M.Sc Thesis

M.Sc StudentShapira Tal
SubjectAnalysis of the "Coin Snapping" Phenomenon in
Multi-Fingered Grasps
DepartmentDepartment of Mechanical Engineering
Supervisor PROF. Elon Rimon
Full Thesis text - in Hebrew Full thesis text - Hebrew Version


The "Coin Snapping" phenomenon is an adverse event in which a body grasped by a multi-fingered robotic arm loses stability as a result of changes in the contact forces that act upon it. In this setting, any small disturbance in position or forces will cause the grasp to "collapse".  In previous studies, the phenomenon was investigated only for a planar body grasped with two fingers. The primary aim of the thesis is to explore the "Coin Snapping" phenomenon in multi-fingered grasps.

The thesis deals with planar grasps of rigid bodies, with frictional and pointed fingers that obey linear force-displacement laws. The focus of the thesis is on the "Coin Snapping" phenomenon that occurs when the grasp's equilibrium stops being a local non-degenerate minimum of the potential energy.

Under the above-mentioned assumptions, the following grasps were investigated - a generalized planar grasp with k fingers and planar grasps with two, three and four equally stiff fingers.

At first, a mode of changing the contact-forces in the initial grasp was defined. Subsequently, an equilibrium equation and a stability test were developed for each grasp. An equilibrium diagram was defined to graphically show all of the grasp equilibrium orientation positions as a function on the preload. Finally, the values in which the "Coin Snapping" phenomenon occurs were calculated.

The "Coin Snapping" phenomenon was found to occur in five different patterns which can be explained by the Bifurcation Theory. It was found that increasing the preload causes either of two main patterns of the phenomenon - a gentle pattern in which the grasped body starts to rotate steadily, and a crude pattern in which the grasped body escapes towards the nearest stable position.

The different types on the "Coin Snapping" phenomenon were demonstrated in the following experiments: a) a planar grasp with two equally-stiff fingers; b) a planar grasp with three fingers of different stiffness coefficients. In each case, numerous combinations of normal and tangential stiffness coefficients were tested. The results of the experiments matched the theoretical calculations to a great extent.

In Summary, the "Coin Snapping" phenomenon, including its various patterns, occurs at values that can be calculated for any grasp, depending on the grasp's geometry and fingers' stiffness. The results of the thesis may be used for more carefully designed multi-fingered grasp in order to avoid the "Coin Snapping" phenomenon.