as piezoelectric types, and bearing types, such as air, also need evaluation. The data gathered so far is valuable, but more testing encompassing these points develops a more complete and thorough comparison.

All in all, system resolution does not necessarily allow small step size. The ball-screw example illustrates how some drive technologies may need tens or hundreds of counts before a move can be made repeatably.

Minimum step capability is direction-dependent. Although this may seem obvious for some drive technologies, such as those that are screw based, even the direct drive stage demonstrated some lost motion during direction reversals. A noncontact bearing can completely remove these types of artifacts.

And finally, approach applications carefully and with an appreciation of the difference between resolution and step size. Some coarse-positioning requirements will not need fine-stepping capability while others will.

This study contrasts among the per formance of var ious stage families, but applications ultimately dictate stage choice. Thoughtful drive and bearing choices only enhance the chances of success in applications that need short, repeatable, and precise moves.

Make Contact
Aerotech Inc.
(412) 963-7470,


A capacitance probe measures the absolute position of the test jig.


Commands given to the ball-screw specified moves of 100, 200, 500, and 1,000 nm with each step. While the motor moved the proportional amount for each length, motor response did not translate into actual movement of the stage. Hysteresis is clearly present even with the largest movement of 1 μm/step.


Direct-drive stages using linear motors fared better but still exhibited some hysteresis from bearing nonrepeatability. The error distance of 1 to 2 nm was too small for any corrective moves with a 10-nm system resolution.

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