In this paper, we propose a model of embodied communications focusing on entrained body movements. Moreover, we implement a robot system that applies our proposed model. The proposed model emphasizes that, in order to achieve smooth communications, it is important for a relationship to emerge from a mutual entrained gesture, and for a joint viewpoint to be obtained by the relationship. Psychological experiments were carried out to explore the validity of the model. Concretely speaking, the aim of the experiments was to investigate correlations between body movements and utterance understanding in human-robot communications involving giving/receiving route directions. Results showed that subjects can communicate with a robot smoothly but only when the robot sufficiently practices gestures which entrain the subjects' body movement, whereas the subjects are unable to correctly understand the robot's utterances without such practice. The reason for this is that, without practice, no relationship emerges between the subjects and the robot due to the lack of a mutual entrained gesture, and moreover, no joint viewpoint is obtained. The results also verified the validity of the proposed model.