--- title: "Inversions of single slider crank chain" subject: "Theory of Mechanism and Machine I" chapter: 1 key: "semester_6/theory_of_mechanism_and_machine_i:slider-crank-chain-four-inversions" source: https://www.bctengineer.com/q/semester_6/theory_of_mechanism_and_machine_i/slider-crank-chain-four-inversions site: BCT Engineering --- # Inversions of single slider crank chain Theory of Mechanism and Machine I · Chapter 1: Introduction - Asked in: year not given, 8 marks - Video: [Single slider crank mechanism | single slider crank mechanism inversion || Single slider crank chain](https://www.youtube.com/watch?v=Pp1yEK8hgQo) — Gear Institute Mechanical Engineering Videos and Physics by Gear Institute - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/theory_of_mechanism_and_machine_i/slider-crank-chain-four-inversions - Whole chapter: https://www.bctengineer.com/md/semester_6/theory_of_mechanism_and_machine_i/chapter-1 ## Question What is a kinematic chain? Explain the inversions of a single slider crank chain with one practical application of each inversion. ## 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. ## Answer #### 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. ```text 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 | ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is an inversion of a kinematic chain? A. Reversing the direction of the input link B. Replacing a lower pair by a higher pair C. Fixing a different link of the same chain to get a different mechanism D. Adding one more link to the chain Answer: C. Fixing different links of the same chain one at a time gives different mechanisms, each called an inversion. (Key point: Kinematic chain and inversion) 2. A single slider crank chain consists of: A. Four links with four turning pairs B. Four links with three turning pairs and one sliding pair C. Three links with two turning pairs and one sliding pair D. Four links with two turning pairs and two sliding pairs Answer: B. It has crank, connecting rod, slider and frame joined by three turning pairs and one sliding pair. (Key point: Parts of single slider crank chain) 3. Fixing the cylinder (frame) of the single slider crank chain gives which mechanism? A. Whitworth quick return B. Hand pump C. Oscillating cylinder engine D. Basic reciprocating engine or compressor mechanism Answer: D. With the cylinder fixed the crank rotates and the slider reciprocates, as in a reciprocating engine or pump. (Key point: Inversion 1 application) 4. Which inversion is obtained by fixing the crank, and what is a typical use? A. Whitworth quick-return motion in a shaper B. Hand pump C. Reciprocating IC engine D. Oscillating cylinder engine Answer: A. Fixing the crank gives the Whitworth quick-return motion (also the rotary Gnome engine). 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