Robots are widely used in automation because of their flexibility. However, there are still challenges to enhance the effective use of robots in machining process due to unexpected vibration/chatter. Instead of time-consuming trial and error, this paper proposes an expanded mode coupling chatter theory that suits robot kinematics and enables industrial application due to accurate mode coupling chatter prediction. This research allows determination of mode coupling chatter occurrence with respect to constantly changing parameters of robotic kinematic and practical contemplation before setting up the physical robot, workpiece and tool for machining. Firstly, the mathematical model of the robot structure is established and combined with chatter theory. A deepened analysis of stability criteria is carried out followed by experimental validation of the theory. By carrying out this chatter analysis, a software tool based on an algorithm was developed to help determine the stable setup, including machining parameters, robot pose, travel direction and workpiece setup, for a certain robotic machining application. The developed prediction algorithm ties vibration occurrence to machining force direction and magnitude that makes it applicable to various machining operations.