An electric servo combines a motor, feedback sensor and drive controller. This example shows a rotary motor driving a guided screw carriage through a direct coupling. The calculator converts incremental encoder cycles, decoding mode and screw lead into feedback counts and nominal position resolution.
Electric Servo Interactive Calculator
Explore a servo-driven screw carriage and compare encoder feedback resolution. Choose real quadrature decoding modes and the distance advanced per screw revolution.
Equation Used
- Motor encoder and screw rotate together through a 1:1 coupling.
- Only ×1, ×2 and ×4 quadrature decoding are offered.
- Lead errors, compliance, backlash and missed counts are excluded.
- Animation prescribes motion; no controller dynamics are solved.
Ideal 1:1 coupling. Feedback resolution is not an accuracy or motor-sizing prediction.
A motor, encoder and screw axis
The motor turns the coupling and screw. Bearings hold the screw axially, and the guide constrains the nut carriage to translate instead of turning with the shaft. One screw revolution advances the carriage by one lead. The rear encoder reports motor rotation; in this direct-coupled example motor and screw turns are equal.
The drawing keeps the motor, frame, guides and bearing housings stationary. The rotating screw surface and the carriage follow the same lead relationship. The carriage makes an outward-and-return movement corresponding to two shaft revolutions in each direction.
A working servo drive compares commanded and measured motion and controls motor output. The animation prescribes motion to explain the geometry; it does not simulate that control loop, motor current, acceleration limits or following error. Dimensions other than axial lead and travel are illustrative.
Choose encoder decoding and screw lead
Enter electrical cycles per encoder revolution, often described as encoder lines or pulses per channel. Check the encoder specification: some products already quote the fully decoded count number, which must not be multiplied again.
The decoding choices are ×1, ×2 and ×4. In forward motion with A leading B, ×1 counts one selected A edge per cycle, ×2 counts both A edges, and ×4 counts both edges of both channels. The enlarged signal drawing highlights the selected edges.
Screw lead is distance advanced in one revolution. Lead equals pitch for a single-start screw, but a multi-start screw advances by the number of starts multiplied by its thread pitch. This calculator uses lead.
Convert encoder counts into linear resolution
For L electrical cycles per revolution and decode multiplier D, counts per revolution are C=LD. Angular feedback resolution is 360/C degrees per count.
With direct coupling and screw lead P in millimetres per revolution, linear feedback resolution is P/C millimetres per count, or 1000P/C micrometres per count. Feedback density is C/P counts per millimetre.
These are unit conversions for an ideal direct drive. A gearbox would require its ratio in the conversion, and a linear encoder on the carriage would measure a different point in the transmission.
These calculations compare nominal encoder resolution. Motor torque and duty-cycle sizing require separate load and motion information.
Default 2500-cycle encoder and 10 mm lead
At ×4 decoding, 2500 electrical cycles per revolution become 10000 counts per revolution. A 10 mm lead produces 1 µm per count, 0.036° per count and 1000 counts per millimetre.
At ×2, the same hardware gives 5000 counts per revolution and 2 µm per count. At ×1 it gives 2500 counts and 4 µm per count. Changing decoding does not physically change the screw lead or the carriage travel per revolution.
Changing lead to 20 mm while retaining ×4 decoding doubles linear travel per revolution and gives 2 µm per count. Angular resolution remains 0.036° per count.
Resolution is not measured accuracy
Encoder quantization describes a feedback increment, not guaranteed positioning accuracy, repeatability or minimum controllable motion. Screw lead error, backlash, compliance, sensor error, missed counts and control behavior can affect the actual carriage position.
This calculation does not select a motor or establish torque, speed, thermal capacity, bandwidth or settling time. The nominal two-revolution replay is a mechanism demonstration, not a commanded operating profile for a real stage.
Sensor calibration, mechanical condition and controller tuning all affect the actual response. A servo can report an incorrect position if its sensing or mechanical transmission is faulty.
Electric servo questions
Why is ×3 not available?
Standard quadrature decoding counts one edge, both edges of one channel, or both edges of both channels. These give ×1, ×2 and ×4 respectively.
Does a smaller count increment guarantee better accuracy?
No. It improves nominal feedback granularity, but the full machine determines positioning accuracy.
Why does decoding leave the animation travel unchanged?
The same shaft turns still advance the nut by the same screw lead. Only the count scale changes.
Why does screw lead affect linear but not angular resolution?
The encoder senses shaft angle. Lead converts that angle into translation.
Is the signal diagram an entire revolution?
No. It enlarges one electrical cycle; the encoder supplies the entered number of those cycles per revolution.
References
- NI: Data Acquisition — Troubleshooting Incorrect Encoder Readings — ×1, ×2 and ×4 quadrature decoding.
- THK: Ball Screw — rotating screw and nut construction for conversion between rotary and linear motion.
- Thorlabs K-Cube brushed DC servo driver manual — encoder counts, gearbox ratio and lead in motion calibration.
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