This paper shows the coordinates influence on singularity of a three degree-of-freedom structure, namely, three-Universal-Prismatic-Spherical (3-UPS) parallel manipulator. Rotational coordinates, which are chosen to define the orientation of the platform, affect the singularity of the manipulator. Euler parameters, which don't have any inherent geometrical singularity are utilized, however they are dependent coordinates. This paper shows the advantage of Euler parameters rather than Euler angles as the rotational coordinates for the manipulator. Additionally, the real loci of singularity for the manipulator due to its structure are predicted.