Parallel mechanisms (PMs) offer significant advantages compared to serial mechanisms, particularly in terms of enhanced precision and increased rigidity. However, the traditional non-redundant six-degree-of-freedom (DOF) PMs still face limitations, including a restricted orientational workspace and the occurrence of singular configurations. This paper presents a novel (6+3)-DOF 3-P[RR-RRR]SR kinematically redundant PM. Firstly, the kinematic model of the proposed PM is established, serving as the foundation for analyzing singularities and workspace. Subsequently, a method is proposed that locks some actuators in an ergodic manner to derive the local optimal transmission index (LOTI) of the proposed PM, enabling the evaluation of motion/force transmission performance. The dimensional parameters of the 3-P[RR-RRR]SR PM are optimized to obtain an enhanced transmission workspace without singular configurations. Finally, the prototype development and experimental verification are conducted, with results demonstrating that the 3-P[RR-RRR]SR PM can completely avoid singular configurations and offers a large orientational workspace.