Theory of Machine
When the addenda on pinion and wheel is such that the path of approach and path of recess are half of their maximum possible values, then the length of the path of contact is given by (where r = Pitch circle radius of pinion, R = Pitch circle radius of wheel, and φ = Pressure angle)

[(r + R) cosφ]/2
[(r + R) sinφ]/2
[(r² + R²) sinφ]/2
[(r² + R²) cosφ]/2

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Theory of Machine
In a four bar chain or quadric cycle chain

Three are turning pairs and one is a sliding pair
One is a turning pair and three are sliding pairs
Each of the four pairs is a turning pair
Two are turning pairs and two are sliding pairs

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