US825363A - Calculating-machine. - Google Patents

Description

No. 825,363. PATENTED JULY 10, 1906.

J. VERMBHREN. CALCULATING MACHINE.

APPLICATION FILED SEPT. 2 1901.

2 BHEETS-SIQEET 1.

mflzess 6S java J07" No. 825,363. PATENTED JULY 10, 1906.

J. VERMEHRBN. CALCULATING MACHINE.

APPLICATION FILED SEPT. 20, 1901.

2 SHEETS-SHEET 2.

mhzess as. $2 VB/ILZ'OI" UNITED STATES PATENT OFFICE JQHANNES VERMEHREN, ()F HELLERUP, DENMARK, ASSIGNORTO' AKTIESELSKABET VERMEHRENS REGNEMASKINEE, OF COPEN- HAGEN, DENMARK.

CALCULATING-MACHINE Specification of Letters Patent.

Patented July 10,1906.

Original application filed September 1, 1900, Serial No. 28,786, Divided and this application filed September 20, I901.

I Serial No. '75,695.'

To all whom it may 001mm.-

- Be it known that I, JoHANNEs VERMEHREN,

friction or calculating members, one member cone-shaped, while the of each pair bein other one is shape as a disk or a ring whose edge runs on the outer or inner surface of the conein frictional contact with it, so that the disk or ring is rotated when the cone is rotated. The disk or ring may be mounted in such a manner that its contact-points with the cone have a constant but adjustable distance from the apex of the cone or so that it during its rotation also has a lengthwise motion in the direction of its axis, whereby its consecutive contact points with the cone form a curve the projection of which on the base of the'cone forms a logarithmic spiral. By the combination of said pairs of calculating members with a number of counting apparatus the machine is able to perform multi- .plications and divisions of whole numbers and fractions and multiplications, divisions, involutions, evolutions, and calculations by means of logarithms. q

The accompanfying drawings ive diagrammatical views 0 the improvecI calculatingmachine. I

Figure 1 shows a plane view of the machine desi ned for. multiplications and divisions of who e numbers and fractions; Fig. 2, a slightly diflerent form of the machine designed formultiplications, divisi ns, evolutions, involutions, and calcula s by means of logarithms; and Fi 3, a front view of the machine in Fig. 1. ig. 4 is a plan of one sideof a modified form of'machine.

. In Fig. 1 a machine is shown having two pairs of calculating members a Z and a l, of which the disk-shaped members a and a are connected with a counting apparatus, res ectively, t and t, for registering the comp etc and partial rotation of the said members. The

it runs with its edge on the surface of the cone-shaped member Z (Z) and. that its contact-point with said cone may be set at any desired distance r (r) from the apexof the cone Z (Z) by movin lengthwise the spindle c (0"), to which the disk a (o) is secured, and which spindle is operatively connected with the corresponding countingapparatus t, (27.) The distance may be indicated by the disks themselves on scales 1) p, parallel with the spindles c c. When rotated, the cones ,Z Z rotate the disks a a by friction, and they are mounted on spindles d d, which may be rotated by means of cranks or handles 9 g. The spindles d d may be rotated independently of each other or they may be coupled together, for instance, by means of a clutch operated by a handle f, so that both the spin-v d disk a (a') ismounted in such a manner that set at zero Without turning the spindles c and c, and when now the crank g is turned (the spindles d and (1 being coupled together) the values of the indications of the two counting apparatus will be in the ratio of 1- to r. The multiplication of a figure with a fraction is therefore easily performed by means of this simple machine. If, for example, it is required to take 18% per cent. of a series of numbers (values)that is to say, to multiply the same by fi z the two disks 0 a are set so that 1" equals sixteen and?" equals three, in which case the disk a, and consequently 'the counting apparatus t, connected with a,

will rotate at or Q per cent. 18% per cent.

the speed of the diskn and the counting ap-' paratus t, connected with a. The counting apparatus t" shows in this case the 18% per cent. of the numbers indicated by the count ing apparatus t. i

This mechanism presents great advanta es; s ecially for calculatingfthe exchange va ue 0 bonds and the like. for example, one German mark is eighty-eight oere, Danish, and one French franc equals 72.5 oere, the disks a and a. must be adjusted so as to make 1 equal eighty-eight and r equal 72.5, so that the counting apparatus 13 will indicate the numbar of francs and the other one, i, the corresponding'number of marks but the said arrangement may also be employed for general multiplications, as may be seen from the example quoted. If, for example, any given number is to be multiplied by sixty-seven, it

is the same as multiplying with the fraction It is obvious that the machine may be used for performing divisions also.

