In this article we consider the longitudinal impact of a rectilinear elastic link against a solid using Hertz contact theory. The main objective 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 link are developed by 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. With the Dirac delta function defined as the limit of a sequence of functions we solve the discontinuities due to the impact.