The correct relationship between two connective joint coordinates of a robot manipulator is defined by four link parameters; one is the joint variable and the others are geomatrical values. Also, the basis for all open-loop manipulator control is the relationship between the Cartesian coordinates of the end effector and the joint coordinates. Hence, the fidelity of the Cartesian position and orientation of the end-effector to the real world depends on the accuracy of the four link parameters of each joint. In this paper, a linear analytical model between the six Cartesian errors and the four independent kinds of kinematic errors has been developed. Based on this model, the Cartesian error envelopes due to any combination of four kinds of kinematic errors can be uniquely determined. From the point of view of design, this error model can be used as a guide to minimize the open-loop kinematic errors of the robot manipulator. Finally, a new calibration technique based on this model has also been developed which can be used to correct the kinematic errors of the robot manipulator.