Empirical design of non-circular centrodes

This article presents ideas useful for teaching design and manufacturing of centrodes to generate prescribed generic motion, in Engineering Mechanics or similar classes. The article begins by reviewing the concept of instantaneous center of rotation and its loci, the moving centrode and the fixed centrode, for the planar motion of an arbitrarily shaped rigid body and its connection with design. A practical method is presented to determine the shape of the centrodes for the most common case, where exact equations either cannot be obtained or are so cumbersome as to render them impractical. Finally, the general method is implemented on a concrete example, fabricating the centrodes, and putting them to work. The centrodes are 3D-printed, and the motion generated is compared against the theoretical prediction. The concepts described in this article are motivated from the experience of having taught planar motion in general, and centrode design in particular, in an Engineering Mechanics class. The actual fabrication of the centrodes guided by theoretical design picked the students’ interest in the subject.