A rotating screw advances a captive nut and its attached slide because the guide prevents the nut from rotating while fixed supports prevent the screw from translating. In the ideal kinematic model, one screw revolution advances the slide by one lead.
Rectilinear Motion of Slide by Screw Interactive Calculator
Enter screw lead, speed and turn count to calculate ideal slide speed and travel. The screw rotates while the guided nut and slide move along its axis. Backlash is displayed separately; it does not change the calculated or animated travel.
Equation Used
- The screw is fixed axially and the nut/slide is constrained against rotation.
- Lead is constant and slip, compliance and thermal effects are excluded.
- Enter the axial backlash of the screw and nut. It is shown as a separate gap, without simulating take-up at reversal.
- Thread form, screw diameter, supports, loads, torque, efficiency, critical speed, wear and life are not calculated.
How the screw-driven slide works
The screw is supported so it may rotate but not translate. A nut engages the screw and is attached to a slide constrained by a separate linear guide. Because the nut cannot rotate, screw rotation becomes axial nut and slide travel.
Lead is the axial travel produced by one screw revolution. The calculator uses this relation to link rotary input to linear output. The drawn threads and supports are schematic, not dimensions for manufacturing a screw assembly.
Comparing screw-driven travel
Use the calculator to compare how screw lead and RPM affect feed rate, or how many millimetres of travel a selected turn count produces. A larger lead gives more travel per revolution; increasing RPM increases feed without changing travel per revolution.
These motion calculations are useful when planning a positioning slide. Selecting its screw, nut, motor and bearings also requires load, torque, efficiency, support spacing and manufacturer ratings.
Ideal lead relation
For lead L in millimetres per revolution, screw speed n in revolutions per minute and selected turns N, ideal slide speed is v = Ln/60, feed is Ln and selected travel is x = LN.
The entered backlash b is axial clearance that must be taken up when direction reverses. The displayed b/L percentage compares that clearance with one lead. Backlash is not applied to the ideal travel or speed equations, and this percentage is not an accuracy rating.
Worked example
At 5 mm/rev and 600 rpm, the ideal feed is 3000 mm/min or 50 mm/s. One selected turn gives 5 mm ideal travel. An entered 0.05 mm backlash is displayed separately as a 1% fraction of one lead.
Using the results in a real slide
The animation shows a screw rotating in fixed supports and a nut attached to a separately guided slide. It reverses through the selected travel to make the motion visible. Playback timing is illustrative and capped for viewing; it does not reproduce the calculated feed rate.
Backlash appears as a separate gap indicator. The slide itself follows ideal travel, so the animation does not show the delay while a real nut takes up clearance after reversal.
Check thread geometry, screw diameter, unsupported length, end supports, load, duty, lubrication and alignment when selecting hardware. These determine limits such as buckling, critical speed, torque and service life that the motion calculation does not provide.
Screw-driven slide questions
Is lead the same as pitch?
Lead is the axial travel for one revolution. Pitch is the axial spacing between adjacent threads. They are equal for a single-start screw; for a multiple-start screw, lead equals pitch multiplied by the number of starts. Enter lead in this calculator.
Does the backlash input change the animated travel?
No. The drawing shows the entered backlash as a separate gap indicator. The travel and speed calculations assume ideal motion and do not subtract backlash or simulate its take-up at reversal.
Does the percentage predict positioning accuracy?
No. It is entered backlash divided by one screw lead, expressed as a percentage. It does not include lead error, deflection, thermal expansion or control-system error.
Why is there a travel result at zero RPM?
Travel is lead multiplied by the selected number of turns. It describes the distance those turns would produce. At zero RPM the speed and feed are zero and the animation holds at its start.
Does playback show the actual time needed for the selected travel?
No. Playback reverses through the selected travel at an illustrative rate capped for viewing. Use the calculated speed or feed to evaluate motion timing.
Does a low lead prove the screw is self-locking?
No. Self-locking also depends on thread geometry and friction, which are not inputs here.
Does the RPM input verify critical speed?
No. Check the screw diameter, unsupported length and end-support arrangement against the screw manufacturer’s critical-speed guidance.
Technical references
- DX mechanism, Rectilinear motion of slide by rotation of screw mechanism 1 — demonstration of a screw driving a nut and guided slide.
- Thomson, Lead vs. Pitch — lead is axial travel per revolution.
- Thomson, Precision Metric Ball Screws engineering guidelines — travel-rate and rotational-speed relation.
- Rockford Ball Screw, About Ball Screws — lead and backlash definitions.
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