In the present work, reformulation of the dynamics of a planar two-link manipulator has been presented in the form of joint errors and their derivatives. The linear second-order differential equations with time-varying coefficients represent the Coupled Error Dynamics of the system. In these equations, the non-linear centrifugal and Coriolis terms are expressed as linear functions of joint error rates and the non-linear gravity terms as a linear function of joint errors with time-varying coefficients. After inclusion of linearized version of these terms, the concept of modal analysis is used in the design of a control system for the robot. The developed control approach is compared with the commonly used computed-torque control approach, as applied for a high-speed direct-drive two-link manipulator with revolute joints. Thus in the proposed approach for controller design, the system non-linearities are taken as part of the system representation itself instead of disturbances as assumed in existing approaches.