In what scenario does a gyro have two degrees of freedom?

A gyro has two degrees of freedom when it is supported by two gimbal rings. This configuration allows the gyro to rotate freely along two axes, providing greater flexibility in its movement compared to a single gimbal system. The two gimbals permit the gyro to maintain its orientation in space while being able to navigate movements such as pitch and yaw, which are essential for maintaining balance and stabilizing direction.

In this setup, the inner gimbal allows for rotation around one axis, while the outer gimbal provides rotation around a perpendicular axis. This setup is crucial for applications where orientation and stability are needed, such as in inertial navigation systems and various aerospace technologies.

Other configurations, such as a gyro mounted on a single gimbal ring, restrict movement to just one axis and therefore would not provide two degrees of freedom. Conversely, the use of three gimbal rings allows for three degrees of freedom, enabling rotation around all three axes. A gyro fixed to a frame would eliminate freedom of movement altogether, restricting it to zero degrees of freedom.