US1083370A - Device for maintaining the equilibrium of a pendulum. - Google Patents

Description

W. LUYKEN. v DEVICE FOR MAINTAINING THE EQUILIBRIUM OF A PBNDULUM.

. APPLICATION FILED FEB/29, 1912. 1,083,370.

Patented J an. 6, 1914. t

8 SHEETS-SHEET 1.

w. LUYKEN. DEVICE FOR MAINTAINING THE EQUILIBRIUM OF A PBNDULUM.

' APPLICATION FILED IEB.29, 1912. 7 1,083,370.

. a SHEETS-SHEET 2Q W. LUYKEN. v DEVICE FOR MAINTAINING THE EQUILIBRIUM OF A PENDULUM.

APPLICATION FILED PEB.29, 1912. 1,0 3,370.

Patented J an. 6, 1914.

3 SHEETS-SHBET 3.

residing at Essen-on-the-Ruhr, Germany, e

usrs sri-ersi vrsis r series wILHEmu LUYEKEN, or ESSEN-O'N-THE-RUHB, GERMANY, sssreuon r rerun. KRUI-P ssrrsuosssnnsoaerr, or menses-reissues, GERMANY.

- DEVICE FOR MAI NTKINING THE EQUILIBRIUM 0.? A PENDU'LUM.

Specification of Letters Patent.

Patented Jen. it, 1914.

Application filed rebmar 29, 19-12. Serial No. sewer To all whom it may concern Be it known that I, WILHELM LUYKEN,

subject of the Emperor of Germany, have invented a certain new and useful Improvement in Devices for Maintaining the Equilibr'ium of a Pendulum, of which the following isra specification This invention relates to a device for preserving the equilibrium of a pendulum suspended from a swinging body, and consists in the employment of a revolving disk car ried in a swinging frame for producing the moment tor influencing the pendulum so as to preserve the equilibrium; and that the axis of rotation of the revolving disk swings .in resonance with the body from which the pendulum is depending.

In the accompanying drawings is represented one embodiment of the invention under the supposition that such. a pendulum is hung in a gun turret of an armored battle ship and in consequence can turn, together with the gun turret, around an axis that is perpendicular when the ship is in equilibrium;

The drawings illustrate in Figure 1 elevation-of the device; Fig. 2 a side elevation of Fig. 1 seen in the direction. ot the arrow in Fig 1. F ig. 3 a top plan view of Fig. 1; Fig. 4 a section on line of Fig. 1, seen from above; Fig. a diagrammatic cross section of the ship and the gun turret along line 5-5 of Fig. 4; the following figures are in larger scale nainely Fig. 6 a diagrammatic section on line 6-0 of Fig I), seen from above; and Fig; 'l" a diagmmumtic elevation of the pendulum seen in the direction of the arrow 24 in Fig. 6.

The pendulum A is hung on a. universal bearing in the turret B, Figs. 5 and 6. For this purpose; a frame C, Figs. 1-, 2 and 4, is carried to swing on two trunnious in two bearing stands B which are rigidly secured in the gun turret, and in this frame the pendulum A is hung on two truunions a the axis of which intersects at right angles-the axis of the trunnions o. The pendulum A is provided with a crosshead situated above the frame C on which two disk can riers D, each with a pair of trunnions (Z are supported to swing n hearings a. The oscillation axes of the dish carriers l) coinoide with each other and perpendicular iliary pendulum J. e site to each otnei to a plane drawn through the axes of the trunnlons a and the center of gravity of the pendulum A. In each of the two c'arriers D is situated a revolving disk E, driven by an electric motor D and a1- ranged so that its axis of revolution may swing in'a plane perpendicular to the axis of thetr'unn'ions 01 Each of the two trunnions al located nearest together, on'the disk r carriers D, is provided with a bevel wheel sector d. Each of .the two hovel wheel sectors d is in mesh with one of two other bevel wheel sectors F, situated diametrically opposite each other but connected to form one piece and rigidly securedon one end of a shaft F,- which is parallel to the t-runnions a. 0n the other end of the shaft F 'is suspended an auxiliary pendulum F with considerable damping. The gearing-ratio is equal to one between the bevel wheel sectors F and disc tern consists of two disk carriers G which.

