Lecture 18 Scotch yoke mechanism as 2nd 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 2) / 2nd Slider]

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

Link - 3 = Sliding Element  [as Revised Coupler and Sliding Element other than Revised Frame / 1st Slider = Originally Slider (Link - 4) 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

2nd Slider (Originally 2nd link Crank of Crank -Slider Mechanism is converted into 2nd slider) is made stationary / fixed = Frame (Revised link-1)

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

Originally 4th link (1st  Slider) of Crank - Slider mechanism 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  2nd 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 original slider (1st Slider) .

1st Slider has a horizontal prismatic pair with yoke.

Yoke has vertical prismatic pair with 2nd Slider as Frame.

1st 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 vertical direction in 2nd 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 4 has a revolute pair with link 1 and a prismatic pair with link 3 along the horizontal direction. Similarly link 2 has has a revolute pair with link 1 and a prismatic pair with link 3 in vertical 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 2 fixed, that is, slider 2nd. So one can see that Double slider / yoke ( follower) , the output link can have vertical movement with respect to the fixed link (slider 2nd) 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 2nd 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 2nd inversion of 2R-2P / RRPP mechanism is also known as 2nd inversion of Crank - Double slider Mechanism