Significant attention in recent years has been given to obtain a better understanding of human joint ranges, measurement, and functionality, especially in conjunction with commands issued by the central nervous system. While researchers have studied motor commands needed to drive a limb to follow a path trajectory, various computer algorithms have been reported that provide adequate analysis of limb modeling and motion. This paper uses a rigorous mathematical formulation to model human limbs, understand their reach envelope, delineate barriers therein where a trajectory becomes difficult to control, and help visualize these barriers. Workspaces of a typical forearm with 9 degrees of freedom, a typical finger modeled as a 4- degree-of-freedom system, and a lower extremity with 4 degrees of freedom are discussed. The results show that using the proposed formulation, joint limits play an important role in distinguishing the barriers.