A Leeds Crown Court judge jailed 37-year-old David Riley for seven years after hearing his crimes had a lasting impact on his victims.
Prosecutor Patricia Doherty said Riley - who claimed to have suffered a breakdown after an argument at work - deliberately drove his Ford Transit van into cyclist Gonzalo Munoz Lopez on North Street in Leeds city centre at around 5.20pm on February 10.
Mr Lopez was knocked off his bike and suffered injuries including four broken bones in his right foot.
Minutes later Riley, of Nowell Crescent, Harehills, drove the wrong way along Scott Hall Road in Leeds before deliberately crashing his van into two cars in queuing traffic.
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Riley got out of the van while carrying an axe and opened the driver's door of another Ford Transit van which had stopped at traffic lights.
Miss Doherty said Riley told the van driver Mark Castle: "Get out, get out or I will hit you with this axe. The defendant was screaming and shouting and swinging the axe into the vehicle's cabin, hitting the dashboard three or four times."
Mark Castle, his son son Mason and a second passenger got out of the van before Riley stole it and drove off the wrong way along Scott Hall Road.
A few minutes later Riley abandoned the stolen van on Otley Road in Headingley and approached a Volvo being driven by Anthony Brown, whose wife and two young children were also in the car.
Miss Doherty said Riley was holding an axe as he tried to open the car door as Mr Brown's family screamed, adding: "Mr Brown said he was shaking the axe at him like a tomahawk."
The court heard that after Mr Brown drove away Riley tried to get into two other cars on Otley Road.
Riley then used the axe to break the lock on a delivery bicycle outside the Kentucky Fried Chicken shop on Otley Road before riding away on the bike.
The court heard Riley dumped the bicycle in St Chad's Rise and fled on foot.
When he handed himself in to police three days later on February 13, Riley told officers that he used cannabis and amphetamines and believed he was being followed when he committed the offences and feared for his safety.
Father-of-four Riley admitted causing serious injury by dangerous driving, dangerous driving, robbery, theft, threatening a person with a bladed article and failing to stop after an accident.
The court heard cyclist Mr Lopez had to leave his job as a sales assistant as a result of his injuries and return to Spain.
The court was told Mr Castle had suffered stress and anxiety and Mr Brown's young daughter had undergone counselling following the ordeal.
Mitigating, Katy Rafter, said Riley had taken over running his late father's scrap yard after his father committed suicide in 2014.
Miss Rafter said: "This had a profound effect on his own mood and mental health.
"On the day of these offences the defendant had an argument with an employee of his at work and that made him become extremely anxious. He perceived people had been watching him and so took possession of the axe ."
Miss Rafter added: "Mr Riley believes he had something of a mental breakdown on that day. He wholly accepts his actions. He would like, through me, to apologise to the victims of all these offences."
Jailing Riley for seven years and banning him from driving for four years , recorder Simon Eckersley told him: "Over it appears three or four miles, you left a trail of chaos, devastation and injury."
After the sentencing hearing, Detective Inspector Richard Holmes, of Leeds District CID, said: “Riley was responsible for a frightening series of incidents over a short space of time.
“He left a cyclist that he knocked down with significant injuries and terrified a number of other people when he confronted them while armed with an axe.
“This all took place in busy public areas on a Saturday afternoon, and the dramatic circumstances of the incidents themselves and the police activity on the ground to find him caused understandable concern in the community.
“We hope that knowing he has now been brought to justice and had to answer for his actions will provide some reassurance to the victims and the wider community.”