Fixture design is one of the main factors which affect the final product quality. Proper design of fixture plays an important role in ensuring the required tolerance of the product. Proper placement of locators is one of the prominent factors in fixture design. Locators are elastic: they deform under clamping and machining forces causing rigid body displacement of the workpiece which in turn affects the part quality. In this article, a 3-2-1 type of fixturing system having elastic locators around a considerably rigid rectangular workpiece is considered. A genetic algorithm is proposed, which uses a fitness function that evaluates the positioning error of the workpiece under external forces and torque. Among several variables, 12 variables, which define the placement of locators, are chosen to be optimized while minimizing the positioning error of the workpiece at the point of action of machining force. The proposed algorithm optimizes the 12 interlinked variables, within the specified region, for machining force and torque at a single point. However, when the cutting tool moves to any other point on the workpiece, it is observed that either the workpiece loses its contact with any one of the locators or the positioning error increases by a large value. To overcome this issue, the proposed algorithm is further modified for placement optimization to cater for multi-point machining, and the isostatism of the workpiece is ensured by checking the magnitude and direction of displacement (of what?) at each point of workpiece-locator contact. Finally, the original and modified GA algorithms are explained through a case study where the single point optimized placement shows loss of contact when machining force is applied at other points. The placement optimized from the modified algorithm shows that the isostatism of the workpiece remains intact while all four positioning errors are converged towards the same value. The results obtained from the proposed and modified algorithm are verified using ANSYS simulation.

夹具设计是影响最终产品质量的主要因素之一。夹具的正确设计在确保产品所需的公差方面起着重要作用。定位器的正确放置是夹具设计中的重要因素之一。定位器是有弹性的：它们在夹紧力和加工力的作用下会变形，从而导致工件发生刚体位移，进而影响零件质量。在本文中，考虑了一种3-2-1型夹具系统，该夹具系统具有围绕相当刚性的矩形工件的弹性定位器。提出了一种遗传算法，该算法使用适应度函数来评估在外力和转矩作用下工件的定位误差。在几个变量中，有12个变量定义了定位器的位置，选择最优化的刀具，同时最大程度地减小加工力作用点上的工件定位误差。所提出的算法优化了指定区域内的12个相互关联的变量，以便在单个点上加工力和转矩。然而，当切削工具移动到工件上的任何其他点时，观察到工件要么失去了与任何一个定位器的接触，要么定位误差增加了一个很大的值。为了克服这个问题，对所提出的算法进行了进一步的修改，以优化布局以适应多点加工，并且通过检查工件定位器每个点的位移大小和方向（什么？）来确保工件的等静性。接触。最后，通过案例研究说明了原始算法和改进的GA算法，在该案例中，当在其他点上施加加工力时，单点优化放置会显示失去接触。通过修改后的算法优化的位置显示，当所有四个定位误差都朝着相同的值收敛时，工件的等静性保持不变。使用ANSYS仿真验证了从提出的算法和改进的算法获得的结果。