Reprint of: Bounding the locus of the center of mass for a part with shape variation

We study the relation between variation in part shape and variation in the location of the center of mass for a part with uniform mass distribution. We consider a general model for shape variation that only assumes that every valid instance contains a shape PI while it is contained in another shape PE. We characterize the worst-case displacement of the center of mass in a given direction in terms of PI and PE. The characterization allows us to determine an adequate polytopic approximation of the locus of the center of mass. We also show that the worst-case displacement is small if PI is convex and fat and the distance between the boundary of PE and PI is bounded.