Fingertip positions of a multifingered hand

The computation of the fingertip ranges within which the fingers of a robot hand can exert equilibrium forces is discussed. It is shown that in two dimensions this problem is a linear programming problem. Simply taking fingertip positions as variables in an equilibrium equation results in nonconvex nonlinear constraints which involve heavy computation. The effect of changing a fingertip position along an edge is equivalent to the effect of changing fingertip forces of the fingers fixed at both ends of the edge. This equivalence reduces the problem to a fractional programming problem. Fractional programming in turn is reduced to linear programming. The mutual dependence of two or more fingers is also examined