When one of the links of a kinematic chain is fixed, the chain is known as a mechanism. It may be used for transmitting or transforming motion e.g. engine indicators, typewriters, etc.
A mechanism with four links is known as a simple mechanism, and the mechanism with more than four links is known as a compound mechanism. When a mechanism is required to transmit power or to do some particular type of work, it then becomes a machine. In such cases, the various links or elements have to be designed to withstand the forces (both static and kinetic) safely.
A little consideration will show that a mechanism may be regarded as a machine in which each part is reduced to the simplest form to transmit the required motion.
Single Slider Crank Chain
A single slider crank chain is a modification of the basic four-bar chain. It consist of one sliding pair and three turning pairs. It is, usually, found in reciprocating steam engine mechanism. This type of mechanism converts rotary motion into reciprocating motion and vice versa. In a single slider crank chain, as shown the links 1 and 2, links 2 and 3, and links 3 and 4 form three turning pairs while the links 4 and 1 form a sliding pair.
Link 1 corresponds to the frame of the engine, which is fixed. The link 2 corresponds to the crank; link 3 corresponds to the connecting rod and link 4 corresponds to cross-head. As the crank rotates, the cross-head reciprocates in the guides and thus the piston reciprocates in the cylinder.
We have already discussed that when one of the links is fixed in a kinematic chain, it is called a mechanism. So we can obtain as many mechanisms as the number of links in a kinematic chain by fixing, in turn, different links in a kinematic chain. This method of obtaining different mechanisms by fixing different links in a kinematic chain is known as inversion of the mechanism.
Inversion Definition :
When one of the links is fixed in a kinematic chain, it is called a mechanism. So we can obtain as many mechanisms as the number of links in a kinematic chain by fixing, in turn, different links in a kinematic chain. This method of obtaining different mechanisms by fixing different links in a kinematic chain is known as inversion of the mechanism. Or A Mechanism is a Kinematic Chain with one Fixed Link. The Fixed Link is called Frame. Different Mechanism is obtained by fixing different link in a kinematic chain. The process of choosing the different links in a kinematic chain for the frame is known as Inversion. Thus by fixing one by one links of the mechanism, we can obtain the inversion.
It may be noted that the relative motions between the various links are not changed in any manner through the process of inversion, but their absolute motions (those measured concerning the fixed link) may be changed drastically.
Types of inversion
1. Four bar chain or quadric cycle chain
Coupling rod of locomotive
Watt’s indicator mechanism
2. Single slider crank chain
Bull engine or pendulum engine
Oscillating cylinder engine
Crank & slotted quick return mechanism
Whitworth quick return mechanism
3. Double slider crank
Scotch yoke mechanism
1) Bull engine or pendulum engine:
In this mechanism, the inversion is obtained by fixing the cylinder or link 4 (i.e. sliding pair), as shown in Fig. In this case, when the crank (link 2) rotates, the connecting rod (link 3) oscillates about a pin pivoted to the fixed link 4 at A and the piston attached to the piston rod (link 1) reciprocates. The duplex pump which is used to supply feed water to boilers have two pistons attached to link 1, as shown in Fig.
2) Oscillating Cylinder Engine;
The arrangement of oscillating cylinder engine mechanism, as shown in Fig. is used to convertreciprocating motion into rotary motion. In this mechanism, the link 3 forming the turning pair is fixed. Link 3 corresponds to the connecting rod of a reciprocating steam engine mechanism. When the crank (link 2) rotates, the piston attached to the piston rod (link 1) reciprocates and the cylinder (link 4) oscillates about a pin pivoted to the fixed link at A.
Animation Of Oscillatory Engine :
3) Rotary Engine :
Sometimes back, rotary internal combustion engines were used in aviation. But nowadays gas turbines are used in its place. It consists of seven cylinders in one plane and all revolves about fixed center D, as shown in Fig. while the crank (link 2) is fixed. In this mechanism, when the connecting rod (link 4) rotates, the piston (link 3) reciprocates inside the cylinders forming link 1.
4) Elliptical trammels:
It is an instrument used for drawing ellipses. This inversion is obtained by fixing the slotted plate (link 4). The fixed plate or link 4 has two straight grooves cut in it, at right angles to each other. The link 1 and link 3, are known as sliders and form sliding pairs with link 4. The link A B (link 2) is a bar that forms a turning pair with links 1 and 3.
5) Scotch yoke mechanism:
This mechanism is used for converting rotary motion into a reciprocating motion. The inversion is obtained by fixing either the link 1 or link 3. In this, link 1 is fixed. When the link 2 (which corresponds to crank) rotates about B as center, the link 4 (which corresponds to a frame) reciprocates. The fixed link 1 guides the frame.
Animation Of Scotch Yoke Mechanism :
6) Oldham’s coupling:
An Oldham’s coupling is used for connecting two parallel shafts whose axes are at a small distance apart. The shafts are coupled in such a way that if one shaft rotates, the other shaft also rotates at the same speed. This inversion is obtained by fixing the link 2, the shafts to be connected have two flanges (link 1 and link 3) rigidly fastened at their ends by forging.
