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A novel 3-degrees of freedom (DOF) <italic>RPU&#x002B;UPU&#x002B;SPU</italic> parallel manipulator (PM) is proposed in this study, and its complete kinematics and stiffness are studied systematically. First, the architecture description is discussed, and the inverse and the forward positional posture analysis are studied based on the constraints in the PM. Second, the Jacobian matrix, the velocity model, the Hessian matrix and the acceleration model are derived in explicit and compact forms. Third, based on the virtual work principle, the static model and the deformation decompose method, the stiffness model is built. Meanwhile, the stiffness matrix and the compliance matrix are obtained. Finally, the correctness of the models built in this study are verified by simulative PMs. This study is expected to provide new ideas for the design of PM machine tools.