M.Sc Thesis

M.Sc StudentMeltz Daniel
SubjectThe Problem of Interaction between Rough Surface and a
Kinematical Chain: Theory and Experiment
DepartmentDepartment of Mechanical Engineering
Supervisor PROF. Elon Rimon
Full Thesis text - in Hebrew Full thesis text - Hebrew Version


In order to predict and plan the movement of legged robot, it is necessary to understand the variety of possible interactions that might take place between the legs of the robot and the surface upon the robot stands. Special significance should be given to understanding situations in which the nature of the contact interaction changes. For instance, leg that was static begins to slide or leg that has been sliding breaks contact and detaches from the surface. Those situations can be potentially fatal for the robot stability.

The most common method for modeling the interaction between two rigid rough surfaces, as robot legs and the environment, in which the robot operates, is the Coulomb friction model. For most of the time the Coulomb model supplies sufficient proximity, but never the less, there are situations where the Coulomb model fails. In those situations, the model unable to supply a single and coherent prediction. Instead one gets several opposing predictions (Dynamic Ambiguity) or no prediction at all (Dynamic Inconsistency). In other cases one might face a prediction of infinite forces (Dynamic Jamming).

The first concern of this thesis is a graphical characterization of those failures in the Coulomb model. For the first time there is an attempt to give an intuitive interpretation to the situations in which the model fails to supply a single coherent prediction. As until now those results where solely mathematical. For this aim a graphical tool was developed, C-space Acceleration Diagram, which allows graphical and intuitive representation of the multimodal dynamics, involving frictional contact points. Another tool that was developed is the C-space Velocity Diagram, which allows similar graphical and intuitive representation and solution of impact with friction scenarios. C-space velocity Diagrams are especially useful when one deals with tangential impact. Both C-space Acc Diagrams and the C-space Velocity Diagrams are rooted in C-space based geometrical analysis, of the dynamics of 2D Kinematical chains, which represent robotic mechanisms, coming in contact with frictional surfaces.

The second concern of this thesis is the empirical demonstration of the Dynamic Jamming effect. This demonstration of the Dynamic Jamming is the first of its kind as until now the Dynamic Jamming effect was solely theoretical result. The results of this empirical demonstration were published as a conference article.