In this paper, a number of kinematics problems of a novel 3-DOF 3-RPUR translational parallel mechanism are studied. First, an equation system of the mechanism structure constraint and an initial equation system are established. Second, all forward kinematics are obtained via the continuation approach, the positions of the mechanism corresponding to the solutions are validated. Third, according to the reversal solution of the position and the restriction of links and angles, the ideal workspace and the singularity of the mechanism were analyzed.