Motion dynamics of carrier conveyor dictates motion dynamics of powder or granular materials which are being transported. The carrier conveyor should have oscillatory motion with certain velocity. Trajectory of carrier conveyor should be set so that it creates complex oscillatory motion of powder or granular materials. This should cause optimal motion of transported material in regards of velocity and mass flow. This is possible since the analysis of the system indicates that it can be recognized as typical robotic system with rigid and elastic elements. Dynamic and kinematic models of conveyors for powder and granular materials are developed in this paper. The effects during and after collision of motor anchor and elastic carrier of conveyor are also modeled in this paper. This is important process since this phenomenon is present in the realization of the transportation process. The mathematical model of the mechanism of the conveyor is highly non-linear. It is defined on the principles of classical mechanics. This is important analysis, because this is present during whole task implementation of the mechanism. Influence of motor force on dynamic response of all important magnitudes of conveyor mechanism is done mathematically by mapping with Jacobi matrix.