Witnesses saw Jesse Wright running up Littleover Avenue in pursuit of the youngsters and waving a knife, at midday, on July 24, said prosecutor Abigail Hill.
He hurled a bicycle at a parked car before running on to Fritchley Court, where a man with a baby in a pushchair tried to persuade him to put the knife away.
Wright replied: "No - they're all getting it," and made more threats to kill them, while passing the knife from hand to hand.
A witness in a black Audi, who was waiting for his grandson, heard him shout: "I'll f****** kill you," at the children.
Wright dragged the knife point along the rear window of the Audi, and stabbed a hole in a side panel, before running after the children.
Police arrested him a short while later in a flat on nearby Middleton Court, Ms Hill said. He gave a no-comment interview.
Wright was arrested again on Hathersage Walk, just before 10am, on November 24, after police received reports of a man "covered in blood."
He had blood on his hands and face from self-inflicted injuries, and a Stanley knife was found in his pocket.
On Thursday, Nottingham Crown Court heard he has 18 previous convictions for 27 offences, dating back to 2008, and he was jailed for 12 weeks for battery this year.
Luc Chignell, mitigating, said the defendant had “an awful upbringing,” and started using amphetamine when he was only nine, and heroin at the age of 13.
"He was the only victim of his knife," he said. "He medicates by bingeing on alcohol."
Wright, 34, of Littleover Avenue, pleaded guilty to two counts of criminal damage and two counts of possessing a blade at earlier hearings.
Jailing him for 20 months, Recorder Simon King told him: "It's clear you're a man with demons he has to battle, but that doesn't excuse this behaviour.”
He said the first incident was "undoubtedly provoked," but "there can be no excuse for a man in his thirties running up and down with a knife in his hands and issuing threats to young people."