# Inversion of Double Slider Crank Chain

Double slider crank shaft has two sliding pairs and two turning pairs.
It is named Double Slider Crank Shaft because it has two sliding pairs.
It has two sliders, one frame in which the slider moves and one link which connects the two slide and fix the distance between the two slider.The frame in which the sliders move is a combination of two straight grooves which form a single link and cut each other at right angle.

In different inversion of double slider crank chain :-
i) The frame is Link 1.
ii) First Slider is Link 2.
iii) The bar connecting two slider is Link 3.
iv) Second Slider is Link 4.

There are three important inversions of double slider crank chain. These three are :-
1) Elliptical Trammels
2) Scotch Yoke Mechanism
3) Oldham’s Coupling

Lets see these three inversions in details :-

### 1) Elliptical Trammels :-

This type of inversion is used to draw ellipse. It is also known as Trammel of Archimedes. It can be used to draw ellipse of different sizes. In this inversion Link 1 i.e the frame which is is fixed. Both the sliders Link 2 and Link 4 moves in the grooves of this frame. One slider moves vertically and other slider moves horizontally. The connecting rod Link 3 which connects two sliding bars Link 2 and Link 4 make the motion of these sliding bars constrained. While the two slider moves, the each point in the connecting rod is the locus of an ellipse. Different point in connecting rod will draw a different elllipse.

### 2) Scotch Yoke Mechanism :-

This inversion transforms rotational motion into reciprocating motion.
In this inversion, one of the sliding bars Link 2 or Link 4 is fixed . Let us fx Link 2. As one of the sliding bar is fixed i.e Link 2, the other sliding bar Link 4 can slide, the frame i.e Link 1 can move and the connected rod Link 3 can move. Now , the other slider will rotate around the fixed slider and will draw a circle if its path is traced.The frame or the slotted plate will move to and fro if the horizontal moving slider is fixed and frame will move upward and downward if the the vertical moving slider is fixed.

### 3) OLDHAM’S COUPLING :-

Oldham’s Coupling is used to connect two shafts whose axis are small disatance apart from each other and make them rotate at equal speed.

In this inversion the connecting rod which connects the two bars is fixed i.e Link 3 is fixed . In this inversion the frame i.e Link 1 which have grooves starts rotating as well as the sliders i.e Link 2 and Link 4 also starts rotating as they form turning pair with the connecting rod which is Link 3.

This inversion forms Oldham’s Coupling. Now we will discuss how this is used to connect two shafts whose axis are little apart from each other. These shafts are coupled in such a way that if one shaft rotates, the other shaft also rotates with the same speed.

Image Source : https://www.youtube.com/watch?v=Y5lsvb_gq4o

Two flanges are placed at the end of the two shafts which are to be connected. These flanges are rigidly fastened at the end by forging. Both flanges have grooves . The groove of both flange are perpendicular to each other.
Between these two flanges a central flange is inserted which fits into the grooves of both flanges . In this coupling, the frame which is link 3 is fixed, driving shaft and driving flange for Link 2, Intermediate flange is Link 1 and driven shaft and flange form Link 4.
When the first shaft i.e driving shaft rotates the flange forged to it also rotates and then the central flange placed in the groove of driving flange starts rotating. Then the driven flange also start rotating as center flange is also fixed at the groove of driven flange and as the driven flange rotates, the driven shaft also starts rotating at same speed.