Animation Of Oldham’s Coupling :
6) Beam Engine :
Construction of Beam Engine:
A part of the mechanism of a beam engine (also known as crank and lever mechanism) which consists of four links. Crank AB Connected to link 3. Link 3 is connected to Link 4 which is the lever and centrally pivoted at point D. At the other end of the lever, the Piston rod is connected.
Working of Beam Engine:
In this mechanism, when the crank rotates about the fixed center A, the lever oscillates about a fixed center D. The end E of the lever CDE is connected to a piston rod which reciprocates due to the rotation of the crank. In other words, the purpose of this mechanism is to convert rotary motion into reciprocating motion.
Animation Of Beam Engine :
7. Whitworth quick return motion mechanism.
This mechanism is mostly used in shaping and slotting machines. In this mechanism, the link CD (link 2) forming the turning pair is fixed, as shown in Fig. Link 2 corresponds to a crank in a reciprocating steam engine. The driving crank CA (link 3) rotates at a uniform angular speed. The slider (link 4) attached to the crank pin at A slides along the slotted bar PA (link 1) which oscillates at a pivoted point D. The connecting rod PR carries the ram at R to which a cutting tool is fixed. The motion of the tool is constrained along the line RD produced, i.e. along a line passing through D and perpendicular to CD. from the position DP1 to DP2) through an angle α in the clockwise direction, the tool moves from the left-hand end of its stroke to the right-hand end through a distance 2 PD. Now when the driving crank moves from the position CA2 to CA1 (or the link DP from DP2 to DP1 ) through an angle β in the clockwise direction, the tool moves back from the right-hand end of its stroke to the left-hand end.
It is seen that the time taken during the left to right movement of the ram (i.e. during forward or cutting stroke) will be equal to the time taken by the driving crank to move from CA1 to CA2. Similarly, the time taken during the right to left movement of the ram (or during the idle or return stroke) will be equal to the time taken by the driving crank to move from CA2 to CA1. Since the crank link CA rotates at uniform angular velocity therefore time taken during the cutting stroke (or forward stroke) is more than the time taken during the return stroke. In other words, the mean speed of the ram during cutting stroke is less than the mean speed during the return stroke.
Some questions related to Inversion of Mechanism asked in Gate, IES Exam :
A. Which of the following pairs are correctly matched? Select the correct answer using the codes given below the pairs.
1. Whitworth quick return motion….. Single slider crank chain 2. Oldham’s coupling……………….. Four bar chain 3. Scotch Yoke……………………….Double slider crank chain
Codes: (a) 1 and 2 (b) 1, 2 and 3 (c) 1 and 3 (d) 2 and 3
B. Which one of the following mechanisms represents an inversion of the single slider crank chain?
C. In order to draw the acceleration diagram, it is necessary to determine the Corioli’s component of acceleration in the case of (a) crank and slotted lever quick return mechanism (b) slider-crank mechanism
(c) four-bar mechanism
D. Which mechanism produces intermittent rotary motion from continuous rotary motion?
(a) Whitworth mechanism
(b) Scotch Yoke mechanism (c) Geneva mechanism
(d) Elliptical trammel
E. Which of the following are inversions of a double slider crank chain? 1. Whitworth return motion
2. Scotch Yoke 3. Oldham’s Coupling
4. Rotary engine Select the correct answer using the codes given below: Codes: (a) 1 and 2 (b) 1, 3 and 4 (c) 2 and 3 (d) 2, 3 and 4
Ans. (c) Double Slider Crank mechanism
It has four binary links, two revolute pairs, two sliding pairs. Its various types are: 1. Scotch Yoke mechanism 2. Oldhams Coupling 3. Elliptical Trammel
F. Which of the following are the inversions of the double slider crank mechanism? 1. Oldham coupling
4. Elliptic trammel mechanism Select the correct answer from the codes given below.- Codes: (a) 1 and 2 (b) 1 and 4 (c) 1, 2 and 3 (d) 2, 3 and 4
Ans. (b) The inversions of the double slider crank mechanism are (i) First inversion-Elliptic Trammel, (ii) Second inversion-Scotch Yoke (iii) Third inversion-Oldham’s coupling Thus out of choices given, only 1 and 4 are correct.
G. The Whitworth quick return mechanism is formed in a slider-crank chain when the (a) coupler link is fixed
(b) longest link is a fixed link (c) slider is a fixed link
(d) smallest link is a fixed link
H. Geneva mechanism is used to transfer components from one station to the other in (a) an inline transfer machine
Sachin is a B-TECH graduate in Mechanical Engineering from a reputed Engineering college. Currently, he is working in the sheet metal industry as a designer. Additionally, he has interested in Product Design, Animation, and Project design. He also likes to write articles related to the mechanical engineering field and tries to motivate other mechanical engineering students by his innovative project ideas, design, models and videos.