In this paper, the mathematical analysis of the robot effective mass is presented. The calculation of this effective mass and its ellipsoid are included. The relationship between the robot effective mass and the external force (collision) affecting the robot end-effector is investigated. The effective mass is analyzed using different robot configurations and different end-effector positions. This analysis is conducted using 2-DOF and 3-DOF planar robots and executed using MATLAB. The results from this analysis prove that the robot effective mass depends on the its configurations and end-effector position. Effective mass can thus be considered as one of the criteria in optimizing robot kinematics and configuration.