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We propose a numerical method for the approximation of the solution of a variational inequality. The study takes its origin from [1], where a theorem of existence and unicity is proved and from [2], where a procedure is indicated by means of which one can obtain the solution as the common limit of two monotone sequences, the first one being non increasing, the second one non decreasing, whose terms are solutions of elliptic midly non linear problems. In [2] an iterative procedure for the solution of these problems is indicated. The paper aims at describing a numerical procedure for the approximation of the solution. We start by observing that, to obtain a solution within a given approximation, only one of the above mildly non linear problems need be considered, and we construct a convergent difference scheme for the approximation of the solution of such a problem. Finally, an estimate of the error made in this double approximation is given. © 1974 Instituto di Elaborazione della Informazione del CNR.

In this paper procedures are described allowing the calculation of the cutter position at any given time in two axis, contouring, numerically controlled machinetools. It is assumed that input data define the profile being machined and the cutter offsct and feedrate. The profile consists of straight lines and arcs. It is allowed the cutter offset to be redefined during the machining operation. Procedures mainly consist of a staircase approximation of the theoretical tool-path, as defined from the geometry of the profile and the cutter offset. They require only additions, subtractions and comparisons and are intended for implementation by low-cost special purpose computers.