In modern CNC machine tools, the backlash has been eliminated by

The correct option is preloaded ball screws.

Detailed Explanation:

1. Understanding Backlash:
Backlash is the play or clearance caused by gaps between mating parts in a mechanical system, such as a screw and a nut. When the direction of rotation of the screw is reversed, there is a momentary lag before the nut starts moving in the opposite direction. In high-precision CNC (Computer Numerical Control) machine tools, this lag introduces positional errors that compromise machining accuracy and repeatability.

2. Why Preloaded Ball Screws Eliminate Backlash:
Ball screws convert rotational motion into linear motion with high efficiency using spherical balls circulating between the screw shaft and the nut. To eliminate the axial play (backlash), these ball screws are "preloaded". Preloading is accomplished by inserting balls that are slightly larger than the groove space, or by using a double-nut system tensioned against each other. This creates a continuous internal compressive force (preload) that removes any clearance or axial play between the balls, screw grooves, and nut grooves. As a result, bidirectional movement becomes instantaneous and highly precise.

3. Why Other Options Are Incorrect:

• Rack and pinion: While commonly used for long-travel linear motion, standard rack and pinion setups naturally suffer from backlash due to gear tooth clearances unless complex dual-pinion split systems are used.
• Ratchet and pinion: A ratchet mechanism permits motion in only one direction and prevents backward motion, which is unsuitable for continuous bidirectional precision control in CNCs.
• Slider crank mechanism: This converts rotational motion to reciprocating linear motion (or vice versa) using mechanical linkages, which inherently have joint clearances and kinematic limitations that do not eliminate backlash.