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?

The correct option is 1000.

Analysis of the Figure:
The schematic diagram depicts a CNC linear positioning axis where a stepper motor (labeled as "Motor that rotates in discrete steps") is directly coupled to a lead screw ("screw"). As the motor rotates in discrete angular steps, the screw rotates (as indicated by the circular arrow on the right), converting the rotational motion into the linear displacement of a "Nut" and a "Table" mounted on it (indicated by the horizontal double-headed arrow above the table).

Step-by-Step Derivation:

1. Determine the linear travel per motor step (Resolution or Basic Length Unit):
The pitch of the screw is the linear distance the nut (and table) moves when the screw completes one full revolution (360 degrees). Here, the pitch is given as 5 mm.
The motor completes one full revolution in 50 discrete rotational steps. Therefore, the linear displacement of the table per single step is:

$\text{Linear displacement per step}=\frac{\text{Pitch of the screw}}{\text{Number of steps per revolution}}$

Substituting the given values:

$\text{Linear displacement per step}=\frac{5\text{ mm}}{50\text{ steps}}=0.1\text{ mm/step}$

2. Calculate the total number of controllable locations:
The total horizontal traverse length of the table is 100 mm. The controllable positions are discrete locations separated by the minimum step resolution (0.1 mm) along the total traverse length.

$\text{Total number of controllable locations}=\frac{\text{Total traverse length}}{\text{Linear displacement per step}}$

Substituting the values:

$\text{Total number of controllable locations}=\frac{100\text{ mm}}{0.1\text{ mm}}=1000$

Thus, the table can be positioned at 1000 distinct controllable locations along its traverse range.