For the selected ideal lead-screw model, thread lead L is the axial nut travel per screw revolution. With thread pitch p and z thread starts, L = pz. At screw speed n rpm, ideal linear speed is v = nL/60 in millimetres per second.
Selected Lead-Screw Kinematics
Explore nominal lead and ideal axial speed for a selected thread pitch, start count and screw speed.
Equation Used
- The nut is prevented from rotating while the screw rotates.
- Nominal lead equals selected thread pitch multiplied by integer starts.
- The selected speed is steady and nonnegative.
- Manufacturing error, compliance, backlash, load, friction, efficiency, dynamics and limits are excluded.
The secondary figure uses the same selected pitch, thread-start count and screw speed as the calculator.
Selected lead-screw model
A rotating screw and translating nut form a helical pair. If the nut is prevented from rotating, relative screw rotation produces axial travel. One complete revolution advances the nut by the screw lead.
Pitch is axial spacing between adjacent thread forms. Lead is travel per revolution. They are equal for a single-start thread, while a multi-start thread has Lead = pitch × starts.
What this calculator demonstrates
Select thread pitch, integer thread-start count and screw speed. The calculator returns nominal lead, ideal travel rate in millimetres per minute, ideal linear speed and angular speed.
This is a kinematic identity for a selected screw and does not choose a screw or motor. It does not calculate torque, thrust, efficiency, friction, backlash, lead error, critical speed, buckling, load rating, acceleration, thermal growth or service life.
Ideal screw kinematics
For pitch p and z starts, L = pz. With n in revolutions per minute, the ideal travel rate is q = nL millimetres per minute and v = nL/60 millimetres per second. Angular speed is ω = 2πn/60 radians per second.
The result uses nominal geometry. NSK's lead-accuracy terminology distinguishes nominal, specified and actual travel; a real assembly can deviate through manufacturing error, load, temperature and compliance.
Default selected example
For p = 5.0 mm, z = 2 starts and n = 600 rpm, nominal lead is 10.0 mm/rev. The ideal travel rate is 6,000 mm/min, ideal linear speed is 100.0 mm/s and angular speed is 62.83 rad/s.
These values do not establish that a particular screw, support arrangement, nut or motor can operate at that speed or carry a given load.
Scope and correction boundary
The removed page called its input pitch while treating it as lead, supported only a hidden single-start assumption and reported an invented force index relative to 5 mm. A pitch ratio alone is not a thrust calculation because torque, efficiency, thread geometry, friction and losses were absent.
The former article also mixed lead screws, rack-and-pinion drives, cams and slider cranks while supplying unsupported product specifications, tolerances, operating limits, failure diagnoses and a fabricated pick-and-place example. Those claims and the unrelated video are removed.
Questions
What is the difference between pitch and lead?
Pitch is spacing between adjacent thread forms. Lead is axial travel per revolution. Lead equals pitch multiplied by the number of thread starts.
Is calculated speed the actual axis speed?
It is the nominal steady kinematic rate. Acceleration, control profile, compliance, slip and travel error are excluded.
Does smaller lead prove more thrust?
No. Lead affects ideal mechanical ratio, but actual thrust also requires applied torque, efficiency, friction, thread form, support and load data.
Can the result set maximum rpm?
No. Permissible speed depends on the specific screw diameter, unsupported length, mounting, product design and manufacturer rating.
Technical references
- Machine Design, Leadscrew Basics — defines lead as travel per revolution and distinguishes pitch from lead for multi-start threads.
- NSK, Precision Machine Components catalog — defines nominal, specified and actual travel and the associated lead-accuracy terms.
- THK, Conditions of the Ball Screw — shows that real screw selection also requires load, stroke, speed, support, accuracy, motor and service-life conditions.
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