are mounted to oscillate around a couunou axis which is parallel with the axis of the trunnions z as wellas of two revolving disks i ch are driven by electric motors 1" and arranged onthe carriers (1' in he samemanuor as the revolving disks E on the carriers 1). Another auxiliary pendulum J with considerable damping is a"o provided on the main pendulum A the I I "if oscillation ofwhich is perpendicular to a plane drawn through the center of gravity of the main pendulum and the axis of the trunnions a This auxiliary pendulum J, which is fastened on a shaft J has gearing" connection with the disk carriers G through the bevel wheel sectors J. 9 arranged in such a manner that disk carriers G must oscillate withthe some angular velocity as the auxeciion oppov to what is r\ o idulmii F and case with the ausi disk earl i l both for the s oi: iolntion oil the revolving disks oi right angles with their axes of oson, when the auxiliary. pendnlums in their middle 'osition; and that the if 'olvit the revolving disk cu.i." ,i not with oil in-ts situated theres of oscillation of the n olvinp; isl; curl-lore At the tree end of one of the trunnions a is located on inductor which consists of on ermature rigidly connected with this trun nion, having a winding a, with a magnet stand rigidly connected with the frame and the field of which the girl nature is situated From the oscillations of theship,

electroniotoric force will then be generated in the inductor o a which is proportional to the angular velocity of the relative oscillotion between the main pendulum A. and the frame (l On the shaft F of the auxiliary pendulum F is furthermore l'oceteden armature having a Winding f W l11Cl1 can swing in e magnet stand a rigidly secured to the main pendulum A, in oonsonence with the auxiliary pendulum F so that an electroi'ootoric 'force will be generated in thein doctor, comprising the armature and the magnet stand a, which is proportionate w th the angular velocity of the auxiliary pendulum 1. This armature carries beside the winding 1", also a hollow copper cylinder {)2 which in well known miinner produces t e above mentioned dumping pendulum F The exciting windings 0 a of the magnet stands a al connected to 21 network. lid. of constant tension by moons of the conducting "Wires K, Fig. l. The two rinzilure windings f are by means of the conducting Wires N, coupled with the excit-- ing Winding p of a generator P, built as a series wound continuous current dynamo; which gene'utor ope'otes it separately excited motor Q by means of Leonard connections. On one of the two trunnions c is lurlhornmre fastened an armature With' windi of which con oscillate in e rno%netnd i that is rigidly attached to the can loch ll belonging thereto, actuated by illution of the ship and in consononce iiil'h the frame C; whereby an electromo torir l'oroe will be eneratcd in the inductor comprising t megnebstand b and itTIllflblll'Ll; which electroi'notoric force is pro )ortionate with the angular speed ofthe frame (3. An armature having a winding i is fesioi d to a shaft J of the auxiliary pendulum J which :irn'iaturo adopted to oscillate in consononce with the auxiliary. pei'iduluni J in n inegnet stand a which is.

fill

connected with. the main pendulum re'oy on electromotoric force is goenen the inductor '5 a proportionon. with il i lie auxiliary pendulum no; l the immature oi rigidly u: revolving disk system D El, so that.

of the auxiliary noasmo this #inductoris provided with a hollow copper 0 linder which constitutes the dumping devioe for tl nuxilinry pllbll lllllllli'l J. The exciting windings b and o of the magnetstonds o and o are, in the some manner asthe exciting; winding 0* and a, connected with the net-work M by means of the Wiring K F The armature windings c and 2'" are, by means of the Wiring K, series c0nnected with the exciting Windin r of the :ltlfl'll by the oscillation of the ship For this purpose it is only necessary, on thefone hand, to move in oonsoimnce with the name (l and by IIlBiIIl-S of the motor T, the part of the universal bezirin of the platform which corresponds to the rame C, which part may be considered as seen through the cross-head o of the main pendulum; and on the other hand to move the. platform itself, relatively to this port of its universal beurin s by means of the motor Q; so that the re etive angular-position of both perls always a recs with the relativeangular position oi the main pendulum A and tbcfframe C. That this problem can be solved by means of the motors Q and T will be shown in the'follow ting. I

