In the latest International Terrestrial Reference System realization (ITRF2014) combination model, new types of displacements have been introduced by means of mathematical functions. The addition of these functions has led to the implementation of new constraints to define the reference frame. This work was anticipated by A. Dermanis (2008) who derived constraint equations for different kinematic models. This paper presents the fundamental theoretical concepts that have been used to derive the latest International Terrestrial Reference Frame (ITRF). A new physical interpretation of the partial inner constraints involving transformation parameters is presented to supplement earlier work. By reviewing the various possibilities that could have been implemented to enhance the ITRF coordinate variations, this paper justifies the ITRF2014 chosen kinematic model and why it still does not include functions suggested by Dermanis (2008).