The work includes a large engineering and infrastructure upgrade project, focusing primarily on the carriages, chassis and emergency brakes, which will help ensure that the tramway can keep running in the future.
Last year the company celebrated its 140th anniversary, and the tramway is among the oldest in the country.
The trams and chassis were lifted by crane onto two lorries, and a small crowd of people gathered to watch the spectacle at the tramway, which runs between Foreshore Road and St Nicholas Cliff.
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It is the first time the carriages have been removed, and the Central Tramway Company will be closed until Easter as the revamp and refurbishment takes place.
Martin Hudson, Project Manager with Wheelsets UK, which is carrying out the work, said: "The chassis are 88 years old, and the cabs are from 1968. The chassis are worn out and corroded."
The Central Tramway Company is owned by the Purshouse family; daughter Amy Bartle said: "We trust Martin and the team. It’s about making sure it’s back in service in good time, so it was really more that there wasn’t anything unexpected that presented itself because once you start taking it apart and removing parts there are some unknowns.
"They had assessed the integrity of some of the parts, but once you start moving those parts, it was whether any of that integrity was going to be an issue. So far it all looks to be holding steady so they can do the lifts.
"They’re moving parts, they’re exposed to the elements so it needed to be done and there’s never really a good time so we’ve been trying to find the best time."
Helen Galvin, General Manager of the company, said: "The trams are being taken away for the first time ever, it’s a big deal for us losing the trams. We’ve had specialised engineers come in and what they’ve had to do is separate the carriages from the chassis itself.
"The actual work is on the chassis, it’s going to be new. Whilst it’s in the workshop in Rotherham, they’re going to do work on the carriages as well.
"It’s a massive undertaking because we’ve never lifted them out before. It’s our livelihood dangling in the air, it’s a big deal really."