👉 Gear math is a fundamental concept in mechanical engineering that deals with the relationship between the rotational speeds and torques of interconnected gears. When two or more gears are meshed together, the gear ratio—the number of teeth on one gear divided by the number of teeth on another—determines how they interact. For example, a larger gear with more teeth will rotate slower than a smaller gear with fewer teeth, but it will exert more torque. This relationship is expressed as the product of the gear ratios: \( \frac{R_1}{R_2} = \frac{T_2}{T_1} \), where \( R_1 \) and \( R_2 \) are the radii (and thus number of teeth) of the gears, and \( T_1 \) and \( T_2 \) are their respective torques. This principle is crucial for designing machinery where specific speed and torque requirements need to be met, such as in automotive transmissions, robotics, and industrial equipment. Understanding gear math allows engineers to optimize gear systems for efficiency, power transmission, and mechanical advantage.
