Leverage - Speed Ratio

Speed Ratio

The requirement for power input to an ideal mechanism to equal power output provides a simple way to compute mechanical advantage from the input-output speed ratio of the system.

Power is the product of force and velocity. The power input to a gear train with a torque T_A applied to the drive pulley which rotates at an angular velocity of ω_A is P=T_Aω_A.

Because the power flow is constant, the torque T_B and angular velocity ω_B of the output gear must satisfy the relation

which yields

This shows that for an ideal mechanism the input-output speed ratio equals the mechanical advantage of the system. This applies to all mechanical systems ranging from robots to linkages.