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Although tremor is one of the most common movement disorders, there are few effective tremor-suppressing options available to patients. Gyrostabilization is a potential option, but we do not currently know how to optimize gyrostabilization for tremor suppression. To address this gap, we present a systematic investigation of how gyrostabilizer parameters affect tremor suppression in a single degree of freedom (DOF). A simple model with a single DOF at the wrist and a gyroscope mounted on the back of the hand was used to focus on the most basic effects. We simulated the frequency response of the system (hand + gyroscope) to a tremorogenic input torque at the wrist. Varying system parameters one at a time, we determined the effect of individual parameters on the system’s frequency response. To minimize the bandwidth without adding significant inertia, the inertia and spin speed of the flywheel should be as high as design constraints allow, whereas the distance from the wrist joint axis to the gyroscope and the precession stiffness and damping should be kept as low as possible. The results demonstrate the potential of gyroscopic tremor suppression and can serve as foundation for further investigations of gyroscopic tremor suppression in the upper limb.