It is important to maintain high kinematic reliability for robotic manipulators so that their positional errors are with acceptable limits at a required level of probability or reliability. This work accounts for random dimensions and random joint angles of robotic mechanisms and develops an efficient reliability method that can quickly and accurately predict the kinematic reliability of robotic manipulators. The kinematic reliability is defined by the probability that the actual position of an end-effector falls into a tolerance sphere, which is centered in the target position with its radius equal to the error tolerance. The motion error, which involves three dependent coordinates of the end-effector, is at first transformed into a function with only independent standard normal variables, and then the saddlepoint approximation is applied to compute the kinematic reliability. The transformation and the use of saddlepoint ensure high accuracy and high efficiency since no random simulation is needed. Examples are presented to demonstrate the accuracy and efficiency of the proposed method.

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