In this paper, we propose methods estimating untwisting torque of a twisted yarn that is the main cause of wale skew and predicting the skewness angle in a plain knitted fabric by using estimated untwisting torque. In general, as untwisting torque of a twisted yarn cannot be measured or estimated, snarl index obtained from untwisting test is used as one of its performance index. In this paper, untwisting test is modeled considering untwisting torque. Then, untwisting torque can be estimated by adjusting it so that simulated snarl index coincides with actual snarl index measured with untwisting test. Next, wale skew is also modeled considering untwisting torque. Then, the skewed knitted shape can be simulated with the estimated untwisting torque. In the above two models, the shape of a yarn, which is assumed to be a linear elastic object, and its potential energy are described by using the differential geometry. Minimizing the potential energy under geometric constraints, the stable shape of the yarn, which is physically valid, can be derived. Finally, the validity of our proposed method is verified comparing the simulated shape of a skewed fabric with the actual shape of the fabric.
