The closed Cohen class time-frequency resolution obtained by the linear canonical transformation free parameter embedding method depends on the parameter selection, and the lower bound described by the uncertainty principle can represent the time-frequency resolution limit. Therefore, studying the uncertainty principle of the closed Cohen class time-frequency distribution plays an important part in guiding significance for the optimal parameter selection. In this paper, by constructing the relationship of two-dimensional separable linear canonical transform between the N-dimensional free metaplectic transformation and the closed Cohen class time-frequency distribution, we studied the uncertainty principle of closed Cohen class time-frequency distributions, including types of Heisenberg, Hardy, Donoho, Nazarov, Beurling, Logarithmic, Entropic, and etc. For the first four categories, except for the closed Cohen class time-frequency distribution uncertainty principle based on free metaplectic transformation, there are also expressions generalized from the traditional Cohen class time-frequency distribution. Finally, the equivalence of the uncertainty principle obtained by the two methods is proved.