Patent GB-191200194-A (GB)
Title: Improvements in Machines for Solving Equations.
Inventor: NOWAK JOSEF
IPC: G06G3/00
Filed: 1912-01-02
Granted: 1913-01-02
Abstract: 194. Nowak, J. Jan. 2, 1911, [Convention date]. Electric-circuit equations, solving.-Relates to machines for solving the determinants connecting the. electromotive forces, conductances, and current-strengths of and in a network of electric conductors, of the kind comprising a gear corresponding to each network equation and in which the conductances are represented by the radii or teeth of the gears and the electromotive forces and currents by angles of rotation. The gears are combined in sets constituting nodalpoint gears so arranged that the projection of any axis taken in the nodal-point gear will coincide with the corresponding nodal-point in the diagram of the network to be calculated. Fig. 1 shows a network having nodes 1, 2, 3, 4 and feeding-points I, II, for any node 1 of which the equation is:- + e1 g11 - e2 g12 - e3 g13 = i1 and so on, e1 &c. representing the electromotive forces at the nodes, i1 &c. the algebraic sum of the currents at the nodes, g12 &c. the conductance of the conductor 1, 2, and g11 &c. the sum of the conductances of the wires meeting at a node. Fig. 2 shows a machine arranged for the above-described network, in which the rotations of the shafts I, II, III, IV correspond to the electromotive forces, and the ratios of the gearing between these shafts and the differential epicyclic gears correspond to the conductances; thus the equation for the node 3 is represented by the train of gearing which sums the rotations of the electromotive - force shafts modified by the gearings g31, g32, g33, g34 according to the conductances, and combines all such rotations by means of the three epicyclic gears D6, D7, D8 into a resultant rotation of a shaft i3, which is proportional to the current at the node. According to one modification, the electromotiveforce and current shafts are arranged in line, one within the other, and sleeves thereon make the necessary connexions between the epicyclic gears; a network may then be represented by means of a number of these nodal-point gears with suitable connecting-members, the projections of their axes upon a plane at right-angles coinciding with the nodal-points of the diagram. According to another plan, the various sections of one of these nodal-point gears are not in line but are arranged at angles to one another with bevel-gear and universal-joint connexions. The gears may also be arranged to reproduce the ring connexions of air lines and the bus-bar joints of underground cables. The nodal-point gears of the point 2 are shown in Fig. 11, spurwheels being used in place of shafts for connecting the separate differential gears D3, D4, D5. In order to obviate the necessity for large velocity-ratios introduced by the series of coefficients g11, g22, &c. in the above series of equations, a more symmetrical form. may be used:- (e1-e2) g12 + (e1-e3) g13 + (e1-eI) gII = i1 which affords further the means of reading off the current (e1-e2) g12 in the conductor 1, 2, for example, in terms of the rotations of certain shafts. Fig. 12 shows a nodal-point gear for the same node 2 adapted for this form of equation, the rotation (e2-e4) g24 which, for instance, has to be introduced into the differential gear D5 being derived from an independent combination (not shown) of the rotations e2 and e4 together with a spur-wheel gearing for introducing the conductance, and since this quantity occurs in two equations, it is transmitted to two nodal-point gears.