We conducted a study of a museum guide robot’s attempt at engaging and disengaging the audience at predetermined points in time during a guided tour. We used “ethnomethodology” as a tool for our study and analysis. In this paper, we describe how we developed, tested, and analyzed a museum guide robot system that borrows cues from social scientists to manage an audience. We have described how we began our study, the previous studies that we referred to, the initial attempts to test our concept, the development of the system, the real-world experiments, and the analysis of the data that we collected. We have described the tools of engagement and disengagement that the robot has used and presented the results of our statistical analysis of the experimental data. Most prominently, we found that a verbal gesture called “summative assessment” and a nonverbal gesture called the “lean-back” gesture are very effective as tools of disengagement. These tools help a robot guide to manage the audience in the same way as a human guide. Moreover, we found that a combination of the aforementioned two gestures is more effective than employing them separately.