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### Scotch Yoke Mechanism Design Equations and Calculator

Machine Design and Mechanics

Scotch Yoke Mechanism Design Equations and Calculator

This is an example of a Scotch Yoke mechanism for sine and cosine functions. The Scotch Yoke is a mechanism for converting the linear motion of a slider into rotational motion of a crank or vice-versa. The slider part is directly coupled to a reciprocating yoke with a slot that engages a pin on the rotating part, as shown below.

Preview: Scotch Yoke Mechanism Calculator

Scotch Yoke Mechanism Design Equations

Displacement in the Y Axis Equation
Y = C sin α

Crank Arm Length for Required Displacment
C = Y / sin α

Displacement in the X Axis Equation
X = C cosα

Displacement in the X Axis Equation
C = X / cos α

Where:

Y = Displacement in the Y Axis (in, mm)
X = Displacement in the X Axis (in, mm)
α = Angle of Rotation (degrees)

Application Examples Scotch Yoke Mechanism

Cardan gearing and a Scotch yoke in combination provide an adjustable stroke. The angular position of the outer gear is adjustable. The adjusted stroke equals the projection of the large diameter, along which the drive pin travels, on the Scotch-yoke’s centerline. The yoke motion is simple harmonic.

Reference:
Handbook of Machining and Metal Working Calculations, Ron A. Walsh 2001
Forming and Forging Manual, ASM
Air Engines Theodor Finkelstein