Theory of Machine
Idler pulley is used

All of the listed here
For applying tension
For increasing velocity ratio
For changing the direction of motion of the belt

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Theory of Machine
In the below figure, PC is the connecting rod and OC is the crank making an angle θ with the line of stroke PO and rotates with uniform angular velocity at ω rad/s. The Klien's acceleration diagram for determining the acceleration of the piston P is shown by quadrilateral CQNO, if N coincides with O, then

Acceleration of the piston P is zero and its velocity is maximum
Acceleration and velocity of the piston P is zero
Acceleration and velocity of the piston P is maximum
Acceleration of the piston P is maximum and its velocity is zero

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