In a polar-coordinate body-and-arm assembly denoted TRL, which description best matches its motion configuration?

• A. It consists of a fixed arm with only rotational motion on a single axis.
• B. It consists of a sliding arm (L joint) actuated relative to the body, which can rotate about both a vertical axis (T joint) and a horizontal axis (R joint).
• C. It uses three translational joints aligned parallel to each other.
• D. It uses a single rotary base without linear motion.

Answer: (B)

Polar-coordinate motion combines a variable radius with two angular motions. In this TRL configuration, the L joint provides the sliding, changing the reach (radius) of the arm relative to the body, while the T joint rotates about a vertical axis (yaw) and the R joint rotates about a horizontal axis (pitch). Together, these three joints allow the end of the arm to reach points described by radius and two angles, which is exactly what a polar-coordinate system uses.

So the description that matches is the one where the arm slides relative to the body to set the radius, and the assembly can rotate about both a vertical axis and a horizontal axis. Without sliding, you’d lose control of the radius; without two perpendicular rotations, you wouldn’t achieve the polar-angle positioning.