Three pairs of signature partners' transition energies of Thallium (Tℓ) odd mass superdeformed (SD) nuclei's (A ~ 191-195), were fitted with the experimental one using the Bohr-Mottelson four-parameter collective rotational model. We chose the Bohr-Mottelson four-parameter rotational energy formula because it has been reported that it has excellent compatibility with the γ-ray transition energies. The four model parameters were extracted using a suitable search program. Harris's method was used to calculate the superdeformed rotational bands' (SDRBs) bandhead spins. The values of the adopted parameters, which were obtained using a simulated fitting search software, were used to measure the rotational frequency, dynamic J (2) , and kinematic J (1) moments of inertia to the transition energies. When compared to the experimental values, there is a great deal of agreement J (2) and J (1) have been studied as a function of increasing rotational frequency. The suggested staggering function was used to investigate the ΔI= 1 energy staggering in Tℓ odd mass SD nuclei.