Understanding Load-Stroke-Resolution Tradeoffs Across Actuator Technologies

Every actuator technology lives within a bounded region of the load-stroke-resolution space. No technology excels at all three simultaneously, and the reasons are rooted in fundamental physics rather than manufacturing limitations. Understanding these boundaries helps engineers avoid the trap of specifying requirements that no single actuator can meet, and it clarifies why multi-stage architectures exist.

This article maps those boundaries with specific numbers for five actuator technologies: piezoelectric stacks, piezoelectric (ultrasonic) motors, servo motors, stepper motors, and voice coil actuators.

Image: Nanomotion Ltd.

The Three-Parameter Space

Load (force): The continuous force the actuator can apply to the workpiece, in newtons. Not peak force; not stall torque converted to linear force through an idealized screw. The actual sustained force available during operation, accounting for thermal limits, duty cycle, and drivetrain efficiency.

Stroke (travel): The total range of motion, in millimeters. For rotary actuators, this is the linear equivalent through whatever transmission connects motor to load.

Resolution: The minimum incremental motion that the system can reliably and repeatably execute in both directions, in nanometers. Not the encoder resolution. Not the theoretical microstep size. The actual measured bidirectional MIM at the point of work, under load, in the intended operating environment.

The Fundamental Limits

Why High Force and High Resolution Conflict

Consider a stiff actuator holding a load. Any disturbance (vibration, thermal drift, electrical noise in the driver) produces a position error proportional to the disturbance force divided by the system stiffness. To achieve high resolution, you need either very high stiffness (so disturbances produce tiny displacements) or very low disturbance (isolation from all external forces).

Now consider the actuator itself as a source of disturbance. A motor that can produce 1,000 N of force needs a driver that controls current (and therefore force) to within a fraction of the resolution-limited force. For 1 nm resolution with 50 N/micrometer stiffness, the force noise must be below 0.05 N, which is 0.005% of 1,000 N. Achieving 0.005% force control requires extremely low-noise drivers, high-resolution DACs (20+ bits), and careful shielding.

In electromagnetic actuators, force noise comes from current noise, quantization, and electromagnetic interference. In piezo stacks, force noise comes from voltage noise (amplified by the stack stiffness). In piezo motors, the friction contact introduces force quantization effects that limit resolution.

The practical result: high-force actuators have proportionally higher force noise floors, which limits their resolution. This is not a manufacturing defect; it is a signal-to-noise ratio problem.

Why Long Stroke and High Resolution Conflict

Long stroke requires either a large actuator (big piezo stack, long motor travel) or a transmission mechanism (ball screw, belt, lever). Both introduce errors:

Large actuators have proportionally larger thermal drift (coefficient of thermal expansion times length), proportionally larger hysteresis (for piezo stacks, hysteresis is a percentage of stroke), and proportionally larger sensitivity to mounting distortions.

Transmission mechanisms introduce backlash, pitch error, compliance, and friction, all of which degrade resolution. A 300 mm ball screw has cumulative pitch errors of 3 to 10 micrometers. A 300 mm linear encoder has interpolation errors of 5 to 50 nm. Using the encoder bypasses the screw errors but adds cost and does not eliminate backlash.

The practical result: maintaining nanometer-level resolution over millimeter-scale strokes is exponentially harder than maintaining it over micrometer-scale strokes.

Why Long Stroke and High Force Conflict

Long stroke at high force means high energy transfer, which means heat. Every actuator technology has a continuous power limit set by its thermal capacity and cooling mechanism.

A servo motor producing 100 N through a ball screw at 100 mm/s delivers 10 W of mechanical power and dissipates 20 to 50 W of electrical power as heat. This is manageable. The same motor producing 100 N at 500 mm/s delivers 50 W mechanical and dissipates 100+ W as heat. Thermal management (heat sinks, fans, liquid cooling) becomes a significant part of the system design.

For voice coils, the I^2*R heating problem is severe at high force and long stroke because both high force (high current) and long stroke (continuous motion) are required simultaneously.

For piezo stacks, long stroke requires either a very long stack (expensive, fragile) or a lever/flexure amplifier (which reduces force by the amplification ratio). A 10:1 lever amplifies 15 micrometers to 150 micrometers but reduces the 3,000 N blocking force to 300 N.

Image: Nanomotion Ltd.

