Power screws convert rotary motion into linear motion, so they are used in vises, jacks, clamps, presses, and actuators. This cheat sheet helps students connect screw geometry to motion, force, torque, and efficiency. It is useful for solving engineering mechanics problems where friction and thread shape strongly affect performance.
The core ideas are pitch, lead, lead angle, friction angle, torque to raise or lower a load, and mechanical advantage. For a single-start screw, lead equals pitch, while multi-start screws move farther per revolution. Self-locking occurs when friction is high enough that the load cannot back-drive the screw without applied torque.
Key Facts
- Lead is the axial distance a screw advances in one full turn, so lead L = pitch p x number of starts.
- For a single-start screw, lead L = pitch p because there is only one thread helix.
- The lead angle is found from tan lambda = L / (pi dm), where lambda is the lead angle and dm is the mean thread diameter.
- For a square thread raising a load, torque Tr = W dm / 2 x tan(lambda + phi), where W is load and phi is the friction angle.
- The friction angle is defined by tan phi = mu, where mu is the coefficient of friction.
- For a square thread lowering a load, torque Tl = W dm / 2 x tan(phi - lambda) when the screw is self-locking.
- A power screw is self-locking when phi > lambda, which is approximately the same as mu > tan lambda.
- Ideal screw efficiency without collar friction can be estimated by efficiency e = tan lambda / tan(lambda + phi).
Vocabulary
- Power screw
- A screw mechanism designed to convert rotational input torque into linear force or motion.
- Pitch
- The axial distance from one thread to the next matching point on an adjacent thread.
- Lead
- The axial distance a nut or screw advances during one complete revolution.
- Lead angle
- The angle between the thread helix and a plane perpendicular to the screw axis at the mean diameter.
- Friction angle
- The angle phi whose tangent equals the coefficient of friction, so tan phi = mu.
- Self-locking
- A condition where the load cannot cause the screw to rotate backward without an external torque.
Common Mistakes to Avoid
- Confusing pitch and lead is wrong because they are equal only for a single-start screw. For a multi-start screw, lead = pitch x number of starts.
- Using the outside diameter instead of the mean diameter is wrong because torque and lead angle formulas use dm, the approximate diameter where thread force acts.
- Ignoring units in tan lambda = L / (pi dm) is wrong because lead and diameter must use the same length unit before calculating the ratio.
- Assuming every power screw is self-locking is wrong because self-locking requires phi > lambda, or approximately mu > tan lambda.
- Forgetting collar friction is wrong in real designs because a thrust collar can add significant torque beyond the thread torque.
Practice Questions
- 1 A single-start screw has a pitch of 4 mm. What is its lead?
- 2 A four-start screw has a pitch of 2.5 mm. What distance does the nut move in 6 revolutions?
- 3 A square-thread power screw has L = 6 mm, dm = 30 mm, and mu = 0.15. Find the lead angle and decide whether it is self-locking.
- 4 Explain why increasing the number of starts can make a screw faster but less likely to be self-locking.