What would be the result if the sun gear is held, the carrier is the input number, and the ring is the output member?

When the sun gear is held stationary, the carrier is used as the input, and the ring gear serves as the output, the mechanism of the automatic transmission results in a gear reduction. This occurs because when force is applied to the carrier, it rotates while the sun gear remains fixed. As the carrier rotates, this causes the ring gear to turn at a slower speed relative to the carrier.

In this configuration, the input speed at the carrier is effectively reduced at the output (the ring gear), which means that the output speed is less than the input speed. The ratio of the gear reduction is determined by the sizes of the gears involved, specifically the number of teeth on the sun gear versus the number of teeth on the ring gear. This principle is a fundamental characteristic of gear systems and is utilized in various automatic transmission designs to optimize power and performance while maintaining the engine's operational efficiency.

Other configurations, like direct drive, overdrive, or reverse, would involve different arrangements of input and output with various gear interactions, which are not the case here. In this situation, because the mechanism is set up to reduce speed rather than change direction or maintain speed, gear reduction is the correct outcome.