The object of this paper is mixing devices consisting of rods which make periodic motions in a vessel. The topological character of the mixing is related to automorphisms on punctured disks and also to braids. Nielsen-Thurston theory shows that such devices corresponding to pseudo-Anosov automorphisms give efficient mixings. In this paper, we study such mixing devices constructed from hypotrochoid curves. We make use of two techniques for showing given mixing devices yield pseudo-Anosov automorphisms. One is cut and paste arguments in 3-dimensional topology applied to the exteriors of the closures of corresponding braids. The other is the theory of covering spaces applied to mixing devices with symmetries.