As far as art history is concerned, it was like mixing ammonia, nitrate and a match. When Marcel Duchamp, Francis Picabia and Man Ray all met, swilled into each other's circles by the international art scene and wartime migrations, they formed an explosive cocktail of talents. Together, most famously, they were responsible for launching Dada on New York.

The story is familiar. A revolutionary idea, born in a small Zurich cabaret as a response to the atrocities taking place at that time in the trenches of the First World War, soon took on a life of its own. It ran defiantly amok, crossing countries and continents, spreading creative anarchy. Laughing in the face of academic convention, it was significantly to alter the course of our cultural history. Its irreverent reverberations are still very much felt today.

Now Tate Modern launches its big new spring show: Duchamp, Man Ray, Picabia. It will no doubt bring to mind this destructive (and so short-lived) Dada moment, along with the Surrealist movement that grew up alongside it. Certainly, if you want to see the most famous objects of this era you will not be disappointed. Scattered through this exhibition are pieces that have become synonymous with some of Modernism's maddest ideas.

Here is the domestic iron with a row of tin tacks stuck onto its surface, there are the drawings that turn machine parts into smutty sexual jokes; here is the bicycle wheel balanced on a kitchen stool and there, of course, is the world's single most famous item of sanitary furniture: the public urinal that Duchamp transformed into a work of art. Fountain has come to be seen as the paradigm of the “ready-made” - the creation of which may well count not simply as the most radical but also as the most influential artistic idea to emerge from the previous century. Duchamp certainly suspected as much and he played with all sorts of permutations, from putting his name to someone else's painting to contemplating claiming the Woolworth's building for one of his creations.

And yet, keeping these objects in a gallery creates an all-too-familiar paradox - the sort of dilemma that the wilfully contradictory (and often self-contradictory) Duchamp would have delighted in. The whole point of the ebulliently negative Dada revolution was to break down traditions. “Can one make works of art which are not works of art?” was the question. And yet, just a few decades later, iconic works of the era are enshrined in our galleries, neatly parcelled up into historical periods. Even as we preserve these pieces, we destroy them. We may keep their substance but we lose their spirit.

Can this spirit ever be revived? Can the electricity of the original idea, ever galvanise the objects back to artistic life? This latest Tate show offers a fresh look. For a start, it removes the artworks from their neatly compartmentalised cabinet of chronology and sets them in the more atmospheric context of the friendships that inspired them - relationships that not only predated Dada but lasted long after Surrealism had faded out of fashion.

On the face of it, Duchamp, Man Ray and Picabia made slightly unlikely friends. When, in 1911, the 33-year-old Picabia, a dandified bon-vivant with a fat private income, a flamboyant lifestyle and a passion for fast cars, first encountered the cerebral Duchamp, almost a decade his junior with an air of elegant detachment and a taste for chess, the encounter was hardly promising. But “we were friends from that moment”, Duchamp recalled. And a couple of years later, when the diminutive, fast-talking New York photographer Man Ray entered the equation, the three somehow added up to more than the sum of their parts.

As this show explores the affinities and parallels between their pieces, we see the currents of energy that run between them, sparking ideas and igniting enthusiasms, spawning experiments and setting off chain reactions. These men, for all their many differences and despite the many periods that they spent apart, clearly shared an intellectual chemistry.

Themed galleries examine different areas of interest: movement for instance is the subject of one gallery as the artists try to free the image from the stasis of the picture plane; the machine, the icon of the avant-garde, is the subject of another; and, in a third, the spectator can study their exploration of glass as a medium. Liberated by Duchamp's landmark The Bride Stripped Bare by her Bachelors, Even (The Large Glass), which leaves the experience of looking so ambiguous, Picabia and Man Ray both begin what was to become a continuing play with ideas of transparency, the former painting an image of his own on to a hinged window, the latter - for whom, as a photographer, glass and light were essential - recording and elaborating on Duchamp's work with his camera lens.

Frequently the artists collaborated directly, borrowing each other's expertise, turning up in each other's images, lifting ideas and offering alternative takes. Was it Picabia's mischievous iconoclasm that first gave Duchamp the impetus to escape from Cubism? Did Man Ray's innovative use of doubled and solarised images give Picabia the idea for his transparency paintings, in which he puts down pictures layer upon layer? Would Man Ray ever have made his Objects of Affection without Duchamp's ready-mades as a model? The spectator swirls through this show on a swift-flowing current of intertwining ideas. There may be some 350 pieces, but they are determinedly conceptual. You don't need to pause to admire the brushwork. You can trot along pretty quickly if you keep up with their pace.

But what this exhibition captures most freshly is the high-spirited friendship that was to last more than five decades. Of course, these artists helped each other professionally. But they also took holidays, attended parties, went on drunken rampages, raided girlfriends' fridges and played games of chess together. They dressed up in drag, tried out silly hairstyles and put on hats and poses, which they recorded in photographs. They shared a sense of humour, revelling in ridiculous puns, a rolling wordplay and endless sexual innuendo that could turn almost anything into a smutty in-joke - and the important thing is that the visitor is invited in on the gag.

It may be difficult to remember why Duchamp's canonical 1912 Nude Descending a Staircase should have got New Yorkers queueing 40 deep to gawp and make fun. It seems so safely familiar. But, seeing it in the context of this show, perhaps we can recapture a sense of its subversive energy. Compare it with Duchamp's works of the previous year, and you can see how abruptly he abandoned his safe brand of Cubism. But then add an element of mischief - the idea that the Cubists were being laughed at - and you begin to tap in to that frisson that first gave it life. Now remember as you walk on, that it might be you who is being made ridiculous. Duchamp's sense of humour is an acid test.

It is this restlessly teasing, relentlessly testing, provocatively playful imagination that, made all the clearer in the context of intimate friendships, lends life to this show. The trouble is, Duchamp was only in his mid-thirties when he abandoned art, hardly ever to return. And with his withdrawal the impetus of this show peters out.

There are plenty more works by Picabia, who changed styles as frequently as most of us change our underpants. There are lots of images by Man Ray. But they can't convince that he was anything much more than the supreme stylist so familiar from the fashion plates.

Duchamp was the pivotal point of this artistic friendship. He was the match that made the mixture explode.

Duchamp, Man Ray, Picabia is at Tate Modern (020-7887 8888), from Thurs

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