A lead screw converts rotation into linear travel when its nut is prevented from turning. Explore the guided carriage and calculate turns, travel and speed, then estimate thrust from entered torque and screw efficiency.
Ideal Lead-Screw Translation Calculator
Enter screw lead, rotational speed, run time, input torque and assumed screw efficiency. Results are ideal kinematic and energy-balance quantities, not component ratings.
Equation Used
- Lead is constant and the nut is constrained against rotation.
- Speed, torque and entered efficiency remain constant over the stated interval.
- Backlash, compliance, acceleration, guide friction, preload, buckling, critical speed and ratings are excluded.
Each revolution advances the guided nut by one screw lead. The thrust estimate uses entered torque and efficiency; component ratings, acceleration, backlash and guide friction require additional information.
Guide constraint and screw lead
A prismatic guide constrains a carriage to one translational degree of freedom. A screw and nut provide the drive: when the nut is prevented from rotating, each screw revolution advances it by the screw lead.
The guide defines the path; the drive supplies motion. The calculation assumes a rigid, perfectly aligned screw and guide.
Ideal screw motion and thrust
Use the calculator to compare travel, speed and torque-derived thrust for the entered values. It does not select a screw, guide, motor, bearing, coupling, structure, limit device or control system.
Constant-lead screw identities
THK gives the equivalent torque relation T=F L/(2 pi eta). Efficiency is entered by the user; it is not predicted.
Calculation example
For a 5 mm/rev lead, 120 rpm, 3 seconds, 1 N m and 85% assumed efficiency, the calculation gives 6 turns, 30.0 mm travel, 10.0 mm/s and about 1,068 N of torque-derived thrust.
Limits of the ideal screw calculation
Real selection requires the exact screw, guide, support geometry, duty cycle, load, speed, acceleration and manufacturer ratings.
Lead-screw translation questions
Does the force result rate a real screw?
No. It is the rearranged ideal torque relationship using an entered efficiency.
Does travel include backlash or compliance?
No.
Can the result select a motor or guide?
No. Acceleration, inertia, friction, buckling, critical speed and ratings are outside this model.
Authoritative engineering references
- MIT, Transmissions and Guides: screw lead as forward motion per rotation and the role of linear guidance.
- THK, Examples of Calculating Driving Torque: torque, axial force, lead and efficiency relationship.
- THK, Efficiency and Thrust: official lead-screw efficiency and thrust guidance.
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