“I was glad they asked me, because it was for a good cause,” said Luciana Valle, a kindergarten teacher who was 31 two years ago when her son, Matteo, was one of the first babies extracted with the device. Because Matteo weighed almost nine pounds, “it really helped,” she said in a telephone interview. “His head came out on my second push.”

The W.H.O. will now oversee tests on 100 more women in normal labor in China, India and South Africa, and then on 170 women in obstructed labor.

In a telephone interview from Argentina, Mr. Odón described the origins of his idea.

He tinkers at his garage, but his previous inventions were car parts. Seven years ago, he said, employees were imitating a video showing that a cork pushed into an empty bottle can be retrieved by inserting a plastic grocery bag, blowing until it surrounds the cork, and drawing it out.

That night, he won a dinner bet on it.

At 4 a.m., he woke his wife and told her the idea that had just come to him. (His own children were born without problems, he said, but he has an aunt who suffered nerve damage from birth.)

His wife, he recalled, “said I was crazy and went back to sleep.”

The next morning, a somewhat skeptical friend introduced him to an obstetrician. “You can imagine these two guys in suits in a waiting room full of pregnant ladies,” he said.

The doctor was encouraging, so he kept working. Polyethylene replaced the bag his wife had sewn, and the jar was replaced by a plastic uterus.

With the help of a cousin, Mr. Odón met the chief of obstetrics at a major hospital in Buenos Aires. The chief had a friend at the W.H.O., who knew Dr. Merialdi, who, at a 2008 medical conference in Argentina, granted Mr. Odón 10 minutes during a coffee break.