Technology-by-Technology Analysis

Piezoelectric Stack Actuators

Operating region:

• Force: 10 to 30,000 N (size-dependent)
• Stroke: 5 to 500 micrometers (native); 0.5 to 2 mm (amplified)
• Resolution: 0.01 to 1 nm (closed-loop with capacitive sensor)

Boundary physics:

The strain limit of PZT ceramic is approximately 0.1% to 0.15%. This sets an absolute ratio between actuator length and maximum displacement. A 10 mm stack produces 10 to 15 micrometers. A 100 mm stack produces 100 to 150 micrometers. To reach millimeter strokes, you need either:

1. A stack over 700 mm long (impractical: fragile, expensive, low resonance frequency)
2. A mechanical amplifier (flexure lever, hydraulic amplifier) that trades force for stroke

Flexure amplifiers with ratios of 5:1 to 20:1 are common. A 10:1 amplifier on a 15 micrometer stack produces 150 micrometers of stage travel but reduces stiffness by 100x (stiffness scales as the inverse square of amplification ratio) and blocking force by 10x. The resonance frequency drops by the square root of the stiffness reduction.

For a 150 micrometer amplified piezo stage:

• Stiffness: 0.5 to 5 N/micrometer (versus 50 to 500 N/micrometer for the bare stack)
• Blocking force: 100 to 500 N (versus 1,000 to 5,000 N for the bare stack)
• First resonance: 200 to 800 Hz (versus 5 to 50 kHz for the bare stack)
• Resolution: 0.5 to 5 nm (versus 0.05 to 0.5 nm for the bare stack)

The amplification degrades every performance parameter except stroke. This is the fundamental tradeoff.

Where piezo stacks dominate: Sub-micrometer stroke, sub-nanometer resolution, high stiffness, high bandwidth. No other technology competes for strokes below 100 micrometers at sub-nanometer resolution.

Ultrasonic Piezoelectric Motors

Operating region:

• Force: 0.5 to 50 N continuous (linear types)
• Stroke: 5 to 200 mm (some designs to 500 mm)
• Resolution: 5 to 100 nm (closed-loop with linear encoder)

Boundary physics:

Ultrasonic piezo motors decouple stroke from the piezo element's strain limit by using friction coupling to transfer vibrational motion into continuous linear or rotary travel. The motor vibrates at 20 to 200 kHz, and each vibration cycle advances the moving element by a tiny increment (typically 0.5 to 5 nm per cycle). Speed is proportional to vibration amplitude and frequency.

The force limit comes from the friction contact. Normal preload force (pressing the piezo element against the guide or runner) is typically 5 to 50 N for a single contact point. Drive force is the preload multiplied by the effective friction coefficient (0.1 to 0.3 for typical ceramic-on-ceramic contacts), giving 0.5 to 15 N per contact. Multiple contact points can increase force, but at the cost of increased wear and size.

The resolution limit comes from the contact dynamics. Each "step" of the stick-slip cycle has a minimum increment determined by the contact stiffness, preload, and surface roughness. Below this increment, the motor produces no motion (deadband). Typical minimum incremental motion is 5 to 50 nm for well-designed stages.

The stroke limit is, in principle, unlimited (the motor can keep walking along an arbitrarily long guide rail). In practice, stroke is limited by the guide rail length, encoder length, and cable management. Stages with 200+ mm stroke are commercially available.

Where piezo motors dominate: Millimeter to centimeter strokes at sub-micrometer resolution, with zero-power hold and no magnetic emissions. The unique combination of long travel, fine resolution, compact size, and environmental compatibility is unmatched.

Servo Motors (Rotary with Ball Screw)

Operating region:

• Force: 10 to 50,000 N (with appropriate screw)
• Stroke: 10 to 3,000 mm
• Resolution: 0.5 to 50 micrometers (rotary encoder); 0.05 to 5 micrometers (linear encoder)

Boundary physics:

Servo motors convert electrical power to rotary motion with high efficiency (80% to 95%). The ball screw converts rotary motion to linear motion with moderate efficiency (85% to 95%) and provides mechanical advantage. A motor producing 1 Nm of torque through a 5 mm pitch screw generates approximately 1,100 N of linear force.

The resolution limit is set by the ball screw mechanics: backlash (0.5 to 20 micrometers), pitch error (3 to 10 micrometers per 300 mm), and elastic deformation under load. Adding a linear encoder bypasses the screw errors but not the backlash (unless the encoder is on the load side and the controller compensates actively).

The force limit is generous. Large servo motors with roller screws produce tens of thousands of newtons of linear force. Thermal limits matter but are well-managed with standard cooling.

The stroke limit is essentially unlimited; ball screws are available in lengths exceeding 3 meters.

