A systematic approach is proposed to determine the tensionable workspace of multibody cable-driven mechanisms. The method is also capable of finding analytical descriptions for the boundaries of the tensionable regions for any number of redundant cables used. The presented approach builds upon the available methods for conventional (rigid body) cable-driven mechanisms, i.e., null space analysis and supporting/separating hyperplanes. It extends these methods to the case of a multibody driven by cables. For this purpose, the notion of generalized forces and Lagrange’s method is used to eliminate the constraint forces/moments from the equilibrium equations. This has resulted in a more compact equation form with fewer unknowns. The method is then applied to several one- and two-DOF mechanisms with various cable distributions. Analytical descriptions for the boundaries of their workspaces are found. These boundaries and the resulting regions are then used to improve the design for larger tensionable workspaces.