Automatic computation of bending sequences for wire bending machines

ABSTRACT

Determining a feasible bending sequence, i.e., ensuring absence of wire self-collisions and wire-machine collisions, or even an optimal bending sequence, i.e., minimising time or energy required to perform it, is a difficult and time-consuming task for complex workpieces, even for expert operators. Introducting algorithms for the computation of wire-bending sequences is thus crucial to increase productivity and production flexibility, and to decrease production costs. This work proposes an algorithm to automatically determine an appropriate bending sequence for a given workpiece, bending tool, and machine 3D CAD model, which leverages on a representation of the wire as a robotic manipulator and of a bending sequence as a tree, and on the adoption of A* as graph search algorithm. A cost and a heuristic function, suitable for the wire-bending problem, and an approach to parallelise the execution of A* are introduced, as well. In this way, a computationally simple and efficient wire-bending sequence computation algorithm is devised, able to determine a solution in an amount of time less or equal to the time used by an expert operator, without the need of high computational power. The effectiveness of this algorithm is assessed on two different test cases, relevant to industrial workpieces.

KEYWORDS:

• Bending sequence computation
• bending sequence optimisation
• wire-bending sequence

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1. This additional joint, whose D-H parameters are straightforward and always constant, is not reported in D-H parameter tables.

2. Note that using a tree to represent all the permutations of a set of $N$ bends is an intuitive and convenient way to convey the algorithm for the automatic computation of bending sequences. As far as the algorithm implementation is concerned, however, different techniques can be adopted to determine and store the permutations, e.g., (Fisher and Yates 1948; Sedgewick 1977; Heap 1963), aiming at reducing computational time or memory consumption.

3. Note that, cost function (1) is a translation into a mathematical form of the concept of ‘best bending sequence’. Weight selection is thus application specific, and it represents an important task where the operator experience in the bending process plays a crucial role. In the case studies here reported, weight values have been selected, for the sake of example, to represent a situation in which the linear motion of the wire is faster, or less energy consuming, with respect to turret and wire rotations (see Tables 6 and 10).