Design, configuration and operation modes of spherical 3-_RRR coaxial parallel robot were performed. A mathematical analysis of the robot was made, which consists of inverse and forward kinematic using geometric and numerical methods respectively, using MATLAB environment. Based on the above, eight possible operation and configuration modes were derived. The proposed approach demonstrates that a unique solution for the specific configuration and operation mode of a coaxial robot can be calculated. Moreover, mechanical design of the robot prototype was performed in the SolidWorks design program presented in detail for experimental verification of the performed numerical and simulation analyses. Results obtained from this work can be implemented in the development of real time orientation control systems for coaxial robots. As future works, an analysis of singularities, performance and dynamic will be carried out.