Ever since the release in 1984 of James Cameron’s science-fiction classic “The Terminator,” the movie’s titular robotic assassins have been known for their lack of humor, their indestructible bodies, and for being played by Arnold Schwarzenegger, so it’s fitting that the “Terminator” franchise has been crafted in their image. Seemingly indestructible, it has spawned three movies, dozens of comic books, video games, toys, and now the Fox mid-season replacement series, “Terminator: The Sarah Connor Chronicles,” which is as humorless as a migraine. Unfortunately, there’s no Governator.

The producers of “Terminator: The Sarah Connor Chronicles,” which makes its premiere Sunday evening, regard humor as an unwelcome contaminant. The show’s soundtrack is full of deep rumbles and moans, as if it has indigestion, and every episode is book-ended with a portentous voice-over that’s so hammy it should be served on a biscuit. Groan-worthy lines such as “Know thyself, for what else is there to know” are meant to be taken very, very seriously, and when the show’s hero, John Connor (Thomas Dekker), whines, “I’m not computer hacking, Mom,” you can practically hear the producers snap, “Stop snickering, people.”

If you don’t keep up with your Schwarzenegger movies, here’s the plot: In the near future (2011, plan accordingly), an artificial intelligence defense system called SkyNET is deployed and promptly decides it doesn’t like being told what to do. Cue the total destruction of humanity. But, as always, a brave group of human rebels, led by John Connor, fights the power. To thwart the humans, SkyNET sends indestructible Terminator robots back in time to kill John’s mother, Sarah, before she gives birth to the human messiah (John’s initials are no accident). SkyNET has tried this for three movies and it hasn’t worked yet, hinting that its artificial intelligence might actually be genuine stupidity.

This time around, the future John Connor has sent back in time a foxy, teenage lady Terminator to protect humanity from the evil, adult male Terminators. Named Cameron in queasy homage to the franchise’s founder, she’s played by the nubile Summer Glau (“Serenity”).

One assumes that this series is aimed at people who have always wanted to see “Terminator 2: Judgment Day” remade on a shoestring budget, but maybe there’s an audience who’ll tune in because it’s a heavily promoted franchise extension. One thing’s for sure, they’re not going to be tuning in for the acting. In the role of Sarah, Lena Headey is a by-the-numbers warrior mother trying to convince people that they must fight the Terminator menace; sadly, she couldn’t convince me that she’s hungry, let alone that robots from the future want to kill her teenage son. It doesn’t seem fair to pick on Ms. Glau, given that she has to squeeze out groaners like “In the future, you have many friends” to a despondent John. But as a Terminator, she’s supposed to be an object of physical intimidation, whereas this lightweight couldn’t intimidate a potato chip. When she and one of the evil Terminators fight, they’re both so devoid of life that it’s like watching someone bang two inflatable dolls together.

A flicker of humor shines briefly in the first episode when John and his mother toss an unconscious Cameron out a sixth-floor window rather than carry her down the stairs, but most of the jokes are unintentional. The funniest of them is that it seems we’re headed for a moment when John Connor has to be reminded that trying to French kiss the toaster is never a good idea. There’s also a Latino gang whose members are so stereotypically over-the-top that they might as well be in sombreros.

“Terminator” does solve one serious debate, however. There’s long been a discussion about whether pop culture’s female warriors — Buffy the Vampire Slayer, Lara Croft, etc. — are empowering women or merely fulfilling male fantasies. “The Sarah Connor Chronicles” comes down firmly on the side of male fantasy fulfillment. John sits on the couch while his pistol-packing cougar mommy, who lives only to protect him, and a sexy female robot programmed to worship the ground on which he walks, fight over his affections. It’s a juvenile fantasy that most of us outgrow about the time we encounter an adult female who doesn’t think doing our laundry is the peak of her existence.

But the middle-aged, male creators of this series appear deeply nostalgic for a time when they were the center of their mothers’ lives. However, instead of finding Dr. Phil, they’ve convinced a network to spend millions of dollars so they can act out their fantasies. And that’s pretty funny.