The shaft clamping mechanism clamps a cylindrical shaft such that it will not rotate in a housing. Using ordinary machine tools or the like, portions of the housing that surround the shaft are removed, leaving thin areas that act as hinges. The housing may not be cut all the way through so that the hinged or moving portion of the housing that exerts the clamping force is contiguous with the rest of the housing. Applying force in a plane perpendicular to the axis of the shaft, toward the shaft, in the middle of this hinged portion allows that part of the housing to move very slightly. The housing and shaft may be a close fit so that only a slight amount of movement of the moving part of the housing will be required to clamp the shaft. In order for this mechanism to work, the housing material has to flex slightly at the "hinges". The stationary portions of the housing must also deflect very slightly.