Brooks Atkinson Theatre, New York <!-- none twostar threestar fourstar fivestar -->

If you are, or ever were, a fan of Bob Dylan, arguably America's greatest living singer-songwriter, you should have every reason to celebrate the opening of The Times They are A-Changin' on Broadway, a musical set to his ballads and anthems and staged by the legendary dance director Twyla Tharp.

It was tempting to dismiss this project as misbegotten even before stepping inside the Brooks Atkinson Theatre on 47th Street, where it has just opened. What good could possibly come of marrying high-stepping, dollar-churning Broadway with Dylan, whom some of us still remember as a reclusive counter-culture hero? The very notion seemed vaguely ridiculous and appalling.

But four years ago, Tharp pulled off a spectacular success here with Movin' Out, a musical that told the story of young men on Long Island reunited after serving in Vietnam, with no dialogue at all, told entirely though the songs of Billy Joel. It was showered with awards and ran for three years.

Dylan, in fact, was the one who invited Tharp to give his songs the same stage treatment. If you have been watching Dylan lately, you will not be entirely surprised. In recent years - times indeed have a-changed for him - he has exited his shell, penning a 2004 autobiography and even appearing in advertisements for products ranging from iPods to the lingerie lines of Victoria's Secret.

For Dylan, Tharp has followed the Movin' Out template exactly. She settled on a new narrative - a vagabond circus whose characters include a sadistic impresario Captain Ahrab (Thom Sesma), his mistress Cleo (Lisa Brescia), his innocent and restless son Coyote (Michael Arden) as well as a troupe of clowns - and relied on Dylan's songs as well as the frenetic dancing of the clowns to drive it all along.

Except that Tharp, normally so sure of her step, has stumbled badly. It is not that the muscled high jinks of the clowns, the lighting and the costume design aren't all dazzling. Nor, of course, are you likely to be able to resist entirely the strains of such Dylan classics as "Subterranean Homesick Blues", "Just Like a Woman", "Blowin' in the Wind" and, of course, the song that gives the whole piece its name.

But just as you remember how much you love these never-quite-forgotten songs, so you are likely to wince at the crude manner of their exploitation by Tharp. Was I the only member of the audience to bury my face in my hands as the band began playing "Like a Rolling Stone", while the Tharp-directed dancers frolicked on stage rolling not stones but giant rubber beach balls?

Scores of musicians have covered Dylan songs over the years, from the Rolling Stones to Jimi Hendrix. Arden has a fine voice, for sure, but also baby-face features and thus lacks everything that is gritty and virile about Dylan. A scene that has him descending from the gods, seated upon a crescent moon, while belting out "Tambourine Man" was more risible than moving. However, Mr Sesma, with his wild hair and lascivious leer, worked his numbers, including "Knockin' on Heaven's Door", a little more credibly.

The Times They are a-Changin' is only one of a rash of so-called "juke-box" musicals on Broadway that rely on digging up popular songs and pegging them to a narrative washing line that you hope won't snap under the weight of silliness. Often they do, as with Lennon, another misguided project opened under the guidance of Yoko Ono last year and closed within weeks. Tharp may think she has fused Dylan's songs together coherently, but to me the plot was enigmatic at best.

Another juke-box musical that is absurd in its pretensions at a plot is Mamma Mia!, but because we never took Abba very seriously none of us care and the show will run and run. Dylan is someone that most of us do take seriously, however. Or at least we thought we did before he gave his songs to Tharp and agreed to flog Victoria's Secret thongs.

To 1 April (001 212 719 4099)