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In the present work we have developed a three-dimensional gravitational modelof barred galaxies, in order to study orbital and escape dynamics of the starsinside their central barred region. Our gravitational model is composed of fourcomponents, central nucleus, bar, disc and dark matter halo. Furthermore wehave analysed the model for two different types of bar potentials. The studyhas been carried out for a Hamiltonian system and thorough numerical studieshave been done in order to categorize regular and chaotic motions of stars. Wehave seen that escape mechanism has only seen near saddle points ($L_2$, $L_4$and $L_2^{'}$, $L_4^{'}$) of the Hamiltonian system. Orbital structures in $x$- $y$ plane indicate that this escaping motion corresponds to the two ends ofthe bar. Classifications of orbits are found by calculating maximal Lyapunovexponent of the stellar trajectories corresponding to a specific initialcondition vector. Poincar\'e surface section maps are studied in both $x$ - $y$and $x$ - $p_x$ ($p_x$ is the momentum along $x$ - direction) plane to get acomplete view of the escape properties of the system in the phase space. Alsowe studied in detail how the chaotic dynamics varies with mass, length andnature of the bar. We found that under suitable physical conditions the chaosplays a pivotal role behind the formation of grand design or poor spiralpattern for stronger bars and ring structures for weaker bars.

Role of galactic bars in the formation of spiral arms: A study through orbital and escape dynamics -- I