Abstract: An apparatus for controlling the motion of a weft insertion member in shuttleless looms, the apparatus includes: a triple-threaded variable pitch cylindrical cam, adapted to be secured to the weft insertion member; and a slider, which contains three roller seats to receive six frustoconical rollers, in which the six frustoconical rollers are divided into three groups, each group has two frustoconical rollers, each group of two frustoconical rollers is rotatably received by one roller seat and is located between two adjacent threads of the triple-threaded variable pitch cylindrical cam with different one of the two frustoconical rollers contacting different one of the two adjacent threads so that each thread of the triple-threaded variable pitch cylindrical cam is in mating engagement with two frustoconical rollers from two different groups of the three groups of two frustoconical rollers.