Velocity Ratio of a Simple Screw Jack

What is the expression for the velocity ratio of a simple screw jack?

Is the velocity ratio directly proportional to the pitch of the screw or the number of threads on the screw?

The expression for the velocity ratio of a simple screw jack is:

velocity ratio = 1 / (number of threads on the screw)

Deriving the expression for the velocity ratio of a simple screw jack involves considering the pitch of the screw and the number of threads on the screw. The pitch of the screw is the distance between two adjacent threads, denoted as 'p'. On the other hand, the number of threads on the screw represents the number of complete rotations required for the nut to move a distance equal to the pitch, denoted as 'n'.

When the screw is rotated once, the distance moved by the nut is equal to the pitch 'p'. On the other hand, the distance moved by the screw when the nut moves a distance equal to the pitch is the circumference of the screw, which can be calculated using the formula: circumference = 2πr, where 'r' is the radius of the screw.

By equating the distance moved by the nut to the distance moved by the screw, we can derive the expression for the velocity ratio:

velocity ratio = p / (2πr)

Substitute the value of 'r' (obtained as r = p / (2π)) into the velocity ratio expression, we get:

velocity ratio = 1 / n

Therefore, the velocity ratio of a simple screw jack is inversely proportional to the number of threads on the screw. The more threads on the screw, the lower the velocity ratio, indicating a slower lifting process.