Lecture 19 Scotch yoke mechanism as 4th Inversion of variation of Crank - Slider Mechanism OR Crank - Double slider Mechanism with Double slider (yoke) as Follower Link

Scotch yoke mechanism is a variation of Crank-Slider Mechanism.

Link - 1 =  Frame [ Originally Sliding Element ( Link - 4) / 1st Slider  

Link - 2 = Crank [Originally Frame (Link 1)] 

Link - 3 = Sliding Element [as Revised Coupler and Sliding Element other than Revised Frame / 2nd Slider = Originally Crank (Link - 2) of Crank-Slider Mechanism] 

Link - 4 =Follower Link with two slots perpendicular to each other [Originally Connecting Rod (Link - 3) of Crank-Slider Mechanism that has infinite length].

In other words 

Originally 4th link (1st  Slider) of Crank - Slider mechanism is made stationary / fixed = Frame (Revised link-1)

Original 1st link (frame) is converted into Crank (Revised 2nd Link) that connects 1st slider (Revised frame) and 2nd slider (Revised coupler)

Originally 2nd link Crank of Crank - Slider mechanism is converted into 2nd Slider and is made Revised Coupler (Revised link-3)

Originally 3rd link (coupler) is made of infinite length = Link with two slots perpendicular to each other and acts as Output / Follower link = yoke (Revised  link-4) 

Note : Output link (Yoke) is on right side to that of Input Link (Crank)

For above configuration (of links) , Scotch yoke mechanism is  th inversion of Original Crank - Slider Mechanism with 3rd link connecting rod going to infinity (that is,  Link with two slots perpendicular to each other)  and connecting rod is  redesignated as yoke and acts as Output / Follower link (link -4 )  

In other words, scotch yoke mechanism is a variation of Crank - Slider Mechanism wherein the original coupler link is made of infinite length and that originally 3rd link / connecting rod / coupler link is replaced by a "Link with two slots perpendicular to each other".

Crank  has a revolute pair with frame. 

Crank has a revolute pair with 2nd Slider /                (Originally Crank).

2nd Slider has a vertical prismatic pair with yoke.

Yoke has horizontal prismatic pair with 1st Slider as Frame.

2nd Slider of scotch yoke mechanism transforms Input Motion of rotation (with constant angular velocity) of Crank  into Output Motion of Simple Harmonic Motion [ S.H.M.] of yoke in the horizontal direction in 4th Inversion.

From above information, it is clear that Scotch yoke mechanism under consideration has link 1 that has two revolute pairs at it's either ends. Link 2 has has a revolute pair with link 1 and a prismatic pair with link 3 in vertical direction. Similarly, link 4 has a revolute pair with link 1 and a prismatic pair with link 3 along the horizontal direction.  These two prismatic pairs have an angle of 90° between them.

From such a 2R-2P, that is RRPP chain one can have different mechanism by the process of kinematic inversion. For example, one can hold this link number 4 fixed, that is, slider 1st. So one can see that Double slider / yoke ( follower) , the output link can have horizontal movement with respect to the fixed link (slider 1st) as link 1 ( link that connects 1st Slider and 2nd Slider) undergoes rotary motion with respect to frame.

Thus, scotch yoke mechanism discussed above is also the same 4th inversion of the 2R - 2P Mechanism / RRPP Mechanism.

Note : In above 2R-2P / RRPP mechanism

(1) Link with two slots perpendicular to each other and that acts as Output / Follower link named as yoke (Revised  link-4) is Double Slider.

(2) Original 1st link (frame)  of Crank - Slider Mechanism is converted into Crank (Revised 2nd Link) that connects 2nd slider ( Revised frame) and 1st slider (Revised coupler) acts as Input Link.

 So, above 4th inversion of 2R-2P / RRPP mechanism is also known as 4th inversion of Crank - Double slider Mechanism