Where servo motors dominate: High force (above 100 N), long stroke (above 200 mm), high speed (above 100 mm/s). When the application requires moving heavy loads over long distances at high speed, nothing beats a servo motor with a ball screw.

Direct-Drive Linear Servo Motors

Operating region:

• Force: 5 to 5,000 N continuous
• Stroke: 10 to 3,000 mm
• Resolution: 1 nm to 1 micrometer (with appropriate encoder and bearing)

Boundary physics:

By eliminating the ball screw, direct-drive linear servos remove backlash, pitch error, and coupling compliance. Resolution is limited by the encoder and the bearing system. With air bearings and interferometric encoders, sub-nanometer resolution has been demonstrated.

The force limit is set by thermal dissipation. A linear motor producing 100 N continuous force might dissipate 200 to 500 W of heat, requiring liquid cooling. Force density (N per kg) is lower than for rotary servo with screw drive because there is no mechanical advantage from the screw.

The cost is high: air bearing rails, precision-ground granite bases, linear encoders, and the motor itself. A complete direct-drive linear axis with air bearings costs $15,000 to $80,000.

Where direct-drive linear servos dominate: Semiconductor lithography, flat-panel display inspection, precision scanning at high speed. Applications requiring simultaneous high speed (above 100 mm/s), long stroke (above 100 mm), and high resolution (below 1 micrometer).

Stepper Motors (with Lead Screw)

Operating region:

• Force: 5 to 10,000 N (with appropriate screw)
• Stroke: 10 to 1,000 mm
• Resolution: 1 to 50 micrometers practical (despite theoretical microstep claims)

Boundary physics:

Stepper motors share the servo motor's screw-drive architecture but add the quantization of step-based motion. The resolution floor is set by motor magnetic non-ideality, detent torque, and drivetrain friction, as discussed in detail in the piezo vs. stepper comparison article. Practical MIM is 1 to 5 micrometers for well-built systems with fine microstepping.

The force and stroke capabilities are similar to servo motors of equivalent size, though stepper torque drops rapidly with speed (typically 50% to 80% reduction from low-speed torque at 1,000 RPM).

Where steppers dominate: Low-cost, moderate-precision automation. Resolution above 5 micrometers, speed below 500 mm/s, cost below $500 per axis.

Voice Coil Actuators

Operating region:

• Force: 0.1 to 200 N continuous
• Stroke: 0.01 to 50 mm
• Resolution: 0.5 nm to 100 nm (with appropriate sensor)

Boundary physics:

Voice coils produce force proportional to current, with no position dependence. Stroke is limited by the length of the magnetic gap, typically 1 to 50 mm. Force is limited by thermal dissipation (I^2*R heating). Resolution is limited by current noise and position sensor performance.

The fundamental tradeoff for voice coils is force versus thermal load. High continuous force requires high current, which generates heat proportional to force squared (for a given coil resistance). This creates a sharp boundary: doubling force quadruples heat generation.

Where voice coils dominate: Short-stroke applications requiring constant force over full travel, active vibration isolation, and fast settling. Autofocus mechanisms, hard disk drive head positioning, and precision force application.

The Overlap Zones and Gaps

Zone 1: High Force + Long Stroke + Moderate Resolution

Servo motors with ball screws. This is their home territory. Stepper motors are a cost-effective alternative at lower speeds. No piezo technology competes for force above 100 N and stroke above 200 mm.

Zone 2: Low Force + Short Stroke + Extreme Resolution

Piezo stack actuators. Below 500 micrometers of stroke, sub-nanometer resolution, and stiffness above 10 N/micrometer, the piezo stack is unchallenged. Voice coils can approach this space for very short strokes (below 1 mm) but lack the stiffness and bandwidth of piezo stacks.

Zone 3: Moderate Force + Long Stroke + High Resolution

This is the contested zone where multiple technologies compete, and system architecture (single stage vs. coarse/fine) becomes the key decision.

Requirements in this zone might be: 10 N force, 50 mm stroke, 50 nm resolution. Options include:

1. Piezo motor: A single piezo motor stage can potentially meet all three requirements. Unit cost: $5,000 to $10,000.
2. Direct-drive linear servo: Meets all requirements but at 3 to 5 times the cost.
3. Servo + piezo stack coarse/fine: A servo motor moves the load to within 5 micrometers, then a piezo stack stage (mounted on the servo stage) provides final positioning to 50 nm. Total cost: $5,000 to $15,000. Complexity: high. Performance: excellent.

