For pitch p, integer start count s, speed N and run time t, lead is L = ps, ideal nut speed is v = LN/60, revolutions are Nt/60, and ideal travel is vt.
Ideal Multi-Start Screw Pair Kinematics
Explore ideal pitch, lead, speed, revolutions and travel for a multi-start screw pair.
Equation Used
- Start count is a positive integer.
- The screw rotates at constant selected speed and the nut does not rotate.
- One screw revolution advances the nut by one lead.
- Slip, backlash, compliance, friction, load and structural limits are excluded.
The presentation shows one ideal revolution; output tiles report the selected speed and run time.
Rotating screw and translating nut
The animation shows a screw supported by fixed bearings and a nut constrained against rotation. Each colored trace represents one start; the traces rotate together while the nut advances one lead during one presentation revolution.
The calculator outputs describe the selected speed and run time, while the presentation isolates one ideal revolution so the lead relationship remains visible.
What the calculator determines
Select thread pitch, integer start count, rotational speed and run time. Outputs are lead, ideal linear speed, ideal travel and revolutions.
It does not calculate torque, axial force, efficiency, friction, backlash, critical speed, buckling, stress, wear, life or positioning accuracy.
Ideal screw-pair identities
L = ps, v = LN/60, revolutions = Nt/60 and travel = vt = LNt/60. Pitch is adjacent-thread spacing; lead is axial travel per revolution.
Selected-input example
For p = 5 mm, s = 4, N = 60 rpm and t = 10 s, lead is 20 mm/rev, ideal speed is 20 mm/s, revolutions are 10 and ideal travel is 200 mm.
Scope and design boundary
More starts increase lead at fixed pitch, increasing ideal translation per revolution. Real screw selection also depends on load, torque, efficiency, self-locking or backdriving, lubrication, alignment, supports and duty cycle.
Unsupported application, performance, material, maintenance and tolerance claims are removed.
Questions
Are pitch and lead the same?
Only for a single-start thread. For s starts, lead is ps.
Why is speed divided by 60?
N is entered in revolutions per minute and the output is per second.
Does zero rpm give zero motion?
Yes; speed, revolutions and travel are zero.
Can this select a screw?
No.
References & Further Reading
- Wikipedia contributors. Leadscrew. Wikipedia
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