The study of the sub T-g relaxation in a semi-rigid polymer family for which the size of the lateral chain varies from one carbon to three carbon atoms have been performed. We used an entropic model proposed by Hutchinson et al. [Macromolecules 33 (2000) 5252] introducing a new parameter x(delta) called the entropic non-linearity parameter. For our samples we found x(delta) = 0.45 +/- 0.05. On comparison with the data obtained on other linear polymers, we have shown that the rigidity of the main chain involves an increase in the entropic non-linearity parameter x(delta). Furthermore, we have shown, by using the fragility concept, that this new entropic model is conceptually equivalent to the Random Walk Model proposed by Arkhipov et al.