Lecture 21 Oldham Shaft Coupling : 1st Inversion of variation of Crank - Slider Mechanism OR Double Crank Mechanism ( Crank - Crank Mechanism) with Double Slider in the form of cylindrical disc as Coupler Link.

The first inversion of variation of Crank - Slider Mechanism OR Double Crank Mechanism (with Double slider as Coupler Link) is obtained by fixing the link that has revolute pair at both ends . 

The  coupler link-3 ( Double slider)  has a prismatic pair (P4) in the horizontal direction with link 4 (1st slider) and prismatic pair (P3) in a vertical direction with link 2 (2nd slider). 

So, thus if one rotate link 2 (2nd slider) which is in translation with couplar link 3 ( Double Slider ) which is again in translation with link 4 ( 1st slider of 2R2P mechanism / Original Slider of  Crank - Slider Mechanism). 

Thus link 4 ( 1st slider) and link 2 ( 2nd slider) have only relative translatory Motion. 

In other words, they have the same angular motion. 

Thus, this mechanism known as Oldham coupling can be used to connect two parallel shafts: one at O2 ( vertical direction) and other at O1 ( horizontal direction) and transmitting unity angular velocity ratio.

In other words, the first inversion of Crank - Double slider - Crank Mechanism is obtained by fixing the connecting link between two sliders. 

Link - 2 (2nd slider) may also rotate about O2 and Link -4 (1st slider) may rotate about O1. 

If 2nd link (2st slider) is rotated through a definite angle, then couplar link - 3 ( Double Slider) and the other slider (1st) / link 4 must rotate through the same angle, and, as rotation takes place, the couplar link -3 (Double Slider) will slide relative to each of the two sliders (1st and 2nd).

The 'Oldham shaft coupling' is an example of this inversion.

Kinematic links of Oldham shaft coupling :

Fixed link = Frame = Connecting link between 1st Slider( link - 4) and 2nd Slider( link - 2) 

Input Shaft / Driving Crank = Driving Shaft with 1st Sliding element (half coupling) /    link - 2 / 2nd Slider

Couplar Link = Double Slider = cylindrical disc with a tounge passing diametrically across each face and the two tongues at right angles to each other

Output Shaft / Driven Crank = Sliding element 2nd (half coupling) plus Driven Shaft / 
link - 4 / 1st Slider

Kinematic pairs of Oldham shaft coupling :

There is a revolute pair (O2) between link 1 (frame) and link 2 (Input Shaft / Slider 2nd).

There is a prismatic pair (P3) between the single groove cut diametrically across the face of half coupling of Input shaft (slider 2nd / link-2) and the first protruding tounge passing diametrically across one face of couplar link / link -3 (Double slider) opposite to that of face of half coupling of Input Shaft.

There is a prismatic pair (P4) between the second protruding tounge passing diametrically across the other face (opposite to that of first face) of couplar link / link -3 (Double Slider) and the single groove cut diametrically across the face of half coupling of Output shaft (slider 1st).

There is a revolute pair (O1) between link 1 (frame) and link 4 (Output Shaft / Slider 1st).
Note : 

The first protruding tounge passing diametrically across one face of couplar link / link -3 (Double Slider) and the second protruding tounge passing diametrically across its opposite to first face are perpendicular to each other.





Geometric Motion characteristics of various kinematic links of Oldham shaft coupling:

Input Motion = Rotation of Input Shaft with Slider 2nd (half coupling) with respect to frame (Originally link - 1)

Relative motion between the single groove cut diametrically across the face of half coupling of Input shaft (slider 2nd / link-2) and first protruding tounge passing diametrically across one face of couplar link / link -3 (Double slider) opposite to that of face of half coupling of Input Shaft is that of sliding.

Relative motion between second protruding tounge passing diametrically across the other face of couplar link / link -3 / Double Slider ( that is perpendicular to first tounge passing diametrically across its opposite first face) and the single groove cut diametrically across the face of half coupling of Output shaft (slider 1st) is also that of sliding.

Output Motion = Rotation of Output Shaft with Slider 1st (half coupling) with respect to frame (Originally link - 1)

Oldham shaft coupling is used for transmitting constant angular velocity between two parallel but eccentric shafts.

Study Guide for Four-Link Planar Mechanisms

Quiz: Short-Answer Questions

Answer the following question in 2-3 sentences each, based on the provided source material.

4. What is the purpose of an Oldham's coupling, and what is its main practical limitation?

Answer Key

4. An Oldham's coupling is a mechanism used to connect two parallel shafts and transmit a unity angular velocity ratio, meaning both shafts rotate at the same speed. Its main limitation is that it is only efficient when the offset between the shafts is not very large, as significant power is lost to friction in the two prismatic pairs.