Jamming may occur during the loading of the workpiece in the fixture and cause an improper locating process or damage to the workpiece, fixture, and loading system. Consideration of the jamming phenomenon is a necessary task in the planning of the workpiece loading strategy. In the present paper, the minimum norm principle is used to present an analytical model for predicting the jamming occurrence conditions through calculating reaction forces at the contact points. The implementation of this model results in an optimization problem that is solved using the augmented Lagrange multiplier method. The proposed model is applied to two well-known jamming problems, namely the peg-in-hole and block and palm configurations. Numerical analysis is also conducted in Adams software to verify the theoretical predictions. Finally, the experimental setups are fabricated for these configurations to validate the theoretical predictions and numerical results. The results show that the maximum errors between the theoretical predictions and experimental results are 14.4% and 3.8% for the jamming-out angle in the peg-in-hole study and jamming-in travel in the block and palm problem, respectively. Moreover, the worst-case error of 6.9% is obtained for the theoretical prediction of the jamming-in travel of block compared to the numerical result. Agreement between the theoretical, numerical, and experimental results proves the capabilities of the suggested model in the accurate prediction of the jamming occurrence conditions and its potentials for use in the three-dimensional jamming-prone fixturing systems.

在将工件装载到夹具中的过程中可能会发生卡塞，并且会导致不正确的定位过程或损坏工件，夹具和装载系统。在设计工件加载策略时，必须考虑卡塞现象。在本文中，最小范数原理被用来提供一个分析模型，通过计算接触点的反作用力来预测干扰发生的条件。该模型的实现导致优化问题，该问题可以使用增强型拉格朗日乘数法来解决。提出的模型适用于两个众所周知的卡塞问题，即孔内钉和块状和手掌状。在Adams软件中也进行了数值分析，以验证理论预测。最后，为这些配置制造了实验装置，以验证理论预测和数值结果。结果表明，钉入孔研究中的卡塞角和块体和手掌问题中的卡塞行程，理论预测值与实验结果之间的最大误差分别为14.4％和3.8％。此外，与数值结果相比，对于块的卡塞行程的理论预测获得了6.9％的最坏情况误差。理论，数值和实验结果之间的一致性证明了所建议的模型在准确预测干扰发生条件及其在易受三维干扰的夹具系统中使用的潜力方面的能力。