For an Oldham coupling used between two shafts, which among the following statements are correct?

I. Torsional load is transferred along shaft axis

II. A velocity ratio of 1:2 between shafts is obtained without using gears.

III. Bending load is transferred transverse to shaft axis.

IV. Rotation is transferred along shaft axis.

The correct option is I and IV.

To understand why this is the correct choice, let us analyze the function and characteristics of an Oldham coupling step-by-step:

1. Understanding Oldham Coupling:
An Oldham coupling is a mechanical joint used to connect two parallel shafts that have lateral (radial) misalignment. It consists of three main components: two outer discs (flanges) keyed to the driving and driven shafts, and a middle floating disc that has tongues on both sides oriented perpendicular to each other. The tongues fit into corresponding slots on the outer discs, allowing sliding motion to accommodate the misalignment.

2. Analyzing Statement I (Torsional load is transferred along shaft axis):
The fundamental purpose of any coupling, including the Oldham coupling, is to transmit torque (torsional load) from the driver shaft to the follower shaft. This torque is successfully transferred around and along the axes of the shafts. Therefore, Statement I is correct.

3. Analyzing Statement II (A velocity ratio of 1:2 between shafts is obtained without using gears):
An Oldham coupling is a constant velocity coupling. This means that the driving and driven shafts rotate at the exact same angular speed at every instant. The velocity ratio is strictly 1:1, not 1:2. Therefore, Statement II is incorrect.

4. Analyzing Statement III (Bending load is transferred transverse to shaft axis):
Oldham couplings are specifically designed to absorb lateral misalignment through the sliding motion of the central disc. This sliding mechanism prevents the transmission of bending moments or transverse bending loads from one shaft to the other, thereby protecting the shafts and bearings from stress. Therefore, Statement III is incorrect.

5. Analyzing Statement IV (Rotation is transferred along shaft axis):
The coupling directly transfers rotary motion from the input shaft to the output shaft along their parallel axes. Therefore, Statement IV is correct.

Conclusion:
Since only statements I and IV are true, the correct answer is indeed I and IV.