Lecture 17 Scotch Yoke Mechanism - a variation of Crank - Slider Mechanism

(a) 4th Inversion

(b) 2nd Inversion

      Scotch yoke mechanism is a variation of Crank - Slider Mechanism (Variation of 2nd Geometric Motion Transformation of Four bar linkage / (planar) mechanism with coupler of infinite length and follower as sliding element) 

Note: 

Link - 1 = Frame [Originally Sliding Element (1st Slider) / Link 4) in 4th Inversion.

And

Link - 1 = Frame [Originally Sliding Element (2nd Slider) / Link 2)  ] in 2nd Inversion.

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

Link - 3 = Sliding Element (as Revised Coupler and Sliding Element other than Revised Frame / 2nd Slider) in 4th Inversion

And

Link - 3 = Sliding Element (as Revised Coupler and Sliding Element other than Revised Frame / 1st Slider) in 2nd Inversion

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

In other words

Originally 4th link =1st Slider is fixed / made Stationary  = Frame (Revised link-1) in 4th Inversion

And 

Originally 2nd link =2nd Slider is fixed / made Stationary  = Frame (Revised link-1) in 2nd Inversion

Originally 1st link Frame is converted into Input Link = Crank (Revised link-2)

Originally 2nd link (crank) is converted into 2nd  Slider [(Revised link-3) as Coupler Link] in 4th inversion

And 

Originally 4th link (slider) is converted into 1st Slider [(Revised link-3) as Coupler Link] in 2nd inversion

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)

Scotch yoke mechanism is 2nd inversion as well as 4th 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 3rd link ( coupler link) is made of infinite length and 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) / 1st Slider, respectively, in (4th Inversion) / 2nd inversion.

2nd Slider / 1st Slider , respectively, in both  2nd inversion and 4th Inversion has a , respectively, vertical prismatic pair / horizontal prismatic pair with yoke (follower link).

Yoke has horizontal prismatic pair/ vertical prismatic pair with Frame (link-1), respectively, in 4th inversion / 2nd inversion .

2nd Slider / 1st Slider ( as Motion Transfer Link / Coupler Link), respectively, in 4th Inversion / 2nd inversion of scotch yoke mechanism transforms Input Motion of rotation (with constant angular velocity) of Crank [Input Link] into Output Motion of Simple Harmonic Motion [ S.H.M.] of yoke [Follower Link / Output Link] in the horizontal direction/ vertical direction, respectively.

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 / 2 fixed, that is, slider 1st / 2nd . So one can see that Double slider / yoke ( follower) , the output link can have horizontal movement / vertical movement with respect to the fixed link (slider 1st / 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 4th inversion / 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 4th inversion / 2nd inversion of 2R-2P / RRPP mechanism is also known as 4th inversion / 2nd inversion of Crank - Double slider Mechanism

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.

3. Explain the primary function of a Scotch-Yoke mechanism and the specific type of motion it produces.

Answer Key

3. A Scotch-Yoke mechanism is used to convert uniform rotary motion into simple harmonic translatory motion. Unlike a slider-crank mechanism which produces periodic but not purely harmonic motion, the Scotch-Yoke's output is a pure simple harmonic motion, represented by the equation x = L₂ cos(ωt).