The 3-RPS parallel manipulator analysed in this paper is developed for the ankle rehabilitation device. Its architecture was achieved through novel methodology introduced in . Three revolute axes intersect at one point that becomes the center of rotation of the ankle rehabilitation device. The intersection point will be placed as close as possible to the ankle joint. By using algebraic approach, namely the Euler parametrization, the manipulator is described by a set of seven constraint equations. A primary decomposition is computed over a set of seven constraint equations. It turns out that the 3-RPS parallel manipulator with intersecting R-axes has two 3-dof operation modes, namely x1 =0 and x2 = 0. These two operation modes are different from operation modes belong to the 3-RPS parallel manipulator introduced by Hunt . The moving platform in both operation modes can perform coupled rotational motions and one vertical translational motion. However, the motion types in each operation mode cannot be easily distinguished. Therefore, the workspace of each operation mode is parametrized to recognize the physical characteristics of position and orientation of the moving platform.