This paper presents a novel approach using adaptive neuro-fuzzy techniques to design controllers for planar cable-driven serial chain robots with variable configurations. The approach consists of two key components: (1) deriving dynamic models for cable-driven serial chain robots which are independent of their structure, and (2) adaptively determining the optimal cable connection points. Traditional methods face challenges in obtaining accurate dynamic equations for cable-driven serial chain robots with high degrees-of-freedom, hence neural networks are employed to estimate the model. In order to handle the variability in cable connection points, adaptive fuzzy methods are utilized. The proposed adaptive neuro-fuzzy controller algorithm introduces two new indices, namely cost-of-redundancy and degree-of-redundancy, to effectively address redundancy concerns. Additionally, the algorithm efficiently reduces the search space for finding the optimal configuration. Simulation results for a planar 3 degrees-of-freedom cable-driven serial chain robot using this algorithm showcase a noteworthy 42% reduction in cost-of-redundancy and an impressive 53.125% reduction in search space.