Inversion of Mechanism

By BYJU'S Exam Prep

Updated on: September 25th, 2023

Before going into detail regarding the Inversion of Mechanism, let’s first understand the basics of the mechanism. When a set of links is connected in such a way that the last link’s one end is connected to the first link’s one end. and each link moves in relation to the others. This configuration is known as a closed kinematic chain. A mechanism is created when one of the kinematic chain’s links is fixed. Mechanisms are widely employed for motion transmission and modification of motion.

If a mechanism or group of mechanisms are connected, they can turn one source of energy into productive work in addition to transmitting motion. It’s known as a machine. For example, a slider-crank chain is a mechanism, but in a reciprocating IC engine, the same mechanism can turn the chemical energy of fuel into mechanical effort by adding specific attachments. As a result, the IC engine is a machine. Let’s take a closer look at the inversion of the mechanism.

Download Formulas for GATE Mechanical Engineering – TOM & Vibrations

Define Inversion of Mechanism

A mechanism is a kinematic chain in which one of the links is fixed. Fixing different links of the same kinematic chain can provide different mechanisms. These are known as inversions of the mechanism. The number of mechanisms obtained by modifying the fixed link is equal to the number of linkages.

All additional mechanisms will be known as inversions of the original mechanism, with the exception of the original mechanism. The motion of a mechanism’s links relative to each other is unaffected by its inversion.

Inversions of Four Bar Chain

The four-bar linkage is one of the most useful and frequent systems. The crank is the link in this mechanism that can complete a full revolution (link 2). The oscillating link is known as a rocker or lever (link 4). The coupler is the connector that connects these two (link 3). The frame is represented by Link 1.


Figure: Inversions of Four Bar Chain

Download Formulas for GATE Mechanical Engineering – Manufacturing Engineering and Materials

Double Crank Mechanism

The double crank mechanism, which comprises four links, is used to connect the coupling rod of a locomotive. The equal-length linkages AD and BC operate as cranks in this system and are attached to their respective wheels. The link CD serves as a coupling rod, while the link AB is fixed to maintain a constant distance between them. The purpose of this device is to transfer rotary motion from one wheel to the other.


Figure: Double Crank Mechanism

Crank and Lever Mechanism

The figure shows the beam engine mechanism, also known as the crank and lever mechanism, which consists of four links. When the crank spins around the fixed center A in this mechanism, The lever rotates around a fixed point D. The piston rod reciprocates due to the rotation of the crank, and the end E of the lever CDE is attached to it. In other words, the mechanism’s aim is to convert rotary motion into reciprocating motion.


Figure: Crank and Lever Mechanism

Download Formulas for GATE Mechanical Engineering – Machine Design

Double Lever Mechanism or Watt’s Indicator Mechanism

Figure shows a Watt’s indication mechanism, commonly known as a Double lever mechanism, which has four links. Fixed link 1, link AC with link CE, and link BFD are the four links. It should be noted that BF and FD form a single connection because they have no relative motion. CE and BFD’s link acts as a lever. The link BFD’s displacement vector is proportional to the pressure of gas acting on the indicator plunger. The tracing point of E at the end of link CE traces out an essentially straight line with any tiny displacement of the mechanism. Full lines depict the mechanism’s initial position, whereas dotted lines depict the mechanism’s position when the gas acts on the indication plunger.


Figure: Double Lever Mechanism or Watt’s Indicator Mechanism

Inversions of Single Slider Crank Chain

This is a kinematic chain having four links. It has one sliding pair and three turning pairs. Link 2 has rotary motion and is called a crank. Link 3 has got combined rotary and reciprocating motion and is called connecting rod. Link 4 has reciprocating motion and is called a slider. Link 1 is a frame (fixed). This mechanism is used to convert rotary motion to reciprocating and vice versa.


Figure: Inversions of Single Slider Crank Chain

Bull Engine or Pendulum Engine

The inversion is achieved in this mechanism by securing the cylinder or link 4 (i.e. sliding pair), as shown in Figure. When the crank (link 2) rotates, the connecting rod (link 3) oscillates around a pin fixed to link 4 at A, and the piston attached to the piston rod (link 1) reciprocates.


Figure: Bull Engine

Oscillating Cylinder Engine

The figure depicts the configuration of the oscillating cylinder engine system. It transforms reciprocating motion into rotary motion. Link 3 that forms the turning pair is fixed in this system. The connecting rod of a reciprocating steam engine mechanism corresponds to link 3. The piston attached to the piston rod (link 1) reciprocates when the crank (link 2) turns, and the cylinder (link 4) oscillates around a pin pivoted to the fixed link at A.


