The robot pose errors detection is a key step to realize the kinematic calibration. The six-dimensional geometrical errors detection using a single CCD camera and elaborately designed targets is proposed. A model of rigid body displacement and its 2D image mapping, which is constructed based on 4 spatial features and 2 vanishing points of a parallelogram geometric constraint, can be used to achieve precise positioning of the position and pose of the end-effector. By taking a Delta robot as a demonstrator, experiments of kinematic calibration will be carried out to verify the validity and effectiveness of the proposed approach. The outcomes will lay a solid theoretical foundation for the low-cost and fast kinematic calibration of the robot.