Theory of Machine
Idler pulley is used

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

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Theory of Machine
The magnitude of velocities of the points on a rigid link is

Inversely proportional to the distance from the points to the instantaneous center and is perpendicular to the line joining the point to the instantaneous center
Directly proportional to the distance from the points to the instantaneous center and is parallel to the line joining the point to the instantaneous center
Directly proportional to the distance from the points to the instantaneous center and is perpendicular to the line joining the point to the instantaneous center
Inversely proportional to the distance from the points to the instantaneous center and is parallel to the line joining the point to the instantaneous center

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