Instead of having the disks 0. a secured to the spindles c c the arrangement may also be such that the disks take their spindles along with them when they rotate, but can be moved lengthwise on the spindles, and of course the spindles c 0 must always be able to turn the counting apparatus t t when the disks are rotated by means of the cones. The improved machine may also be rovided with a greater number of pairs of ca culati'ng members than a Z and a l If, for example, four such pairs are used, it is feasible simultaneously to indicate dollars and cents with one counting apparatus and the corresponding values in marks, florins, and francs with the other three. The machine will therefore prove to be of the reatest advantage for money changers and ankers.

In the form shown in Fig. 2 the disks a a, are secured to screw-threaded s indlesc c, which turn in screw-threaded earings, so that they move lengthwise when the disks are rotated. The cones Z Z are mounted as already explained. As now the spindles c and 0 move lengthwise when rotated, it will be seen that the consecutive points of contact of the pairs of calculating members will describe curves on the surface ofl Z, the vertical projections of these curves forming log arithmic spirals on the bases of the cones.

it be assumed that cone Zis rotated at angle d-and that it upon radius 1* takes the disku alon by friction at angle dc at the same time t at the disk 1, has radius R, then we have by a similar consideration as in Amslers planimet'er:

m ma

of the height of the screw, so that H K d 1' d (p I d 1' I and subsequently 18rd Q constant.

It follows that with said infinitely small movement the projection on the base of the cone at the first and last point of contact be- 'tween the disk a and the cone Z always lies upon a line situated on the base of the cone under a constant angle with the radius vector.

The logarithmic spiral has meanwhile just a constant angle between a tangent and radius vector.

When the equation for a logarithmic spiral in polar coordinates is written and when for the sake of simplicity it is desired that the drift of the spiral on which all the projected points of contact are lying shall begin at radius 1 and after ten full rotations end at radius 10 to determine k and a, it is found that 1=7c 6 and 10=7c e whereof 7c=1 and 10=e or r 1 a log e a= 10 21rZ0g. e where screw has nine fillets on the distance which the screw 0 must shift lengthwise, whereas log. 7"

the point ofcontact between the disk a and the conelshifts from radius 1 to radius 10, the radius R of the disk a may easily be figured out, since we have there H equals 1, for We have, as quoted above,

and by diiferentiation from theequation of the spiral:

log. r= 1O .27r We get 1 l g. e (11 1 7 d E) 10 27: that is.

1" d =1O 27:109. do", and therefore we again get l If be accepted as having this dimension and the cone Z or, as shown in Fig. 2, its axis (1, is combined with adisk which is caused to rotate at only one-tenth of the speed of that of Z, the part of a revolution of that disk represents the mantissa of logarithm of the figure which is shown by t. For example, if it shows 789 an angle 6) corresponds to this figure, which may be found from the equation wherefore 5; represents the part of a whole revolution performed by the disk above referred to. If now this disk is combined with athirdcounting apparatus t the said part of the revolution may be read with still greater I accuracy.

It follows from the foregoing description that the counter t may be employed to indicate the mantissa of the log. 1), supposing the counter tindicates the figure p, and in .the same way a fourth counter t combined with the cone Z in the same manner as the above-named counting apparatus t with the cone Z, may indicate themantissa of the log. q if Z shows the figure g. It is therefore rendered possible by adjusting the counter t at the figure p so that the counter t indicates the mantissa of 10gb and by coupling afterward the counters t and t together, while i points at zero, and by then turning handle g so far that counter t indicates g to obtain thatthe counter t indicates the mantissa of lo p+log g. By this means the counter-t wil e brought to indicate the product of p multi lied by g. This machine is therefore capab e of being used for multi lications, and consequently it may be use for divisions also. If, however, the cones Z and Z are not coupled asshown in Fig. 2, but connected together in such a manner-for example, by means of cog ed wheelsthat Z is caused to rotate at dou le the speed of Z, it is obvious that the operator by means of counter t is enabled to indicate the square 5 dealing with extracting root may be perof sedond power of any'figure shown by the counter t, and if the cones Z and Z are -con, nected together in such a manner that Z q is brought to rotate at three times the speed of Z the operator may find at the counter 25 the cube or third'power of the figure shown at the counter t. The machine may a consequently' be employed for calculations of the second and third owers of numbers also. Moreover, all calculations dealing with'raising a number toa hi her power (therefore also the calculation 0 annuities) and those formed by first adjusting the counter t on a number, say p, whereby the counter 15 will indicate the mantissa of log. p. If then the counter t is adjusted to indicate the log. p, it is rendered possible to perform a multiplication or a division, respectively, with the number indicating the higher power of which it is required to raise the said figure or with that representing the root to be extracted. As the result of the operation a logarithm is found to which the counter t must be adjusted in order to indicate with the'counter t the number sought.

