You can count on U2 to never do things by half. They've dangled Trabant cars upside down, emerged from a 40-foot high lemon, phoned up the White House and staged mammoth arena rock pantomimes to beat every band. For their latest party trick, they've built the biggest structure ever to be seen, on any stage, anywhere.

On June 30 at Barcelona's vast Camp Nou stadium, the colossal four-legged stage that's been nicknamed The Claw was unveiled to the world. "I bet everybody is wondering what the hell this is, me too," remarked Gary Lightbody of opening act Snow Patrol. Later that night Bono thanked the Catalan crowd for making it all possible and facilitating the building of a stage that he likened to "a space station designed by Gaudi".

Of course, the eye-boggling centrepiece of the 360° tour wasn't actually designed by Gaudi, but long-term U2 collaborators Willie Williams and Mark Fisher. Williams cut his teeth as a stage and lighting designer for punk bands Stiff Little Fingers and Deaf School. After hearing U2's debut album Boy, he contacted Paul McGuinness for the gig and has worked on every U2 tour since 1982.

After the sensory overload and innovation of Zoo TV and Popmart, Williams and U2 began to dream it all up again. "Towards the end of the Vertigo tour, I began to think about where we could take the live show next," he reveals. "Zoo TV and Popmart were revolutionary shows at the time, but now virtually every stadium act uses a video wall. I knew we had to do something different."

The highly ambitious 360° tour has been in the pipeline for some time. "It's an idea we've been working on for about eight years, much to the scepticism of my band mates and most people in the industry who said it wasn't possible to play like this in the round," Bono has explained. "Our ambition with the production is to create a piece of emotional architecture, using engineering as a way to get closer to our audience, to surround ourselves with them. Can we make our audience the fifth member of the band, almost have them on stage?"

This daunting challenge underpinned the project. "I got the idea from doing indoor shows in the round," Williams says. "Very few artists have done that outdoors. Celine Dion has done stadium shows in the round and the Foo Fighters did one just last year, but it tends to be an indoor format.

"I thought if it could be done in the round, then perhaps we could offset the huge costs involved by increasing the capacity. The band was in the studio and their heads were focused on the album. And in discussions with the U2 organisation, we realised that the cost would be massive. But it really began to come together when I spoke to Mark Fisher about it. Overnight, he emailed me some sketchy drawings of what it might look like and we took it from there."

Williams is equally mystified about what exactly this thing is. "Everyone who sees it says that it looks like something different," he says. "Tintin's rocket. The War of the Worlds. Cactus. Octopus. Claw. Whenever it started to look like something, Mark and I would push it in another direction. But it does look as though it has escaped from a giant space aquarium. I love seeing people's first reaction to it. At the San Siro in Milan, I stood near the entrance and it was amazing to see people come in with their jaws literally dropping."

Staggeringly, there is not just one, but three separate claws. At one tour pit stop, a claw will be under construction. In another, a show will be in progress and a third claw will be in transit in one of the most labour-intensive rock shows ever seen. It takes four days to build the 164-foot high structure, two to set it up for production and 120 trucks to haul it from A to B. It's exactly double the size of the stage that the Stones used for the Bigger Bang tour.

"Up until now, the Bigger Bang tour had the world's biggest stage," confirms Williams. "But now, it would fit under this structure."

After years of planning and plotting, Williams is thrilled to finally see his monster take up residency in the world's biggest stadiums. "It's very emotional seeing the realisation of this idea that we've been working on since 2006. It almost feels like the birth of a child. There is all the depression of pregnancy in the midst of years of preparation and even a little bit of post-natal when it's finally done."

Williams is a full-time member of the U2 touring party, overseeing the construction and execution of every stage. "I made a conscious decision to work on all the shows," he says.

"It's such a vast production I don't think it would be right to head off and do something else after the first six shows or whatever. It's not a project to be half-hearted about. The band knows that, too. I've never seen them be so well-rehearsed for a tour before. Usually, they'll use any excuse not to rehearse and considering their longevity and experience, they probably don't need to that much, but they've really gone for it this time around."

Pulling off such a vast production is nerve-wracking, but, so far, there haven't been any unwelcome spanners in the works. Everyone involved remembers the infamous lemon that wouldn't open on the first night of Popmart.

"The first show tends to be a blaze of manic energy and the second show often falls apart, but so far this has worked so well," Williams enthuses. "Bono has said to me that when they're standing onstage, this thing is so big that it's almost invisible. They have a wide-open view of the audience, so it does create more intimacy, even though that might seem like a stupid word for such a large show. But in the San Siro, it worked really well. It's one of the biggest stadiums in the world, yet it felt like being in a gymnasium."

As a long-standing on-the-road veteran, Williams finds it hard to pick his favourite U2 tour. "It's impossible to choose one. It's a bit like that thing about children again. You love them equally and in very different ways.

"Obviously, Zoo TV was an extremely exciting rollercoaster ride. Seeing The Joshua Tree tour was very exciting, because it was their first peak and the tipping point of their career.

"So far, this has been pretty amazing. It feels like the Beijing Olympics of rock shows, it's the beginning of something and also the end of something. It's impossible to know where it all goes after this."

With Croke Park on tonight's horizon, Williams agrees that there is always something unique about U2 bringing it all back home. "The Phoenix Park in 1983 was a really amazing experience because it was the first time I experienced a U2 homecoming show," he says.

"I really think on the last Vertigo tour there was a sense of a band and a city finally agreeing to get along. Often the reaction to the shows is unequivocally ecstatic, but sometimes there's a lot of fierce criticism. However, during those shows I felt U2 and Dublin had grown up. Their music has been such an integral part of growing up in Ireland and, at the end of the day, the crucial thing is for everyone on all sides of the stage and on the stage itself to have a great day out."

- Eamon Sweeney