Understanding Single Slider Crank Chain Inversions

A single slider crank chain is a fundamental four-link kinematic chain. It consists of the following links:

• Link 1: Frame or fixed link (often the cylinder block in an engine).
• Link 2: Crank (rotating link).
• Link 3: Connecting rod (coupler).
• Link 4: Slider (reciprocating link, like a piston).

These links are connected by three pin joints (revolute joints) and one sliding joint (prismatic joint).

What is an Inversion of a Mechanism?

An inversion of a kinematic chain is obtained by fixing a different link in the chain. By fixing each link in turn, we can get as many inversions as the number of links in the chain. These inversions result in different mechanisms with distinct motions and applications, even though they are derived from the same basic chain.

Inversion when the Cylinder is Fixed

In the standard configuration of a single slider crank chain, the link that is typically considered fixed is the frame or the block which contains the cylinder guide for the slider (piston). This corresponds to fixing Link 1 in our description above.

When Link 1 (the cylinder block/frame) is fixed, the crank (Link 2) is free to rotate, the connecting rod (Link 3) undergoes complex motion, and the slider (Link 4, the piston) reciprocates back and forth within the fixed cylinder. This is the mechanism configuration used in:

• Reciprocating steam engines
• Internal combustion engines
• Reciprocating compressors

This specific arrangement, where the cylinder/frame is the fixed link, is widely known as the mechanism of a reciprocating engine or compressor.

Analyzing the Options

• Quick return mechanism: Often an inversion where the crank or connecting rod is fixed, used in shaping machines and slotting machines for faster return strokes. This is not the inversion with the cylinder fixed.
• Scotch yoke mechanism: This is a different mechanism altogether, although it also converts rotary to linear motion. It is not typically considered an inversion of the standard four-link slider crank chain.
• Oldham’s coupling: This mechanism connects two parallel shafts with offset axes and uses two sliders and a rotating intermediate link. It is not an inversion of the single slider crank chain.
• Reciprocating engine: As explained above, this is precisely the mechanism formed when the cylinder block (Link 1) of a single slider crank chain is fixed.

Therefore, the inversion formed in the single slider crank chain when the cylinder is fixed in the mechanism is the reciprocating engine (or compressor) mechanism.