We propose a novel, gyroscopic device for haptics and hand rehabilitation, named Gymball. It consists of a fully actuated rotor-gimbal assembly encased in an easy-to-grip appealing design. When held, the device generates a gyroscopic torque which causes the user's hand to move about the wrist. Interviews with occupational therapists, simulations, and proof-of-concept models helped determine the design specifications of Gymball. Compared to the existing gyroscopic devices, Gymball has the following advantages. (i) A smaller form-factor with better user appeal while achieving 0.5 Nm torque. (ii) A wire entanglement-free design allowing complete rotations of the rotor-gimbal assembly. (iii) Negligible rotary imbalances owing to a symmetrical design, resulting in haptic signals with minimal vibratory noise. In this paper, we detail the design and analysis of the device. A feasibility study was conducted to validate prospect of using the device for haptic feedback or therapy. Specifically, the study focused on (i) whether the gyroscopic torque generated by the device can passively move the user's hand about the wrist and (ii) whether the produced hand motion can be controlled. The results show that Gymball can successfully generate about 7° of hand oscillations. The amplitude and frequency of the hand oscillations can be controlled using the speed of rotor and gimbal.