The work aims to propose a three-degree-of-freedom parallel mechanism with closed global hinges to find the optimal workspace of parallel mechanism. Based on the reverse solution of the parallel mechanism, the velocity Jacobian matrix was first solved. Then based on the velocity Jacobian matrix, three singular positions of the parallel mechanism were analyzed, and numerical solutions of the singular positions were given. The theoretical reachable workspace of the parallel mechanism after elimination of singularities was simulated. Finally, the dexterity of the parallel mechanism was analyzed to find the position where the dexterity of the parallel mechanism was 0 under the theoretical reachable workspace, and the actual reachable workspace of the moving platform of the parallel mechanism was determined. After singular positions and 0 dexterity positions were eliminated, the x-axis displacement of the actual reachable space of the parallel mechanism was reduced from [−10 mm, 5 mm] to [−9 mm, −5.4 mm], and the z-axis displacement was reduced from [−790 mm, −650 mm] to [−790 mm, −677 mm], and the rotation angle range of the parallel mechanism was changed from [−30°, 80°] of the theoretical range to [32.544°, 64.114°]. The actual reachable workspace of the parallel mechanism is obtained by analyzing the dexterity. It proves that the dexterity has a great influence on the workspace of the parallel mechanism, and thus it provides a certain theoretical basis for applying the parallel mechanism in the design of parallel machine tools.