Performance Quality, Sensitivity, and Tolerance Specification of Mechanisms
Abstract By employing Taguchi’s concept to mechanism synthesis, this paper presents the theory and technique to identify a robust design, which is the least sensitive to the tolerances, for mechanisms and to determine the tolerance specification for the best performance and manufacturability. The method is demonstrated in finite and infinitesimal position synthesis. 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 specification 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 is readily adaptable to almost any form and type of mechanical system, including multiple-loop linkages and mechanical assemblies or even structures.