“I wanted to save some money for a change,” he said. He spent his first two years here working full time as a computer programmer (which he still continues part time today) while living in a crowded duplex apartment that sometimes boasted upward of 15 roommates. “My parents are musicians,” he said, “so I really avoided going down the path of the struggling artist. That’s my biggest fear in life.”

At first, he tried to create a machine that would peck out Scott Joplin’s ragtime piano piece “The Entertainer” in rudimentary percussion, but space constraints made it impossible. He continued leading occasional youth workshops around the world. During the 2011 Venice Biennale, he organized 40 children to create a Goldbergian plant-watering device in the shade of the Greenhouse at the Venice Giardini. He had been invited by the Italian arts organization Microclima, whose members had seen his work on YouTube. Mr. Herscher, however, had to find private investors to finance the event, which he did by appealing to the national pride of his fellow New Zealanders. While these workshops were fun, he said, he missed having the freedom to create things by himself and on his own time. So he decided to find an apartment that would let him build again. Not surprisingly, it wasn’t an easy search.

“Joseph had quite specific requirements,” said Mr. Herscher’s roommate Olivia Lynch, 25, a communications coordinator at the British Broadcasting Corporation who is an old friend from New Zealand. These included private roof access, ample common space and — perhaps most important — roommates who would put up with an inventor’s workbench next to the kitchen sink and the possibility of something out of the children’s game Mouse Trap taking over the living room.

After looking at more than 20 apartments, Mr. Herscher called Ms. Lynch at work to explain that he’d found the perfect place. There was just one small problem: two other people had already put down deposits, and if they didn’t sign the lease in the next 20 minutes, the apartment would be gone.

“I said, ‘Joseph, tell them we’ll pay six months in advance,’ ” Ms. Lynch recalled. “So he jumped on his bike and wrote a check for $17,000.” By June, they had moved in. After a few trips to Ikea (where most of Mr. Herscher’s supplies came from), he was back in the Rube Goldberg business. But one issue remains: what to do with the machines when they are finished. As of now, Mr. Herscher has no idea; he has no gallery representation and has never sold a machine.

“It’s going to be hard to find a place that will show them,” he said, looking down at a ceramic bowl that had shattered in two during a test of the fuses. His planned devices will incorporate things like hot irons, chemical reactions and live animals, and he worries they will be a difficult sell. But he’s not letting that stop him. “I hope that New York’s such a complicated place that there might be somewhere that’s interested.”