Gear train

**Basic Concepts of Gear Trains**:
– Gear teeth designed based on the radius of the pitch circle.
– Speed ratio computed from radii and number of teeth.
– Mechanical advantage determined by the number of teeth.
– Gear trains amplify or reduce torque based on the number of teeth.
– Power transmitted from input gear to output gear.
– Gear teeth designed for smooth rolling without slipping or jamming.

**Analysis and Formulas**:
– Analysis using virtual work for gear trains with one degree of freedom.
– Mechanical advantage as the ratio of output torque to input torque.
– Ratios of angular velocities, radii, and number of teeth equal in gear trains.
– Gear ratio in a simple gear train with two gears determined by the number of teeth.
– Total reduction in double reduction gear sets calculated by multiplying reductions of each stage.

**Gear Train Components and Operations**:
– Gear trains consist of input (drive gear) and output (driven gear).
– Gear ratio inversely proportional to the radius and number of teeth.
– Torque ratio equal to the gear ratio.
– Idler gears used to reverse direction or transmit rotation among distant shafts.
– Idler gears ensure the same direction of rotation for driver and driven gear.

**Automotive Applications**:
– Gear sets utilized in various areas of automobile drivetrains.
– Gear trains crucial for transmission systems in internal combustion engine vehicles.
– Gear ratios carefully designed for optimal performance in automotive engineering.
– Gear ratios in transmission: 1st gear – 2.97:1, 2nd gear – 2.07:1, 3rd gear – 1.43:1, 4th gear – 1.00:1, 5th gear – 0.84:1.
– Axle ratio and differential play a role in multiplying with transmission ratio.

**Calculation and Performance**:
– Formulas available to calculate speed based on tire circumference and gear ratios.
– Wide-ratio vs. close-ratio transmission impact on gear ratios.
– Speed calculations in inches per minute can be converted to mph.
– Progression impacts RPM drop between gears in different ratio transmissions.
– Understanding ring and pinion gears and conversion formula for in/min to mph.