Uncontrollable shaking in the human wrist, caused by pathological tremor, can significantly undermine the power and accuracy in object manipulation. In this paper, the design of a Tremor Alleviating Wrist Exoskeleton (TAWE) is introduced. Unlike the works in the literature that only consider the flexion/extension motion, in this paper, we model the wrist joint as a constrained 3D rotational joint accounting for the coupled flexion/extension (FE) and radial/ulnar deviation (RUD) motions. Hence TAWE, which features a 6 degree-of-freedom (DOF) rigid linkage structure, aims to accurately monitor, suppress tremors and provide light-power augmentation in both FE and RUD wrist motions. The presented study focuses on providing a fundamental understanding of the feasibility of TAWE through theoretical analyses. The analytical multibody model of the forearm-TAWE assembly provides insight into the necessary conditions for control, which indicates that reliable control conditions in the desired workspace can be acquired by tuning the design parameters. Nonlinear regressions are then implemented to identify the information that is crucial to the controller design from the unknown wrist kinematics. The proposed analytical model is validated numerically with V-REP and the result shows good agreement. Simulations also demonstrate the reliable performance of TAWE under controllers designed for tremor suppression and movement assistance.