Errors caused by manufacturing or temperature variation are very important and necessary when analyzing the kinematics problems. They are of two types: the link dimension error and the joint clearance. In traditional kinematics we do not consider the effects of these errors. One gives an ideal assumption "without any error" when dealing with the kinematics problems. This paper systematically applies to above two error types and combines with the 4 X 4  transformation matrices to resolve the kinematics problems. Moreover, this paper derives the error responses, i.e., sensitivities. From these sensitivities, we can easily understand and predict the kinematic effects due to the errors.

kinematics, transformation matrix, error, sensitivity.