What consists of two cranks and a stationary piece called the line of centers connected by a connecting rod?

The correct answer is grounded in the fundamental components of what constitutes a four-bar linkage. A four-bar linkage consists of four links: two cranks (which are typically connected to the input and output), a connecting rod, and a stationary frame or ground link known as the line of centers.

In this setup, the two cranks rotate around fixed axes, and the connecting rod acts to link the movement of these cranks together. As one crank rotates, it drives the movement of the second crank through the connecting rod, allowing for a wide variety of motion profiles. The stationary piece, or line of centers, is critical in maintaining the structure and ensuring that the linkage operates correctly.

This mechanism is pivotal in various applications such as robotics, automotive engineering, and machinery design, where precise control of motion is required. The four-bar linkage is often praised for its versatility and efficiency in converting rotary motion into linear motion or in generating complex motion paths.

In summary, the two cranks, connecting rod, and stationary piece work together cohesively to define the operational characteristics of a four-bar linkage system.