  Adopting the fully quantal triaxial particle rotor model, the candidate
chiral doublet bands in odd-$A$ nuclei $^{103}$Rh and $^{105}$Rh with $\pi
g_{9/2}^{-1}\otimes\nu h^{2}_{11/2}$ configuration are studied. For the doublet
bands in both nuclei, agreement is excellent for the observed energies over
entire spin range and $B(M1)/B(E2)$ at higher spin range. The evolution of the
chiral geometry with angular momentum is discussed in detail by the angular
momentum components and their probability distributions. Chirality is found to
change from chiral vibration to nearly static chirality at spin $I=37/2$ and
back to another type of chiral vibration at higher spin. The influence of the
triaxial deformation $\gamma$ is also studied.
