Various structures for the spherical parallel robots have been proposed. The 3-RRR Spherical parallel robot and its specific structures like Agile Eye/Wrist is one of the most famous spherical parallel robots. In this article a new approach is proposed for modeling the direct kinematic problem of this robot to obtain all assembly modes. Utilizing the spherical geometry of the robot, two coupled trigonometric equations are obtained through using the angle-axis representation. Next, the two coupled equations are solved using Sylvester’s elimination method which leads to a polynomial of eight degrees. Finally, two examples are provided which having eight real solutions (assembly modes) and confirming the assembly modes is performed by a commercial modeling software package. The eight real solutions can be concluded that the degree of the obtained polynomial is the minimum and the proposed modeling is optimal. The advantage of the proposed method is the use of two evident geometric angles in solving the direct kinematic problem of the robot. Also, the proposed approach can be used for other similar robots such as the 3-RRS spherical robot.