Explanation:

Transmission dynamometers are devices used to measure the torque and power output of a transmission system. They are typically used in automotive and industrial applications to test and evaluate the performance of transmissions.

Transmission dynamometers can be classified into several types based on their operating principles and construction. The options provided in the question are hydraulic dynamometer, Prony brake dynamometer, and rope brake dynamometer. However, none of these options is correct for a transmission dynamometer.

- Hydraulic dynamometer: A hydraulic dynamometer uses fluid pressure to measure torque. It typically consists of a rotor and a stator with vanes or blades. As the fluid flows through the rotor, it causes the rotor to rotate, and the torque can be measured based on the fluid pressure and flow rate. While hydraulic dynamometers are commonly used for measuring torque in various applications, they are not specifically designed for transmission testing.

- Prony brake dynamometer: A Prony brake dynamometer uses friction between a brake shoe and a rotating shaft to measure torque. It consists of a brake shoe that is pressed against the shaft, creating a frictional force. The torque can be measured based on the force applied and the radius of the shaft. Prony brake dynamometers are often used for testing small engines and motors but are not suitable for transmission testing.

- Rope brake dynamometer: A rope brake dynamometer uses a rope wound around a drum to measure torque. The rope is attached to the output shaft of the transmission, and as the shaft rotates, it causes the drum to rotate. The torque can be measured based on the tension in the rope and the radius of the drum. Rope brake dynamometers are commonly used for testing small engines and motors, but they are not specifically designed for transmission testing.

In conclusion, none of the options provided (hydraulic dynamometer, Prony brake dynamometer, and rope brake dynamometer) are suitable for measuring torque and power output in a transmission system. Transmission dynamometers are specialized devices designed specifically for testing and evaluating transmissions.