To broadly explore the rationale behind more socially acceptable robot design and to investigate the psychological aspects of social acceptance of robotics, a cross-cultural research instrument, the Robot Assumptions Questionnaire (RAQ) was administered to the university students in Japan, Korea, and the United States, focusing on five factors relating to humanoid and animal-type robots: relative autonomy, social relationship with humans, emotional aspects, roles assumed, and images held. As a result, it was found that (1) Students in Japan, Korea, and the United States tend to assume that humanoid robots perform concrete tasks in society, and that animal-type robots play a pet- or toy-like role; (2) Japanese students tend to more strongly assume that humanoid robots have somewhat human characteristics and that their roles are related to social activities including communication, than do the Korean and the US students; (3) Korean students tend to have more negative attitudes toward the social influences of robots, in particular, humanoid robots, than do the Japanese students, while more strongly assuming that robots' roles are related to medical fields than do the Japanese students, and (4) Students in the USA tend to have both more positive and more negative images of robots than do Japanese students, while more weakly assuming robots as blasphemous of nature than do Japanese and Korean students. In addition, the paper discusses some engineering implications of these research results.