Screw Simple Machine

A screw is essentially an inclined plane (a ramp) wrapped helically around a central cylinder. The ramp forms the threads of the screw. When you rotate a screw, the rotational effort slides along the helical ramp, converting the circular motion and torque into a linear advance and powerful force along the shaft. The horizontal distance of one full rotation is the circumference of the cylinder ($2\pi r$), and the vertical height gained is the thread pitch ($p$).

A screw can pack a massive mechanical advantage because the vertical distance traveled (pitch $p$) is extremely small relative to the effort distance traveled in one circular loop ($2\pi R$). For example, if a handle rotates in a circle with a radius of 20 cm (circumference $\approx 125.6\text{ cm}$) and the screw thread pitch is only 2 mm, the ratio of input-to-output travel is $125.6 / 0.2 = 628$. Achieving a mechanical advantage of 628 with a lever would require a lever arm that is extremely long and structurally impractical.

A screw is "self-locking" if it remains stationary under a load without slipping back when the input torque is removed. This occurs because the static friction force opposing sliding along the threads is greater than the gravity component pushing the load down the thread ramp. Mathematically, it requires the lead angle (thread angle $\alpha$) to be less than or equal to the static friction angle ($\phi_s = \arctan\mu_s$), or simply: $p \le 2\pi r_m \mu_s$. C-clamps, bolts, and jackscrews must be self-locking for safety. A screw fails to lock (rolls back) if the pitch is too steep or if the thread coefficient of friction is extremely low (e.g., well-lubricated ball screws).

Thread pitch ($p$) is the axial distance between two consecutive thread ridges. Decreasing the pitch means the threads are closer together. This increases the Ideal Mechanical Advantage ($\text{IMA} = 2\pi R / p$), meaning less input effort force is required to lift a load. However, the trade-off is speed: because the pitch is smaller, the screw advances a shorter distance per turn. Therefore, you must spin the handle many more times to travel the same linear height, trading off speed/distance for force amplification.

Real screws experience high friction losses because the threads slide against each other under massive normal forces (the load being supported). The surface-to-surface sliding contact spreads over the entire helical path. This generates large frictional torques that resist movement, converting a large portion of the input work into heat. Despite this low efficiency, screws are highly valued because they provide massive force amplification and the critical self-locking safety feature.