The twist was a more complicated dance than people think in retrospect it occurs to me and was a truly sexy and sinuous thing. As demonstrated here in many clips but best expressed I reckon by Uma Thurman and John Travolta in Tarantino's 'Pulp Fiction' and the other clips here do quite a bit to express this too it was one funky dance. Here the somewhat trad arrangement of the song by the legendary Sam Cooke duration g the intro one might be forgiven for thinking "Meh!' and then Sam finds the groove and blows us all away and I defy you not to dance or at worst to tap your sock feet!

again from the wonderful blog
BEHIND THE GROOVES by Jeff Harris

On this day in music history: March 24, 1962 - “Twistin’ The Night Away” by Sam Cooke hits #1 on the Billboard R&B singles chart for 2 weeks, also peaking at #9 on the Hot 100 on the same date. Written by Sam Cooke, it is the third chart topping single for the R&B and pop vocal icon from Clarksdale, MS. Making the move from independent label Keen Records to major player RCA Records in 1960, Sam Cooke doesn’t miss a beat in the transition, scoring a big hit with the classic “Chain Gang” (#2 R&B and Pop). Though with the exception of “Cupid” (#20 R&B, #17 Pop), Cooke hits a slump in 1961, when five of his singles chart poorly or not at all. Looking for something to pull himself out his chart stagnation, the singer turns to the latest pop cultural phenomenon for inspiration. A sensation in the US and worldwide since Chubby Checker emerges on the scene with “The Twist”, Checker’s record achieves the unheard of feat of topping the Billboard Hot 100 in two separate runs on the charts in September 1960 and January 1962. Also in late 1961, New Jersey based band Joey Dee And The Starliters are quickly moving up the charts with “Peppermint Twist Pt. 1”, which replaces “The Twist” at number one after its second time at the top. Cooke writes “Twistin’ The Night Away”, and plays the finished song for his producers Hugo Peretti and Luigi Creatore. Hugo and Luigi agree with Cooke that it’s a hit, and quickly move to record it. “Twistin’” is recorded at RCA Studios in Hollywood, CA on December 18, 1961, with members of the famed Wrecking Crew studio collective including arranger Rene Hall (Marvin Gaye), Earl Palmer (drums), Tommy Tedesco, Clifton White (guitars), Red Callender (bass), Ed Beal (piano), Jackie Kelso, John Ewing, Jewell Grant (saxophones) and Stuart Williamson (trumpet). Released on January 9, 1962, the song quickly demonstrates that Sam Cooke is far from over. Entering the Hot 100 at #70 on February 3, 1962 and #20 on the R&B singles chart on February 17, 1962, the single rises up both charts quickly. “Twistin’ The Night Away” becomes one of Sam Cooke’s most popular and beloved songs, later being featured in films like “Animal House”, “Innerspace” and “The Green Hornet”. Rod Stewart records the song for his album “Never A Dull Moment” in 1973, re-recording it for the soundtrack of “Innerspace”, appearing along side Cooke’s original version in the film. Drag performer and actor Divine also records a Hi-NRG dance version “Twistin’” in 1985.