An upper-arm wearable exoskeleton has been designed for assistance and functional training of humans. One of the goals of this design is to provide passive assistance to a user by gravity balancing, while keeping the transmitted forces to the shoulder joints at a minimum. Consistent with this goal, this paper addresses the following questions: (i) an analytical study of gravity balancing design conditions for the structure of the human arm, (ii) minimization of transmitted shoulder joint forces while satisfying the gravity balancing conditions, and (iii) possible implementation of these conditions into practical designs using zero-free length springs.