Engineering topics
Publications and source records attributed to Lafferriere, G..
The existence of two- and three-finger grasps in the presence of arbitrarily small friction is shown for two- and three-dimensional smooth objects using a simple technique. No convexity of the objects is assumed. The existence of finger gaits for rotating a planar object using three and four fingers is proved. Additional results for smooth convex objects which describe two different finger gaits using four fingers are presented.
Consideration is given to the problem of optimal force distribution among three point fingers holding a planar object. A scheme that reduces the nonlinear optimization problem to an easily solved generalized eigenvalue problem is proposed. This scheme generalizes and simplifies results of Ji and Roth (1988). The generalizations include all possible geometric arrangements and extensions to three dimensions and to the case of variable coefficients of friction. For the two-dimensional case with constant coefficients of friction, it is proved that, except for some special cases, the optimal grasping forces (in the sense of minimizing the dependence on friction) are those for which the angles with the corresponding normals are all equal (in absolute value).