This work is an incremental extension of adjustable planar four-bar kinematic synthesis theory to consider not only synthesis, but also the elimination of the defects inherent in synthesis. A nonlinear equation system for moving pivot-adjustable planar four-bar motion generation that includes constraints for order defect, branch defect and circuit defect elimination is presented in this work. In the objective function of the equation system, the error between the prescribed and achieved precision positions is minimized. The equation system includes inequality constraints to eliminate order defects and branch defects. The equation system also includes a complete planar four-bar displacement model to eliminate circuit defects.