Position analysis of robotic systems represents the basis of their kinematic and dynamic studies, control, and optimal design. This paper considers position analysis of a novel hybrid robot with six degrees of freedom (6-DOF) composed of two modules, with the main focus on its inverse kinematics. The first module is a 5-DOF redundantly actuated parallel-serial manipulator. It relies on a 4-DOF Delta-type mechanism with the Schönflies motion type and provides its end-effector with three translational and two rotational DOFs. The second module is a 1-DOF rotary table. Using transformation matrices and the product-of-exponentials (PoE) formula, the article derives a closed-form solution to the inverse kinematic problem for the specified relative configuration of the modules. A numerical example illustrates the developed algorithms.