To understand the three Motörhead records that were recently re-released on the Sanctuary label, you have to rewind to the summer of 1969, when a band named Hawkwind emerged from London’s underground scene.

Hawkwind sang a lot about outer space. They played weird instruments. They had an interpretive dancer named Stacia, who often took the stage naked. They played a lot for free, setting up outdoors with an anarchistic freak-out band called the Pink Fairies. Their most lasting hit was a song called “Silver Machine,” set to whirling phase-shifted tape noise and heavily reverbed crash cymbals. This was a band with obvious recreational proclivities, but just in case there was any confusion, they sang songs named “Hashish” and “LSD.”

In 1975, while Hawkwind was touring Canada, the bass player – the same man who sang “Silver Machine” – was arrested for cocaine possession. He got off, because it turned out he didn’t have any cocaine: He had a bunch of amphetamines. They’d arrested him for the wrong thing, and he was free to go.

But the band was less forgiving, and they fired the bass player. Did Hawkwind draw the line at speed? Or did they just think it wasn’t groovy to get arrested? Whatever their motives, Lemmy Kilmister was out.

So Lemmy started putting another band together, one that would be loud, fast, and completely out of control. As Lemmy once said, “if this band moved in next door, your lawn would die.” (There’s a persistent rumor that he taught Sid Vicious to play bass, though Lemmy denies it – it was impossible to teach Sid to play, he once said.)

Lemmy was told that the band’s original name, Bastard, would be enough to keep them off “Top of the Pops” – a hilarious concern, given how they ended up. But just in case, he returned to his drug of choice and named his band after the slang term for a speed freak: Motörhead.

Lemmy famously said that Motörhead didn’t really play heavy metal (though the band is often credited with inventing speed metal), but simply rock ‘n’ roll. Once you understand where Lemmy came from, this makes sense: He just wanted to rock. Still, Motörhead makes other early metal bands (King Crimson, Blue Cheer, Blue Oyster Cult) sound as if they’re playing golf, not rock. Motörhead may not have invented metal, but they defined it.

To listen to Motörhead – preferably in a big, cheap, American car with a loud V8 engine, traveling at deadly speeds, tossing beer cans out the window and eating handfuls of amphetamines – is to understand something about rock ‘n’ roll. This is the limit. This is how far boys with guitars in front of a drum set can go.

The classic Motörhead lineup consisted of Lemmy, “Fast” Eddie Clarke on guitar, and Phil “Philthy Animal” Taylor on drums. The trio released six albums before Clarke departed in 1982 after the big successes of “Ace of Spades” and “No Sleep ‘Till Hammersmith.”

The three reissued albums follow that period. Critics panned them, and fans didn’t like all the changes: various new band members, a dual-guitar sound, higher production qualities. Foolishness. These three records (and the bonus discs that come with them) are stupendously good.

The earliest is “Another Perfect Day” (1983), for which Motörhead recruited Thin Lizzy’s excellent former guitarist, Brian Robertson. He didn’t last long with the band, but he brought a different, more melodic sound. His considerable talent is vividly displayed on the “Live at the Manchester Apollo” bonus disc.

Recoded in 1983, it’s an astonishing concert, and not just because of Lemmy’s wonderful stage presence.(“Is that your boyfriend?” he asks at one point, “Yeah? What a bastard.”) The band is astonishingly tight, loud, and full-on. A standout track is “I’ve Got Mine,”which sounds like a freight train. Robertson’s technical ability and musicianship float above the band’s thumping, chugging rawness. It’s bizarre to hear chorus-oriented, poppy guitar in Motörhead, but it works. And lest there be any doubt that Robertson can shred with the best of them, he tears through “Bite the Bullet,” like it was fired from a .357. This is one of the best rock concerts I’ve ever heard recorded.

“Rock ‘N’ Roll” (1987) is the most recent of the three albums. Stripped-down and raw, it’s reminiscent of Motörhead’s early days. Every song sounds like it was written to be played live.

The middle record, 1986’s “Orgasmatron,”includes two of my favorite Motörhead songs: “The Claw” and “Built for Speed.” The former begins in a furious barrage of locomotive drums, goes through an explosive walk-up, and gets bigger, faster, and more out of control while Lemmy snarls and growls. “Built for Speed” sounds like the riff everyone wants to know when they begin playing guitar. And what could be a more succinct summation of Motörhead than the lyrics: “I was born to rock ‘n’ roll / Gives me all I need / I was born with the hammer down / I was built for speed.”

I am not one to suggest that you listen too closely to rock ‘n’ roll, but think about those lines for a moment, and then ask yourself, as I did, what exactly an “Orgasmatron” is. The word doesn’t sound especially sexual. I mean, it doesn’t sound like anything you’d do with a girl, right?

Consider “The Claw.” This starts as a classic song about a chick at a concert, making eyes at the singer.But there’s another guy there. Rather than sing about how well he’ll treat the girl, Lemmy sings, “Gonna make him cry for sure, He’s going to have to make his own way home.” The woman may be the spark, but what’s important is that the other guy will “know the power of the claw.”

Rock music began, with Elvis Presley and Chuck Berry et al, as a way to get girls both into the club and into bed. But Motörhead? They shut the treehouse door and made rock ‘n’ roll an end in itself. This is a boys club. Lemmy claims “Meet the Beatles” is his desert-island record, but it’s just impossible to imagine him singing “Love Me Do.” Unless he was singing it to a bag of speed.