A modified measure for the parallel cable driven robots is presented in this paper. These robots have additional advantages compared to other robots and even the parallel structures, but they are readily exposed to disturbances. The presence of external wrench (Force-Moment) may be the cause of violation against the motion constraint. The stability measure proposes a number between zero and one that could be the criterion for the evaluation of the robot's ability while returning to its original equilibrium which was influenced by external disturbances. To offer a stability measure, Gibbs-Appell equations and acceleration energy are used. Robot kinematic and dynamic modeling based on Newton-Euler’s method calculates the measure. To illustrate the capabilities of the proposed measure, a 6 DOF cable robot with six cables is simulated. The results of the two simulations are presented and analyzed. The stability measure is depended to kinematic parameters and also to kinetics parameters as cables tension at the beginning of motion. Therefore using the proposed measure one can better evaluate the stability within the wider range of parallel cable robots.