We developed an exoskeleton for neurorehabilitation that covered all relevant degrees of freedom of the human arm while providing enough range of motion, speed, strength, and haptic-rendering function for therapy of severely affected (e.g., mobilization) and mildly affected patients (e.g., strength and speed). The ANYexo 2.0, uniting these capabilities, could be the vanguard for highly versatile therapeutic robotics applicable to a broad target group and an extensive range of exercises. Thus, supporting the practical adoption of these devices in clinics.The unique kinematic structure of the robot and the bioinspired controlled shoulder coupling allowed training for most activities of daily living. We demonstrated this capability with 15 sample activities, including interaction with real objects and the own body with the robot in transparent mode. The robot's joints can reach 200 %, 398 %, and 354 % of the speed required during activities of daily living at the shoulder, elbow, and wrist, respectively. Further, the robot can provide isometric strength training. We present a detailed analysis of the kinematic properties and propose algorithms for intuitive control implementation.