Hamiltonian dynamics of Poincaré gauge theory: General structure in the time gauge

General aspects of the Hamiltonian structure of Poincaré gauge theory of gravity with $R+T^2+R^2$ type of Lagrangian are investigated in the time gauge. The explicit form of the Hamiltonian is found, taking care of the fact that some of the primary constraints exist only if some specific relations among the constants of the theory are satisfied. The consistency conditions of the primary constraints are obtained, and their dynamical meaning is clarified in the case corresponding to the existence of massive tordions in the weak-field approximation of the theory. The way to construct the Dirac brackets is indicated.