The boy is Timmie Merrinoe, played by talented young Richard Eyer. Timmie's father, Tom (Philip Abbot), is the quintessential brilliant parent who sees his only offspring's academic underachievement as a personal failure.
"He's already ten years old and still can't play a decent game of chess," he complains to his wife, Mary (Diane Brewster).
Merrinoe consults the mega-computer he has created, only to be told the machine needs to speak directly to Timmie. Instead, it hypnotizes the boy and plugs in some post-hypnotic suggestions. Timmie bets his father he can win a chess game. If he does, he can have anything he wants. Dad bites -- and loses in three moves.
What Timmie requests is permission to reconstruct Robby, who is currently sitting in disarray in an abandoned lab. Once the job is done, boy and robot become fast friends. Robby builds a kite large enough for Timmie to ride on, but the robot's basic programming prevents it from exposing the boy to anything that dangerous. Determined to fly, Timmie takes Robby back to the computer, where the obstruction is removed. Unfortunately, the computer now commands the robot -- and has implanted some additional instructions. Timmie sneaks aboard a military rocket due to launch in 24 hours, and Robby begins doing neurosurgery on everyone involved with the project. He places an implant in their brains that makes them slaves to the computer.
As the hour for launch nears, it seems the computer will succeed in its plan to rule the world. It fails because it underestimates not only the wisdom of the humans it despises, but the power of something it cannot even imagine -- friendship. When the computer orders Robby to torture Timmie, the robot refuses and, in the end, destroys its "master" to save its friends.