The 4SPRR-SPR parallel robot, which has considerable potential for application in the field of machining, is a novel closed-loop mechanism with a high rigid-weight ratio. Kinematics and workspace analyses of the 4SPRR-SPR parallel robot are key requirements for its application in machining. In this study, the inverse kinematics of the 4SPRR-SPR parallel robot is analyzed using a geometric method based on the mechanism arrangement of the robot. The forward kinematics model is derived by training the vector-quantified temporal associative memory (VQTAM) network, which originates from a self-organizing map (SOM). Furthermore, an improved algorithm is obtained by combining the locally linear embedding (LLE) and VQTAM methods. A boundary extraction algorithm for the workspace analysis of the parallel robot is proposed. The performance of the boundary extraction algorithm is analyzed and compared with that of a global search algorithm; the result indicates that the novel algorithm has the same computational accuracy in addition to higher efficiency. The workspace of the 4SPRR-SPR parallel robot is analyzed using the boundary extraction algorithm. Finally, the 3D model of the 4SPRR-SPR parallel robot is simulated using the ADAMS software to verify the reliability of the proposed algorithms. The simulation results demonstrate the effectiveness of the methods proposed in this study. In addition, the robot kinematics and workspace analysis methods described herein can be extended to other serial and parallel robots. This research provides a theoretical framework for trajectory planning of mechanisms, workspace optimization of robots, and robotic control.