Existing fingertip haptic devices can deliver different subsets of tactile cues in a compact package, but we have not yet seen a wearable six-degree-of-freedom (6-DOF) display. This paper presents the Fuppeteer (short for Fingertip Puppeteer), a device that is capable of controlling the position and orientation of a flat platform, such that any combination of normal and shear force can be delivered at any location on any human fingertip. We build on our previous work of designing a parallel continuum manipulator for fingertip haptics by presenting a motorized version in which six flexible Nitinol wires are actuated via independent roller mechanisms and proportional-derivative controllers. We evaluate the settling time and end-effector vibrations observed during system responses to step inputs. After creating a six-dimensional lookup table and adjusting simulated inputs using measured Jacobians, we show that the device can make contact with all parts of the fingertip with a mean error of 1.42 mm. Finally, we present results from a human-subject study. A total of 24 users discerned 9 evenly distributed contact locations with an average accuracy of 80.5%. Translational and rotational shear cues were identified reasonably well near the center of the fingertip and more poorly around the edges.