The Lower DOF parallel robot rely on strictly geometrical constraints of axis of pairs in and between limbs to obtain the reduced number of DOF .In practice ,these constraints will never been perfectly fulfilled due to the inevitability of errors, and hence produce series bad effects and problems. Using screw theory and set theory as mathematical tools, the DOF and constraint system of 3-CRR parallel robot, were systematically summarized and in-depth studied. Kinematics design of a limited DOF parallel robot, a 3-CRR pure translational parallel robot, is presented that takes into account the error. The errors presented in the paper consist of two kinds. The errors is defined as the position error of rotation center of the platform caused by errors in the kinematics constants, such as axis error The above research results provided an insight into the error of 3CRR parallel robot.