This paper focuses on a class of continuum robot manipulators that uses cables for actuation. In order to realize more natural and various motions like human musculoskeletal, tendon-driven manipulators is studied. It is challenging to design the manipulator structure which consists of bones and redundant muscles. A comprehensive study is presented including the theoretical analysis of the mechanical design, kinematics, dynamics and tracking control of a planar continuum backbone robot. Lagrange's equation is applied to the dynamic problem and the system is controlled by a computed torque/time delay approach. This paper explores the fundamental limitations of dynamic problem for different loading conditions and the behavior is formulated based on the motion constraints. For example, the cable forces are computed considering the yield stress. Moreover the effects of cable configuration are examined by comparing the model performance. Meanwhile, the geometrical parameters have an important effect on manipulation. The analysis is applied on two main robot structures considering geometrically constrained deformable continuum body. The simulation results illustrate the efficiency of the proposed design and controller. Nevertheless, the field of continuum and hyper-redundant manipulation holds great promise also in the experimental domains.