This paper describes the spatial three-dof 3-SUR 1-RU spherical Parallel Platform Robot. This type of robot has been previously proposed by other authors, but the present design, platform-mounted actuators, and application are unique. Further, the inverse kinematics problem is solved analytically. This robot is under development at Ohio University to serve as the active orienting device for aerodynamic testing of unmanned aerial vehicles (UAV) with up to 3 m wingspan. The UAV will be tested on a Windmobile which is a ground vehicle that is driven with the test article on an instrumented truss extended in the front in an undisturbed flow field. This system is an inexpensive substitute for a large-scale wind tunnel for measuring aerodynamic parameters of the UAV.
The three-degrees-of-freedom (dof) of the platform robot are actively controlled by three servomotors (R joints) mounted to the underside of the moving platform and there is a passive fourth middle leg with passive R-U joints for support. The inverse orientation kinematics (IOK) problem is formulated and solved analytically in this paper. Given the three desired Euler Angles, the three required actuator angles are found. Geometrically this analytical solution is equivalent to finding the intersection point of two circles on different planes, independently for each of the three platform robot legs. The analytical solution requires finding the roots of a quartic polynomial. There are at most two real solutions (elbow-up and elbow-down) which means that there are always at least two imaginary solutions to the IOK problem, which are discarded. Examples are presented to demonstrate the platform robot IOK solution algorithm for use in practical platform robot control.