What device is used to transmit mechanical force between two shafts while allowing them to move out of alignment?

The correct answer is the universal joint, which is specifically designed to transmit mechanical power and torque between two shafts that are not perfectly aligned. Its unique construction allows for flexibility in movement, accommodating angular misalignments caused by vibration, thermal expansion, or operational tolerances. This flexibility is crucial in many applications, such as in vehicles or machinery, where the shafts often operate at various angles relative to one another.

In contrast, while trunnions and pillow blocks serve important roles in equipment maintenance, they do not provide the same ability to transmit power across misaligned shafts. Trunnions are typically used as pivot points to allow for rotational movement in specific machinery setups, and pillow blocks primarily support and stabilize rotating shafts but do not facilitate flexibility in alignment. Thus, the universal joint stands out as the appropriate device for this specific mechanical operation.