In this paper, we present an eye–hand coordination simulator for robot arms as a compact cyber-physical science, technology, engineering, and mathematics (STEM) learning unit that links visual perception to robot motion in pick/place interactions with a mobile robot as an automatic guided vehicle (AGV). The unit integrates four domains into one workflow: science (kinematics and motion), technology (sensors, motor controllers, vision), engineering (mechanisms and control states), and mathematics (geometric computation and frame transforms). The pick/place machine prototype includes linear X–Y–Z-axes with rotary and flip joints to realign an item box between a shelf and an AGV. A vision system detects a pair of fiducial circles to estimate the AGV centerline, yaw, and slot positions, while displacement sensors measure stand-off and assist parallel alignment. Performance was evaluated using a mock-up AGV positioned with varied offsets and yaw within a ±10 mm parking tolerance. Across 10 trials, the vision-based estimates of middle-slot X and stand-off Sx closely matched tape measurements, achieving 98–100% accuracy. The results show that the simulator is dependable in vision-guided coordination and usable as a simple, accessible platform for STEM education.