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It is interesting to study the phenomenon of contact interaction with an object and its manipulation using prosthetic mechanism proposed earlier by the authors. The task is made challenging due to the presence of soft fingertips, and the combined action of sliding and rolling at the contact interface. Detailed bond graph modeling of the contact phenomenon for one and two degrees of freedom of the prosthesis is presented. Effects due to softness of the fingertips while manipulating an object, extensibility of actuation strings and their internal damping, bearing friction at joints, etc., which are encountered in the prosthetic system, are modeled.