The double slider crank mechanism consists of two sliding joints connected by a connecting link. This mechanism is commonly used in engines and machines to convert rotary motion into reciprocating motion or vice versa.

When a point on the connecting link is considered, excluding the end points, it traces a path as the mechanism moves through its motion cycle. The shape of this path depends on the dimensions and configuration of the mechanism.

The correct answer is option 'D', which states that the point on the connecting link traces an elliptical path. Let's understand why this is the case.

Understanding the Double Slider Crank Mechanism:
- The double slider crank mechanism consists of a fixed frame, two slider joints, a connecting link, and a crank.
- The crank is connected to the fixed frame and rotates about a fixed axis.
- The connecting link connects the two sliders and is free to rotate about its own axis.
- As the crank rotates, it causes the connecting link to move in a reciprocating motion, resulting in the sliders moving back and forth.

Motion Analysis:
- To analyze the motion of the connecting link, we consider the instantaneous centers of rotation (ICRs) for the different positions of the mechanism.
- The ICR is the point about which the connecting link appears to rotate instantaneously at a particular position.
- For a double slider crank mechanism, there are two ICRs, one for each slider joint.
- By considering the ICRs and the relative positions of the sliders and the connecting link, we can determine the path traced by a point on the connecting link.

Path Traced by a Point on the Connecting Link:
- As the crank rotates, the connecting link moves through different positions, causing the sliders to move back and forth.
- The path traced by a point on the connecting link can be determined by plotting the positions of the ICRs and connecting them.
- By doing so, we find that the path traced is an elliptical shape.

Reasoning:
- The reason why the path traced by a point on the connecting link is elliptical can be understood from the geometry of the mechanism.
- The double slider crank mechanism has a four-bar linkage configuration.
- In a four-bar linkage, the path traced by a point on the coupler link (connecting link) is generally elliptical, except for special cases where it can be a straight line, a circle, or a parabola.
- However, in the case of a double slider crank mechanism, the path traced by a point on the connecting link is generally elliptical.

Conclusion:
- In conclusion, a point on the connecting link of a double slider crank mechanism, excluding the end points, traces an elliptical path.
- This is due to the four-bar linkage configuration and the motion of the mechanism.
- Understanding the path traced by different points on the mechanism is important in the design and analysis of such mechanisms in various mechanical applications.