J. M. Phillips, A. M. Ladd, and L. E. Kavraki, “Simulated Knot Tying,” in Proceedings of The 2002 IEEE International Conference on Robotics and Automation (ICRA 2002), Washington, DC, 2002, pp. 841–846.
Applications such as suturing in medical simulations require the modeling of knot tying in physically realistic rope. The paper describes the design and implementation of such a system. Our model uses a spline of linear springs, adaptive subdivision and a dynamics simulation. Collisions are discrete event simulated and follow the impulse model. Although some care must be taken to maintain stable knots, we demonstrate our simple model is sufficient for this task. In particular, we do not use friction or explicit constraints to maintain the knot. As examples, we tie an overhand knot and a reef knot.
Publisher: http://dx.doi.org/10.1109/ROBOT.2002.1013462
PDF preprint: http://kavrakilab.org/publications/phillips-ladd2002simulated-knot-tying.pdf