A novel 3-UPU parallel mechanism with two rotational and one translational (2R1T) degrees of freedom (DOFs) is analyzed in this paper. The base and moving platform of this mechanism are always symmetric about a middle symmetry plane. The moving platform can rotate continuously about any axis on the middle symmetry plane, so there exists no parasitic motion during the rotation. Using the kinematic influence coefficient theory and the imaginary mechanism method, the first and second order influence coefficient matrix (namely Jacobian matrix and Hessian matrix) of this mechanism are derived. The relations between the velocity and acceleration of the moving platform and the actuated links are obtained. In order to verify the correctness of the theory, two numerical examples are enumerated and varified by the 3D model simulation. The singularities of this mechanism is discussed and the singular configurations of the mechanism, including one kind of limb singularity and two kinds of platform singularities, are obtained.

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