Zone 4: The Impossible Region

There is a region of the load-stroke-resolution space that no single-stage actuator technology can reach:

• Force above 1,000 N
• Stroke above 100 mm
• Resolution below 100 nm

Reaching this region requires either a coarse/fine architecture (servo + piezo) or a custom direct-drive system with extraordinary engineering effort and budget.

Comparison Charts

Force vs. Resolution (at representative strokes)

Technology	Force Range	Resolution	Stroke
Piezo stack	100 to 30,000 N	0.05 to 1 nm	5 to 150 micrometers
Amplified piezo	10 to 500 N	0.5 to 5 nm	50 to 2,000 micrometers
Piezo motor	0.5 to 50 N	5 to 100 nm	5 to 200 mm
Voice coil	0.5 to 200 N	0.5 to 100 nm	0.1 to 50 mm
Servo + ball screw	50 to 50,000 N	500 to 5,000 nm	10 to 3,000 mm
Direct-drive servo	5 to 5,000 N	1 to 100 nm	10 to 3,000 mm
Stepper + lead screw	5 to 10,000 N	1,000 to 50,000 nm	10 to 1,000 mm

Stroke vs. Resolution (at representative forces)

Technology	Stroke Range	Resolution	Force
Piezo stack	5 to 150 micrometers	0.05 to 1 nm	100 to 5,000 N
Amplified piezo	50 to 2,000 micrometers	0.5 to 5 nm	10 to 500 N
Piezo motor	5 to 200 mm	5 to 100 nm	1 to 10 N
Voice coil	0.1 to 50 mm	1 to 100 nm	1 to 20 N
Servo + ball screw	10 to 3,000 mm	500 to 5,000 nm	100 to 2,000 N
Direct-drive servo	10 to 3,000 mm	1 to 100 nm	10 to 500 N

Multi-Stage Architectures

When the application requirements fall outside any single technology's capability envelope, combining technologies in a coarse/fine architecture is the standard solution. Common combinations:

Servo (coarse) + Piezo stack (fine):

• Servo ball screw provides 100+ mm stroke with 1 to 5 micrometer positioning
• Piezo stack flexure stage provides 10 to 100 micrometer fine stroke with sub-nanometer resolution
• Combined performance: 100+ mm stroke, sub-nanometer resolution
• Applications: semiconductor inspection, mask alignment, precision metrology

Voice coil (coarse) + Piezo stack (fine):

• Voice coil provides 1 to 10 mm stroke with micrometer-level positioning
• Piezo stack provides fine positioning with sub-nanometer resolution
• Combined performance: millimeter stroke, sub-nanometer resolution, fast settling
• Applications: atomic force microscopy, nanoimprint lithography

Stepper (coarse) + Piezo motor (fine):

• Stepper with lead screw provides 100+ mm stroke with 5 to 20 micrometer positioning
• Piezo motor provides final positioning to 50 to 100 nm resolution
• Combined performance: long stroke, sub-micrometer resolution, low cost
• Applications: automated microscopy, fiber alignment, optical testing

The overhead of a multi-stage architecture includes: increased system height (stacking stages), reduced stiffness (compliant stack), more complex controls (coordinated dual-loop servo), and higher cost (two stages, two drivers, two sensors). This overhead is justified only when no single technology meets all requirements.

Practical Guidelines

1. Start with the resolution requirement. It is the hardest parameter to improve after the system is built. Choose a technology that meets resolution with margin.

2. Use the minimum stroke that the application requires. Longer stroke always degrades resolution, stiffness, and bandwidth. If the process only uses 2 mm of a 50 mm stage, consider whether a shorter-stroke stage would provide better performance.

3. Distinguish between force for motion and force for holding. Many applications need high force only during acceleration and low or zero force at the operating position. A piezo motor might provide adequate dynamic force with passive holding force far exceeding its drive force.

4. Consider the duty cycle. A voice coil that must hold 50 N continuously generates significant heat. The same voice coil in an application that holds for 100 ms and releases for 900 ms generates one-tenth the average heat.

5. Challenge the requirements. The most common cause of excessive actuator cost is over-specification. Does the application truly need 10 nm resolution, or is 100 nm sufficient? Does it truly need 200 mm stroke, or would 50 mm work with a different fixturing approach? Relaxing one parameter by a factor of 2 can reduce system cost by a factor of 5.

The load-stroke-resolution space is not a flat landscape with technologies neatly divided into sectors. It is a three-dimensional volume where technology envelopes overlap, compete, and leave gaps. Understanding the shape of that volume, and the physics that creates it, is the first step toward choosing the right actuator for any precision application.