A mathematical approach to analysis and optimal design of a fixture locating scheme

In manufacturing engineering, localization accuracy is a key concern in the design of a fixture to specify a locating scheme and tolerance allocation. This paper presents a general analysis methodology that is able to characterize the effects of localization source errors based on the position and orientation of the workpiece. From this methodology, a fixture model is formulated by taking into account the overall errors among the system consisting of the workpiece and the fixture in the design of the fixture locating scheme. With this model, the locating principle and a criterion of the robust optimal design are then proposed to improve the localization quality of the fixture. Some examples are provided and allow for a detailed discussion about how to carry out the optimal design of the locating scheme. A comparative study is also made between the optimal solution and the empirical one. Finally, an experiment is made to validate the fixture locating scheme for a cylindrical workpiece. We conclude that this robust design method effectively achieves stable machining precision in workpieces.