The main objective of this study is to develop an analytical model that incorporates the effect of the general motion on the vibration of elastic elements in kinematic mechanisms. Equations for the translational and rotational motions of the links are developed applying Hamilton’s principle. Kinetic energy that is required for the application of this principle has been derived by utilizing a generalized velocity field theory for elastic solids. This approach provides means to include the inertia terms directly in the equations of motion. Effects such as centrifugal stiffening and vibrations induced by Coriolis forces are accommodated automatically, rather than with the aid of ad hoc provisions. We use Alfrey and Lee analogy to solve the dynamic problem of viscoelasticity.