Understanding the Double Slider Crank Chain

A double slider crank chain is a specific type of kinematic chain. It is derived from the basic four-bar kinematic chain by replacing two turning pairs with sliding pairs. Specifically, it has four links, two revolute joints (turning pairs), and two prismatic joints (sliding pairs). The relative motion between the links causes points on them to trace specific paths.

Inversion of the Double Slider Crank Chain: Elliptical Trammel

One common and important inversion of the double slider crank chain is the elliptical trammel. In this mechanism:

• Two sliders are connected to a connecting link.
• These sliders are constrained to move along two perpendicular straight guides.
• A fixed link corresponds to the space between the two guides (or a fixed point on one guide).
• The connecting link is the coupler.

This mechanism is used to draw ellipses or as a stirring mechanism.

Path Traced by a Link in an Elliptical Trammel

Consider the connecting link in the elliptical trammel mechanism. The path traced by a point on this link depends on the specific point chosen.

• If you consider a point on the connecting link, this point will trace an elliptical path.
• The shape and size of the ellipse depend on the position of the point on the link relative to the two sliders.
• A special case is when the point is at one of the ends of the connecting link where the sliders are attached; these points trace straight lines along the guides.

The question asks about the path traced by "a link connecting". This usually refers to a general point on the connecting or coupler link, not specifically the ends. A general point on the connecting link of a double slider crank chain (like in an elliptical trammel inversion) traces an ellipse.

Analyzing the Options

Let's look at the given options in the context of the double slider crank chain and the elliptical trammel:

• ellipse: As discussed, a point on the connecting link of an elliptical trammel (an inversion of the double slider crank chain) traces an ellipse. This fits the description.
• None of the above: This would only be true if none of the other options are correct.
• A straight line: While the ends of the connecting link trace straight lines, a general point on the link traces an ellipse. The question asks about "a link connecting", implying a point on the link.
• Square: This is not a path traced by any point on a link in this mechanism.

Based on the kinematics of the double slider crank chain, specifically its common inversion the elliptical trammel, a point on the connecting link traces an ellipse.