Discussion
A CNC machine has one of its linear positioning axes as shown in the figure, consisting of a motor rotating a lead screw, which in turn moves a nut horizontally on which a table is mounted. The motor moves in discrete rotational steps of 50 steps per revolution. The pitch of the screw is 5 mm and the total horizontal traverse length of the table is 100 mm. What is the total number of controllable locations at which the table can be positioned on this axis?
Answer: C
The table can be placed at 1000 controllable locations.
One revolution of the screw moves the nut by one pitch, 5 mm, and takes 50 motor steps, so the smallest move, the resolution, is
\[ \begin{aligned} \Delta x &= \frac{5\ \text{mm}}{50} = 0.1\ \text{mm} \\ n &= \frac{100\ \text{mm}}{0.1\ \text{mm}} = 1000 \end{aligned} \]
The 100 mm traverse is therefore covered in 1000 equal increments, which is the count the official key takes. (Counting both end positions as well would give 1001, which is not among the options.)
5000 multiplies the travel by the steps per revolution, as if the screw advanced 1 mm per turn instead of 5 mm. 200 and 2 do not follow from the pitch and the step count: 20 revolutions times 50 steps is 1000, not 200, and 2 counts only the two ends of the travel.
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