Figure: Oscillating Cylinder Engine

Rotary Engine

Rotating internal combustion engines were once employed in aviation. However, gas turbines now take their place. It is made up of seven cylinders in one plane that revolve around a fixed center D, as shown in Fig., while the crank (link 2) remains stationary. The piston (link 3) reciprocates inside the cylinders when the connecting rod (link 4) spins, forming link 1.


Figure: Rotary Engine

Crank & Slotted Quick Return Mechanism

Shaping machines, slot machines, and rotary internal combustion engines all utilize this mechanism. The turning pair’s link AC (i.e. link 3) is fixed in this mechanism, as seen in fig. The connecting rod of a reciprocating steam engine is represented by link 3. The driving crank CB spins around the fixed center C at a constant angular speed. The slotted bar AP oscillates around the pivoted point A due to a sliding block attached to the crank pin at B sliding along it. The motion from AP is transmitted to the ram, which carries the tool and reciprocates along the stroke line R1R2. The ram’s stroke line (R1R2) is perpendicular to the AC produced.


Figure: Crank & Slotted Quick Return Mechanism

Whitworth Quick Return Mechanism

Most shaping and slotting machines employ this technology. The turning pair’s link CD (link 2) is fixed in this mechanism, as indicated in Fig. reciprocating steam engine’s crank corresponds to link 2. The rotating angular speed of the driving crank CA (link 3) is consistent. The slider (link 4) moves along the slotted bar PA (link 1), which oscillates at a pivot point D, and is coupled to the crankpin at A. The ram at R is carried via the connecting rod PR, to which a cutting tool is attached. The tool’s motion is restricted along the RD-generated line, which is perpendicular to CD and passes through D.


Figure: Whitworth Quick Return Motion Mechanism

Inversion of Double Slider Crank Chain

Two sliding pairs and two twist pairs make up the double slider crankshaft. Because it contains two sliding pairs, it’s called a double slider crankshaft. It consists of two sliders, a moving frame, and a link that links the two slides and maintains the distance between them. The frame in which the sliders move is made up of two straight grooves that form a single link and cut at right angles to each other.

Elliptical Trammels

It’s a tool that’s used to draw ellipses. This is a twin slider crank chain inverted. The slotted plate is used to do this (link 4). Two straight grooves at right angles to each other are cut into the fixed plate or link 4. Sliders are links 1 and 3, which create sliding pairs with link 4 as seen in the figure. The link AB (link 2) is a bar that joins links 1 and 3 to form a turning pair. Any point on link 2 such as P traces out an ellipse on the surface of link 4 if links 1 and 3 glides along their respective grooves.


Figure: Elliptical Trammels

Scotch Yoke Mechanism

The purpose of this device is to transform rotary motion into reciprocating motion. The horizontal portion of link 1 slides into the fixed link 4 as the crank 3 revolves as shown in the figure. Control valve actuators in high-pressure oil and gas pipe systems are the most prevalent applications.


Figure: Scotch Yoke Mechanism

Oldham’s Coupling

An Oldham’s coupling connects two parallel shafts with axes that are separated by a little distance or do not coincide. The shafts are connected in such a way that when one rotates, the other rotates at the same rate. With link 2, links 1 and 3 create a turning pair.

Diametrical grooves have been carved into the inner sides of flanges C and D. The round disc intermediate piece (link4) contains two tongues (i.e. diametrical projections) on each face at right angles to each other. The link 4 tongues actually fit into the grooves in the two flanges (link 1 and link 3). In the slots in the flanges, link 4 can slide or reciprocate.

When the driving shaft A is rotated, the flange C (link 1) forces the intermediate piece (link 4) to rotate at the same angle as the flange, and the flange D (link 3) to revolve at the same angle, causing the shaft B to rotate. As a result, the angular velocity of links 1, 3, and 4 is constant at all times. Between link 4 and the other links 1 and 3, there is a sliding action.


Figure:Oldham’s Coupling

Important Topics for Gate Exam
Responsivity Types Of Governors
SR Flip-Flop Types Of Vibration
Norton’s Theorem Welded Joints
P N Junction Diode Round Robin Scheduling
Classless Addressing Scaling In Computer Graphics


Our Apps Playstore
SSC and Bank
Other Exams
GradeStack Learning Pvt. Ltd.Windsor IT Park, Tower - A, 2nd Floor, Sector 125, Noida, Uttar Pradesh 201303
Home Practice Test Series Premium