This paper focuses on the forward kinematic analysis of (6 + 3)-degree-of-freedom kinematically redundant hybrid parallel robots. Because all of the singularities are avoidable, the robot can cover a very large orientational workspace. The control of the robot requires the solution of the direct kinematic problem using the actuator encoder data as inputs. Seven different approaches of solving the forward kinematic problem based on different numbers of extra encoders are developed. It is revealed that five of these methods can produce a unique solution analytically or numerically. An example is given to validate the feasibility of these approaches. One of the provided approaches is applied to the real-time control of a prototype of the robot. It is also revealed that the proposed approaches can be applied to other kinematically redundant hybrid parallel robots proposed by the authors.