This paper describes the synthesis of virtual human head movements while waiting for a response in human-machine interaction systems. The described approach uses a three-dimensional human head model and kinematic chain of rigid elements. We proposed a method to perform a motion sequence of a virtual head in the idle mode. Th is mode is a state when a virtual person or robot performs subtle movements during the waiting phases between different interaction intervals. This form of action removes the problem of character freeze in motion and has a higher degree of user acceptance. This research covers issues related to creating trajectories of motion to rotate the head model's rigid objects. The proposed method has been used to trajectory generation for loop animation and executes smooth movements in the idle mode. Since the used algorithm has low computational requirements and introduces low interaction delays, we can use it in real-time operation in the HMI framework.