9503935 Ting This project addresses the issue of mechanical system design for performance quality and manufacturability by integrating parameter design and tolerance allocation at an early stage in the design process. The project includes three main tasks: (1) characterizing tolerances by geometric tolerance representation, modeling of mechanical assemblies with kinematic chains, and modeling of form tolerances; (2) developing a robust design methodology for mechanical systems that identifies performance characteristics and derivation of system sensitivity indices; and (3) synthesizing tolerances for performance and manufacturability by determining tolerance allocation for performance, manufacturability and cost reduction, and achieving optimal decisions for performance, quality and manufacturability. The approach will be demonstrated in a case study. The results of this research offer an effective method to understand the effects of tolerances on performance. This method treats the tolerance sensitivity of the whole system rather than an individual link. Yet, it allows one to identify unambiguously the relative impact of each individual tolerance on the performance quality and to select a system less sensitive to the tolerances. For mechanism synthesis, it is applicable to any type of synthesis problems, including function, path, and motion generation or finite, infinitesimal and mixed positions. Its effectiveness remains unchanged regardless of the number of desired positions or the number of links. In summary, this research leads to a method which enables designers to vigorously pursue the optimal parameter design and tolerance allocation concurrently in the early stage of the design process. Thus, manufacturing cost reduction, fast product design and prototyping, and off-line quality control is achieved.