Robots have been demonstrated to assist the rehabilitation of patients with upper or lower limb disabilities. To make exoskeleton robots more friendly and accessible to patients, they need to be lightweight and compact without major performance tradeoffs. Existing upper-limb exoskeleton robots focus on the assistance of the coarse-motion of the upper arm while the fine-motion rehabilitation of the forearm is often ignored. This paper presents a wrist robot with three degrees-of-freedom. Using a geared bearing, slider crank mechanisms, and a spherical mechanism, this robot can provide the complete motion assistance for the forearm. The optimized robot dimensions allow large torque and rotation output while the motors are placed parallel to the forearm. Thus lightweight, compactness, and better inertia properties can be achieved. Linear and rotary series elastic actuators (SEAs) with high torque-to-weight ratios are proposed to accurately measure and control the interaction force and impedance between the robot and the wrist. The resulting 1.5-kg robot can be used alone or easily in combination with other robots to provide various robot-aided upper limb rehabilitation.