Development of a palpable virtual nylon thread and handling of bifurcations

Abstract

This thesis presents simulation of a palpable (the thread can be felt using a haptic device) virtual nylon thread, which will be used in suturing training. This work on thread led to discovery of problem of vibrations in haptics when bifurcations are encountered. We have developed a novel technique to handle bifurcations in haptics. The usual numerical techniques involve using second order Taylorseries approximation for energy of the system, and finding the equilibria using standard Newton's method. This fails near bifurcations, places where number of available equilibria change suddenly. And leads to vibrations when feeling such a system using haptic techniques. We use higher order energy approximation tosolve this problem. We show that higher order terms are necessary, but using bifurcation theory prove that third and fourth derivatives of energy (second and third of force) are sufficient.We model first a single variable system which bifurcates, a Zeeman machine. To our knowledge this is the first haptic realization for it. We demonstrate using Zeeman machine that usingthird and fourth derivatives in energy approximation, leads to elimination of vibrations . For a multi-variable system, like a 2D elastic curve, which simulates a tape-like thread which has preferred plane of bending, the number of third and fourth derivatives are huge and finding all of them is computationallyexpensive, an important consideration in haptics for avoiding vibrations due to delayed response. We make use of splitting lemmaand prove that it is sufficient to look for higher derivatives along a specific direction. This significantly reduces the computational load as the higher derivatives can be found easily using numerical differentiation along this direction. The results demonstrate that the algorithm works excellently well.We have developed an energy based method for simulating a nylon thread. The nylon thread is an example of non-linear dynamics. It shows phenomenon such as bifurcations, leading to`snap-through' jumps and large flexible deformation, which is in essence of knotting. We model the thread energy using stretchingand bending energies, and find equilibria. The algorithm developed for handling bifurcations is applied, and works extremely well. Wesuccessfully demonstrate the phenomena associated with a real nylon thread in our virtual thread. Smooth haptic experience isalso achieved. A full description of thread will require inclusion of twisting energy and self-collision detection, and will be dealtwith in future. Nevertheless, our technique for the first time brings out the characteristic features associated with a nylon thread, which are ignored sometimes for more visual realism.