inversions of single slider-crank chain

INVERSIONS OF SINGLE SLIDER-CRANK CHAIN

• From a single slider-crank chain, four different inversions can be obtained by fixing its four links one at a time in turn.

• Table 1.5 shows the inversions of single slider-crank mechanism and their important applications.

Table 1.5. Inversion of single slider-crank chain and their applications

1. First Inversion

• First inversion is obtained when the link 1 (i.e., frame) is fixed and links 2 and 4 are made the crank and the slider respectively, as shown in Fig.1.34. The mechanism thus obtained is known as crank-slider mechanism.

• Applications: 1. Reciprocating engine

(a) Internal combustion engine

(b) Steam engine

2. Reciprocating compressor

3. Reciprocating pump

1. Reciprocating Engine and Reciprocating Compressor

• In both reciprocating engine and reciprocating compressor, the link 1 (i.e., frame) is fixed.

• In reciprocating engine (i.e., in IC engine/steam engine), the link 4 (i.e., the slider) is the driver and the link 2 (i.e., crank) becomes the driven, as shown in Fig. 1.34(a).

• In reciprocating compressor/reciprocating pump, the link 2 (i.e., the crank) is the driver and the link 4 (i.e., slider) becomes the driven, as shown in Fig. 1.34(b).

2. Second Inversion.

• Second inversion is obtained by fixing the link 2 (i.e., crank) of a slider-crank chain.

• As shown in Fig.1.35, when the link 2 is fixed, then the link 3 along with the slider at its end B becomes a crank. This makes link 1 to rotate about O along with the slider which also reciprocates on it.

Applications:

1. Whitworth quick-return mechanism, and

2. Rotary engine.

1. Whitworth Quick-Return Mechanism

• Whitworth quick-return mechanism is used in shaping and slotting machines to cut metals. The forward stroke cuts the metals whereas the return stroke is idle. Also the return stroke is quicker than the forward stroke

• In this mechanism, link 2 (i.e., crank) is fixed, link 3 rotates, link 4 reciprocates and link 1 oscillates as shown in Fig.1.36. The link 3 along with its slider (link 4) rotates in a circle about B. By doing so, the link 1 rotates about A along with the slider which reciprocates on link 1. On the other end of the link 1, there is a point D where link 5 is connected. The other end of link 5 is connected to the ram and tool (link 6). The point D rotates in a circle about point A.

• Forward (or cutting) stroke: Initially, let the slider 4 be at point C₁, then the point D will be at D₁ and hence the tool will be in its extreme left position. As the crank (link 3) rotates counter-clockwise from BC₁ to BC and then BC₂, the point D will move from D₁ to D and then to D₂; as a result, the tool i.e., link 6 will move from E₁ to its extreme right position E₂. The distance between extreme left and right positions is the stroke length. The movement of tool 6 from E₁ to E₂ is known as forward stroke or cutting stroke. The time taken for the forward stroke of tool 6 is proportional to the angle a (i.e., obtuse angle C₁BC₂).

• Return stroke: When the crank further rotates counter-clockwise from BC₂ to BC₁, the point D will move from D₂ to D₁; as a result, the tool will move from E₂ to its extreme left position E₁. The movement of tool from E₂ to E₁ is known as return stroke or backward stroke. The time taken for the return stroke of tool 6 is proportional to the angle B (i.e., acute angle of C₂BC₁).

• Since the driving crank BC rotates at uniform angular speed (N), we can write

• Now the ratio of cutting stroke to return stroke time (β) is given by

• As α is always greater than 180°, therefore ratio (α/360° - α) will be always greater than 1. It means, the time required for cutting stroke is greater than return stroke. Since this mechanism achieves return stroke quicker than the forward stroke, it is called as quick- return mechanism.

Note In Whitworth quick-return mechanism, length of stroke E₁ E₂ = 2 AD.

2. Rotary Engine (or Gnome) Engine

• Rotary engine, also known as Gnome engine, is a multi-cylinder rotary internal combustion engine. It is also known as V-type engine.

