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Friday, July 10, 2015

Differential screw for fine adjustments of precision equipment

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Components of differential screw
Differential screw components
A differential screw is a mechanism that provides very fine motions of machine parts. There are several forms of its configuration.

The picture shows one common form of the differential screws. There are 3 main components as follows:
  • Spindle (differential screw) -- The spindle has two different threads on the same axis.
  • Base -- It's the base of the whole mechanism which has one threaded hole.
  • Nut -- It has one threaded hole with sliding joint. This is the end mover where we will get fine motion. This part may be connected to other machine components to provide precise motion.

How it works

thread A & B and distance for explanation
Different threads on the same spindle / distance between marks
The spindle has two different thread sizes. In this example, the larger one (thread A) has M12 coarse thread which has a pitch of 1.75 mm. Another thread (B) is M10 coarse thread which has a pitch of 1.5 mm.
M10 and M12 threads pitch difference
Pitches (leads) of the differential screw
The pitch (or lead) of a screw is distance the screw advances when it turns one revolution. Therefore, when the handle turns one revolution, thread A rotates one revolution and moves in a distance equal to the pitch of thread A (1.75 mm). Since thread B is on the same spindle, it also moves together with thread A (1.75 mm) and also rotates one revolution. However, thread B connects to the nut which is unable to rotate. So, the nut retracts a distance equal to the pitch of thread B which is 1.5 mm. Hence, the motion of the nut is the advance distance of thread A minus the retracted distance. It is the difference between the pitch of threads. This is why it is called the differential screw.
equation: nut displacement w.r.t. pitch difference and number of turns
Differential screw displacement formula
  • ΔSnut = travelling distance of the nut (mm)
  • LA = pitch of thread A (mm)
  • LB = pitch of thread B (mm)
  • Δθscrew = number of turns of the screw (rev)
From this example, we have ΔSnut = 1.75 - 1.5 = 0.25 mm. That means the nut travels 0.25 mm per each turn of the spindle. As shown in the above picture, the distance between 2 marks is 2.5 mm. Then we need to turn the spindle 10 revolutions so that the nut will travel 2.5 mm.

As we can see from the formula, if we need the nut to move 0.1 mm per one turn of the spindle, we need to select the different screw threads. Since we know that the standard metric coarse threads have the following values:
  • M5, pitch = 0.8 mm
  • M4, pitch = 0.7 mm
The difference between pitches is 0.8 - 0.7 = 0.1 mm which is as per the requirement. So, thread A will be M5 and thread B is M4 and we will get 0.1 mm per turn.

Watch the following video to see how it moves. We use Unigraphics NX4 motion simulation to show all motions.

  • Machines & Mechanisms Third Edition by David H. Myszka


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