Multilink cable-driven manipulators offer the compactness of serial mechanisms while benefitting from the advantages of cable-actuated systems. One major challenge in modeling multilink cable-driven manipulators is that the number of combinations in the possible cable-routing increases exponentially with the number of rigid bodies. In this paper, a generalized model for multilink cable-driven serial manipulators with an arbitrary number of links that allow for arbitrary cable routing is presented. Introducing the cable-routing matrix (CRM), it is shown that all possible cable routing can be encapsulated into a single representation. The kinematics and dynamics for the generalized model are derived with respect to the CRM. The advantages of the proposed representation include the simplicity and convenience in modeling and analysis, where all cable routing is inherently considered in a single model. To illustrate this, the inverse dynamics analysis is performed for two example systems: a 2-link 4-DoF manipulator that is actuated by 6 cables and an 8-link 24-DoF mechanism actuated by 76 cables. The results show the validity and scalability of the generalized formulation, allowing for complex systems with arbitrary cable routing to be modeled and analyzed.