For ease of manufacture, axisymmetric components produced by processes such as forging, casting and moulding are often designed with a taper angle. This paper presents a family of devices for handling such components by their tapered portion. The devices are essentially finger tips, or jaws, to be fitted to standard scissor-type robot grippers. The jaws possess a three-dimensional profile constructed as a stack of v-shaped planar curves. The special jaw profile enables components of different diameters and taper angles to be gripped concentrically without calling for complex movements to reposition the gripper. The equations describing two categories of profile are derived and the optimum selection of profile parameters to yield compact jaws to grip components of a wide range of dimensions is discussed in the paper.