A positive displacement rotary mechanism has three and alternatively four identical rotary helical intermeshing lobes that cooperate with a stationary cylindrical member extending centrally thereof to define a repetitive working space internal of the lobes having boundaries along and between the lobes and along and between the lobes and the cylindrical member which boundaries move on rotation of the lobes to effect expansion and contraction of the working space while repetitively moving same from one of the ends of the lobes toward their other end.