We develop a framework based approach to extract and recognize hand gestures from the video sequence acquired by a dynamic camera, which could be a useful interface between humans and mobile robots. We use Human-Following Local Coordinate (HFLC) System, a very simple and stable method for extracting hand motion trajectories, which is obtained from the located human face and body part. Hand trajectory motion models (HTMM) are constructed by HFLC and hand blob changing factor. In this paper, we apply a principal component analysis (PCA) based approach to improve the recognition accuracy. For further improvement, temporal changes in the observed hand area changing factor are utilized as new image features to be stored in the database after being analyzed by PCA. Each HTMM in the database is classified into gesture categories, or temporal changes in hand blob changes. We demonstrate the effectiveness of the proposed method by conducting experiments on 51 kinds of sign language based Japanese and American Sign Language gestures obtained from 7 people. Our experimental recognition results show better performance is obtained by PCA based approach than the Condensation algorithm based method.