• This type of rotary engine was used in the past as an aero-engine, but now it has been replaced by gas turbines.

• In a rotary engine, as shown in Fig. 1.37, the slider is replaced by a piston and link 1 by a cylinder pivoted at O. Moreover, instead of one cylinder, odd number of cylinders (e.g., five or seven cylinders) symmetrically placed at regular intervals in the same plane.

• The link 2 (i.e., crank OC) is fixed and is common to all cylinders.

• When the fuel burns inside the cylinders, the pistons reciprocate in the cylinders and at the same time the whole assembly of bylinders, pistons and connecting rods rotate about O. The entire mechanical power developed can be obtained in the form of rotation of crank shaft.

• Thus from Fig. 1.37, it will be seen that each piston, connecting rod and cylinder form with the fixed crank OC an inversion of the slider-crank chain.

3. Third Inversion

• Third inversion is obtained by fixing the link 3 of the slider-crank mechanism, as shown in Fig. 1.38. In this, link 2 again acts as a crank and link 4 oscillates.

• Applications: 1. Oscillating cylinder engine, and

2. Crank and slotted lever mechanism.

1. Oscillating Cylinder Engine

• The oscillating cylinder engine mechanism is used to convert reciprocating motion into rotary motion, as shown in Fig.1.39.

• In this mechanism, link 3 is fixed. When the link 2 (crank) rotates, the piston attached to

link 1 (piston rod) reciprocates and the link 4 (cylinder) oscillates about a pin pivoted to the fixed link A.

2. Crank and Slotted Lever Quick-Return Motion Mechanism

• The crank and slotted lever quick-return motion mechanism is mostly used in shaping and slotting machines. This mechanism is also obtained by fixing the link 3, as shown in Fig.1.40.

• In this mechanism, link 1 is a slider which slides in a slotted lever (link 4); link 3 is fixed and link 2 is crank which rotates in clockwise direction about point A in a circle and as a result, the link 4 oscillates about the point O. The link 5 transmits the motion from link OC to ram which carries the tool.

• As shown in Fig.1.40, the extreme positions OC₁ and OC₂ are tangential to the circle. The cutting stroke and return stroke occurs when crank moves from E₁ to E₂ and E₂ to E₁ respectively. This will occur when crank AB moves from B₁ to B₂ through α angle for cutting stroke and from B₂ to B₁ through β angle for return stroke.

• Since driving crank rotates at uniform angular speed, we can write

Time for cutting stroke = α/2π N

and Time for return stroke = β /2π N

• The ratio of cutting stroke to return stroke time (Q) will be given by

Since β is less than α, the time required for return stroke is less than cutting stroke. Thus this mechanism is also called quick-return mechanism.

Note

In crank and slotted level quick-return mechanism, the travel of the tool or length of stroke 

4. Fourth Inversion

• Fourth inversion is obtained by fixing the link 4 of the slider-crank mechanism, as shown in Fig.1.41.

• In this inversion, link 3 can oscillate about the fixed pivot B on link 4. This makes end A of link 2 to oscillate about B and end O to reciprocate along the axis of the fixed link 4.

• Applications:

1. Pendulum pump (or Bull engine), and

2. Hand pump.

1. Pendulum Pump (or Bull Engine)

• This mechanism is used to supply feed water to boilers.

• This mechanism is obtained by fixing the link 4 (i.e., cylinder), as shown in Fig.1.42. In this case, when tink 2 (crank) rotates, link 3 (connecting rod) oscillates like a pendulum about a pin pivoted to the fixed link 4 at A and link 1 reciprocates. This reciprocating motion of link 1 can be used for a pump.

2. Hand Pump

• Hand pump mechanism is also obtained by fixing the link 4.

• Figs. 1.43(a) and (b) show the hand pump mechanism in which link 1 reciprocates vertically in fixed link 4, at the same time link 2 and link 3 will oscillate about the pin joint O₁ and O₂ respectively.