A shimmy is a dance move in which the body is held still, except for the shoulders, which are quickly alternated back and forth. When the right shoulder goes back, the left one comes forward.
1918 sheet music "Everybody Shimmies Now" with Mae West
When the Alamo Theater in Atlanta used a cutout display of Viola Dana with separately mounted shoulders and a mechanism to do a shimmy for the film The Chorus Girl's Romance (1920), the chief of police ordered the mechanism turned off.
Gilda Gray was a Polish-American dancer and actress who popularized a dance called the "shimmy" which became fashionable in 1920s films and theater productions.
Gray c.1920
Gilda Gray as the Hula-Hula Girl in Theatre Magazine, April, 1922
Publicity photo remade into painting, "South Sea Island idyll" by Henry Hintermeister, c. 1922.
Gilda Gray in October 1921