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How are mechanical advantage and velocity ratio related in a machine?

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A diagram displays six types of simple machines with labeled illustrations: inclined plane, wedge, screw, lever, wheel and axle, and pulley, each shown with real-world examples like ramps, axes, screws, seesaws, door handles, and pulleys lifting objects. — simple machine Six simple machines for transforming energy into work.

In a machine, mechanical advantage (MA) and velocity ratio (VR) represent two fundamental, inseparable functions: force modification and motion modification, respectively.1

Mechanical advantage is the ratio of the output force (load) to the input force (effort), while the velocity ratio is the ratio of the input motion to the output motion. When a machine operates with high efficiency, these two ratios are approximately equal. This relationship illustrates a core principle of mechanics: what is gained in force is lost in motion.1

While friction reduces the actual mechanical advantage compared to the theoretical value, it generally does not affect the velocity ratio. Because work output is always less than work input due to energy losses from friction, the efficiency of a machine is always less than 100 percent.12