Understanding Kinematic Chains and Inversions

A kinematic chain is a series of links connected by joints, which forms a closed loop or an open chain with relative motion between the links. When one link of a kinematic chain is fixed, it becomes a mechanism. Different mechanisms can be obtained by fixing different links in the same kinematic chain. These different mechanisms are called the inversions of the original kinematic chain.

What is a Double Slider Crank Chain?

A double slider crank chain is a specific type of kinematic chain. It consists of four links and has two turning pairs and two sliding pairs. In its fundamental form, it has two links that slide relative to each other, and two links that rotate relative to others.

Inversions of Double Slider Crank Chain

There are several inversions possible by fixing different links of the double slider crank chain. Let's look at some common inversions:

• Fixing Link 1 (Frame): This inversion is the basis for mechanisms like the Scotch Yoke mechanism. It converts rotary motion into reciprocating motion or vice versa.
• Fixing Link 2 or Link 3 (Sliders/Blocks): This inversion is used in mechanisms like Oldham's Coupling, which is used to connect two parallel shafts that are slightly misaligned.
• Fixing Link 4 (Connecting Link): This inversion leads to the mechanism known as the Elliptical Trammel. In this mechanism, if a point is traced on the connecting link, it generates an elliptical path.

Analyzing the Options

Let's examine the given options in the context of inversions of the double slider crank chain:

• Engine indicator: This is typically related to inversions of a single slider crank chain (four links: one turning pair, one sliding pair, two revolute pairs). The single slider crank chain is the basis for reciprocating engines.
• Elliptical trammel: As discussed above, the Elliptical Trammel is obtained by fixing the connecting link (link 4) of a double slider crank chain. This device is used to draw ellipses.
• Quick returns motion: Mechanisms for quick return motion (like the crank and slotted lever quick return mechanism or Whitworth quick return mechanism) are inversions of the single slider crank chain, not the double slider crank chain.
• Coupled wheels of a locomotive: The coupling rods connecting the wheels of a locomotive form a mechanism which is an inversion of a four-bar chain, not a double slider crank chain.

Based on the analysis, the Elliptical Trammel is the mechanism that is an inversion of a double slider crank chain.