The problem of developing a reliable on-line flank wear measurement system is treated using the integration of an adaptive observer, based on cutting force measurement, and computer vision. In this part of the paper, the theoretical basis and design of the integrated method is presented. Implementation issues are discussed in Part 2 of the paper along with experimental results. The flank wear is modeled as the summation of two unmeasurable states in a nonlinear dynamic system realized in state space equation form. The inputs to the system are the feed, the cutting speed, and the depth of cut (i.e., the cutting conditions) and the output is the cutting force. Based on a simplified version of this flank wear model, an adaptive observer is designed by combining the observer technique and the recursive least squares parameter estimation algorithm. The designed adaptive observer indirectly measures the flank wear and simultaneously estimates one unknown model parameter, using measurements of the cutting force and the cutting conditions. The adaptive observer is integrated with a computer vision system which can directly measure the flank wear with good accuracy. In the integrated system, the adaptive observer is intermittently calibrated using direct flank wear measurements via computer vision. In this part of the paper, the integrated method is presented without referring to any specific computer vision technique. However, a computer vision technique is developed in Part 2 of the paper for an experimental evaluation of the proposed method. The fundamental idea behind the proposed integrated method is that a less accurate indirect flank wear measuring method (i.e., the adaptive observer) is intermittently calibrated by a more accurate direct measurement method (i.e., computer vision).