Performance quality and tolerance sensitivity of mechanisms

This paper presents a general theory to determine the sensitivity of tolerances to the performance quality of mechanisms and a technique to identify a robust design, which is the feast sensitive to the tolerances. The method is demonstrated in position synthesis of linkages. The sensitivity Jacobian is first introduced to relate the performance tolerances and the dimensional tolerances. The Rayleigh quotient of the sensitivity Jacobian, which is equivalent to Taguchi's signal to noise ratio, is then used to define the performance quality and a sensitivity index is introduced to measure the sensitivity of the performance quality to the dimensional tolerances for the whole system. The ideal tolerance distribution is obtained in closed form. It shows how the tolerance specification affects the performance quality and that the performance quality can be significantly improved by tightening a key tolerance while loosening the others. The theory is general and the technique can be adapted easily for other mechanical systems, including multiple-loop linkages.