- Practice · 8 marks
Inversions of single slider crank chain
Short answer
A kinematic chain is an assembly of links with constrained relative motion; fixing different links gives inversions. Single slider crank chain has four links (crank, connecting rod, slider, frame) with three turning and one sliding pair. Four inversions: 1) fixed cylinder - reciprocating engine; 2) fixed crank - Whitworth quick return; 3) fixed connecting rod - slotted lever quick return; 4) fixed slider - hand pump.
What is a kinematic chain? Explain the inversions of a single slider crank chain with one practical application of each inversion.
Kinematic chain and inversion
A kinematic chain is an assembly of links connected by kinematic pairs so that the relative motion of the links is completely constrained (definite). Fixing different links of the same chain, one at a time, gives different mechanisms. Each of these is called an inversion of the chain.
Single slider crank chain
It has four links: a crank, a connecting rod, a slider and the frame (cylinder/guide), joined by three turning pairs and one sliding pair.
crank 2 rod 3 slider 4
O ---------- A ------- B ==> (guide, link 1)
A chain of four links has four inversions. The first (fixing the cylinder) is the basic engine mechanism.
Inversion 1: fixed link = cylinder (frame)
The basic reciprocating engine or compressor mechanism. The crank rotates and the slider reciprocates.
- Application: reciprocating steam/IC engine, reciprocating pump.
Inversion 2: fixed link = crank
The connecting rod turns about the now-fixed crank pin, and the former cylinder (a slotted link) rotates about the crank centre. The slider moves to and fro in this rotating slot.
- Application: Whitworth quick-return motion (shaper) and the rotary engine (Gnome engine).
Inversion 3: fixed link = connecting rod
The crank still rotates fully about one fixed pivot, while the former cylinder becomes a slotted lever that oscillates about the other fixed pivot, with the slider moving along the slot.
- Application: Crank and slotted-lever quick-return mechanism (shaper), oscillating cylinder engine.
Inversion 4: fixed link = slider
The slider is fixed. The connecting rod oscillates about the pin on the fixed slider, the crank swings, and the former frame (cylinder/plunger rod) reciprocates along the fixed slider.
- Application: hand pump (the handle is the crank and the plunger reciprocates) and pendulum pump / Bull engine.
| Inversion | Fixed link | Application |
|---|---|---|
| 1 | Cylinder | IC engine |
| 2 | Crank | Whitworth quick return, rotary engine |
| 3 | Connecting rod | Slotted-lever shaper, oscillating cylinder |
| 4 | Slider | Hand pump |
✓ Answer checked by Claude Opus 5.5 (high effort)
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