Position Kinematics of a Three-Limbed Mixed Mechanism

Although robotics has traditionally focused on the serial chain structures typical of industrial robots, fully parallel structures such as the Stewart Platform have also found considerable industrial use. Actively coordinated mechanisms which have combinations of serial and parallel characteristics have been practically employed, and can be expected to become more important in the future. There has been very little study of the kinematic and static characteristics of these mechanisms which have combinations of the characteristics of fully serial and fully parallel structures. This work addresses the direct and inverse position kinematics of such a hybrid mechanism with combination of serial and parallel structure which has multiple, actively controlled actuators. While not the most general possible configuration, this particular case does include many important features of the general mechanism, and the solution obtained gives useful insight for developing a general theory of forward and inverse kinematics which will be equally applicable to serial, parallel and combination structures. Such a theory is necessary for rational design of hardware and software for such systems.