Generally speaking, one half of the machine may be used as a logarithmic table, the counter t indicating the mantissas of Briggss' logarithms which correspond to the numbers indicated by the counter t.

In order to insure that the projection onthe base of the cone of the points of contact between the members a and Z when connected by lines shall result in a logarithmic spiral and in order to avoid dependence on friction between the two members, the circumference of disk a may be provided with pointed teeth and the cone Zmay have correspondingcavities or holes the projection of which on the base of the cone when connected by a curve form a logarithmic spiral. In Fig. 2 teeth are shown on the circumference of the disks a a and holes in the cones Z Z. regular motion of the disk 0. in its relation to the cone Z is thus insured by means of teeth and corresponding holes, it is also possible, if desired, to dispense with the screwthreads' of the spindle c of disk a and'with the corresponding threads in the bearing, and it is even feasible, if desired, to cause the spindle c to partake in the rotary movement of. disk a, but without moving in its longitudinal direction. It is, however, also possible to construct the improved calculating-machine in such a manner that the contact-points between the disk a and the cone Z have a constant distance from the apex of the cone, while projection of the contact-points between the disk (1/ and the coneZ form a logarithmic spiral, or vice versa. In such case the counter i may be employed for determining the mantissas of the logarithms of the numbers indicated by the other counter t, or .vice versa. The improved machine may also be provided with a greater number of pairs of calculating members than a Z and a Z. By combining many such pairs of calculating members it is possible to obtain results with more figures than hitherto. As such arrangement, however, is well known, a further description is not necessary. Instead of being mounted to work like a screw in its bearing the s indle 0 might be fixed and be screwthreade so that the disk (1 may be screwed along it like a nut; but in this case therotary motion of the disk (1, must be transmitted to the counter t, for example ,by means of a cyl- 9 5 If the inder C, mounted parallel to spindle c and ac tuated by the pointed teeth of disk (1 engaging the cavities formed along as iral drawn upon the surface of the said cylin. er C. (See Flg. 4.) 1

It will be seen that the construction of this improved calculating-machine is based on a novel principle, which makes it superior to all other machines of this kind by reason of the fact that so many different calculations may be performed on it and by reason of the high speed with which'it works.

Having now particularly described and ascertained the nature of my said invention and in What manner the same is to be performed, I declare that what I claim is 1. In a calculating-machine, a main shaft, a number of cone-shaped friction members carried thereby, a corresponding number of disks having their edges in contact one with each cone, rotary spindles parallel with the slo ing surface of the corresponding cone and each supporting one of the said disks, and a calculating apparatus operatively con nected with each spindle, substantially as described.

2. In a calculatin -machine, a main shaft, a number of cone-s ap ed friction members carried thereby, a corresponding number of disks having t r edges 1n contact one with 7 each cone lengthwise-adjustable rotary spinseaaee dles parallel with the slopingsurface of the corresponding cone andeach supporting one of the said disks, and a calculating apparatus operatively connected with each spindle, substantially as described.

3. In a calculating-machine, a main shaft, a number of primary cone-shaped friction members carried thereby, a corresponding number of disks having their edges in contact one with each cone, rotary spindles parallel with the slopingsurface of the corresponding cones and each adjustably supporting one of the said disks, and a calculating apparatus operatively connected with each spindle, substantially as described.

4. In a calculating-machine, a main shaft,

a number of primary cone-shaped friction members carried thereby, a corresponding number of'disks having their edges in contact with each cone, rotary screw-threaded spindles parallel with the sloping surface of the corresponding cone and each supporting one of the said disks, and a calculating apparatus operatively connected with each spindle, substantially as described.

In witness whereof I have hereunto set my hand in presence of two witnesses.

JOHANNES VERMEHREN. Witnesses:

MARCUS MoLLER, MAGNUS JENSEN. 4

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