Understanding the Double Slider Crank Chain

The question asks about the composition of a double slider crank chain in terms of kinematic pairs. A kinematic chain is an assembly of links and joints that is the foundation of a mechanism.

What is a Double Slider Crank Chain?

A double slider crank chain is an inversion of the basic slider crank chain. It is a kinematic chain with four links and four joints, where all the joints are kinematic pairs. Specifically, it is characterized by having two sliding pairs and two turning pairs.

Links and Joints in a Double Slider Crank Chain

Let's consider a common example or representation of a double slider crank chain:

• Link 1: The frame (fixed link).
• Link 2: Connects the frame to a slider, allowing turning relative to the frame and sliding relative to the slider.
• Link 3: Connects the other slider to Link 2, allowing sliding relative to Link 2 and turning relative to the slider.
• Link 4: Two sliders, each sliding along a guide on the frame (Link 1).

However, the standard representation often involves four links connecting four joints in a loop. A common example is the Scotch Yoke mechanism or the Elliptical Trammel.

Kinematic Pairs in a Double Slider Crank Chain

In a double slider crank chain, the connections between the links form kinematic pairs. Let's look at the types of pairs present:

• Turning Pairs: A turning pair (or revolute joint) allows relative rotation between two links.
• Sliding Pairs: A sliding pair (or prismatic joint) allows relative linear movement (translation) between two links.

In the case of a double slider crank chain, regardless of the specific inversion (like Elliptical Trammel or Scotch Yoke), the chain consists of:

• Two pairs that allow relative rotation (turning pairs).
• Two pairs that allow relative translation (sliding pairs).

For example, in an Elliptical Trammel:

• The two sliders slide along the fixed frame (two sliding pairs).
• The rod connecting the sliders has pins that turn within the sliders (two turning pairs).

Composition of the Chain

Therefore, the double slider crank chain inherently consists of two turning pairs and two sliding pairs.

Let's examine the options provided:

• Option 1: one turning and one sliding pair - This is incorrect.
• Option 2: two turning and one sliding pair - This is incorrect.
• Option 3: three turning pair - This is incorrect.
• Option 4: two turning and two sliding pair - This matches our analysis.

Based on the structure and definition of a double slider crank chain, it must contain two turning pairs and two sliding pairs to form a closed kinematic chain that allows the characteristic motion associated with its inversions.

The composition is always fixed for the basic double slider crank chain before considering inversions, which simply fix different links.