This question requires matching specific industrial robot configurations (P, Q, R, S) with the types of joints that define their 3 degrees-of-freedom (DOF) movement.

Robot Configuration and Joint Type Matching

We need to determine the joint configuration for each listed robot type:

• P: Cartesian Configuration A Cartesian robot moves along three perpendicular linear axes (X, Y, Z). This requires three linear or prismatic joints. Therefore, Cartesian (P) matches with Type 4 (Three prismatic).
• Q: Cylindrical Configuration A cylindrical robot has one rotary joint at the base, one prismatic joint for vertical movement, and another prismatic joint for radial extension. This configuration uses one rotary joint and two prismatic joints. Therefore, Cylindrical (Q) matches with Type 3 (One prismatic and two rotary). Correction: Based on standard definitions, Cylindrical typically uses one rotary (base) and two prismatic (height, reach). The question's option 3 is 'Two prismatic and one rotary'. This matches.
• R: Spherical Configuration Also known as a polar robot, it uses two rotary joints (one for yaw/azimuth, one for pitch/elevation) and one prismatic joint for reach. This configuration uses two rotary joints and one prismatic joint. Therefore, Spherical (R) matches with Type 1 (One prismatic and two rotary).
• S: Articulated Configuration An articulated robot, often resembling a human arm, typically uses multiple rotary joints to achieve flexibility. For a 3 DOF articulated robot, it usually consists of three rotary joints. Therefore, Articulated (S) matches with Type 2 (Three rotary).

Summary of Matches

Based on the analysis:

• P (Cartesian) - 4 (Three prismatic)
• Q (Cylindrical) - 3 (Two prismatic and one rotary)
• R (Spherical) - 1 (One prismatic and two rotary)
• S (Articulated) - 2 (Three rotary)

This corresponds to the matching P-4, Q-3, R-1, S-2.