By utilizing the described. device the two revolving disks E, which possess the same moments of inertia, are driven by the elec' tric motors I) ,tvith the same angular s eed but with av direction opposite to en 0t ier;

loo

and the two revolving disks H wlch like wise possess the some moments of inertia are similarly driven by the electric motors 1. The direction of rotation of the revolving disks E is indicated on the drawingsby the arrows 3 while the direction of rotation of the revolving disks H. is indicated by the arrows 2. Looking at the two disk revolving systems from the-side, from which the bevel wheel sectors F and J appear to lie behind the axis of rotation of the CM'I'IBI'S of oscillation of the auxiliary pendulum F3 As the two disk carriers D always move in opposite directions with theseine angular speed, the two vectors will always deflect the same angle, but in opposition to the direction of tllQ'iIXlS of oscillation of the auxiliary pendulum F"; the two moments genereted by the revolving E will conse; quently give a resultant moment, the vector of which tells in the direction of the axis of -osciliation of the auxiliary pendulum F in the This means that the resultant moment onerales as seen in Fig. 1 always in the plane of the drawing or in a plane- }mrallel thereto.

The moment caused by each single revolving disk will be equal to the product of its moment of inertia, its angular speed and the angular speed of the disk carrier. Or if in the ordinary wey the product of the momentol inertia of the revolving disk and its ungulair velocity. is designated as kinetic mo ment, this revolving disk moment will he "i tothe product of the kinetic moment revolving-disk end the angular veof: the disk frame it the kinetic revo ing disks E, is designated b v de'nd auxiliary pendu is designated W1 angular velocity i therewifingfidisk frame in F that bEiGH- S thereto .1 V :3

T8 each re'volvi disk will then exercise e moment of the magnitude A20. is the deliection of the ziuxilisfi v pendulum F can only ver small on account of its considerable dumping, the angle lav-which the 's oi? the two remixing disk momerts me d ected from the direction of the axis of rsciliation of the auxiliary pendulum'F will similarly always be verysmall. The components of the two vectors falling in the direction of the axis of oscillation of the auxiliary. pendulum therefore be almost exactly designated as Aw, and in come quence the resulting moment of the revolvingdisk system D E be approxin'iately equal to 22mg the vectors of this system being equal to the sum of the above mentioned components. In a similar way it can be shown thdl fthe revolving disk system G H will givein'resultnirt moment which, ionic F 1, always acts in the plane perto thnipiene oi the drawing, nil-l of which or" Will fall the singular velocity of the V w (which lei-zonal to the will be called M lotion oi" the enxilier pendulum J and that the magnitude of t is moment is equal to 25w when the kinetic moment of the revolving disk H is called AT and the angular velocity of the auxiliary pendulum J is called 10 llnesch of the two revolving disk systems the two revolving disks could naturally be substituted by a. single one the kinetic moment of which would have to be twice as lsrge'as the kinetic moment of each single revolving disk, this substitute revolving disk would set up a moment, the vector of which as regards the main pendulum, would not fall in a. constant direction, but would swing in s planeperpendicular to the axis of rotation of the revolving disk frame just as the vectors of the single revolving disks. The vertical component of this vector would correspond to a moment which attempts to turn the main pendulum around the vertical axis through its center of gravity. This moment which, by the Way, will becomparatively smell, is however without influence on the perpendicular equilibriumof the main pendulum. The moment corresoonding to the horizontal components of the vector can in, that case only be considered. This moment agrees, however, with the resultant moment from the two single revolving disks. The axis of oscillation of the auxiliary pendulum F will now be called U and the axis of oscillation of the auxiliary pendu lum J will he called V. As indicated by the arrows in the drawing, (Fig. 3) respectively for the U-axis and the V-exis, that direction will be called positive from which the respective bevel-wheel-sectors F and J ap pear to be situated behind the axis of rotstion'of the corresponding disk carriers D and G. The moment set up bv the revolving disk system D E will he called M and the moment of the revolving disk system G H Both these moments will he considered positive when their vectors full in the positive direction of the U-axis or V-nxis respectively. Should the auxiliary pendulum I, looking from the positive "side of the ll-arns. or,

which means the same, when looking at .it in Fig. 1, turn in the some direction as the hands of a. "clock, then M will be negative when the disk Erevolves in a. direction denoted. by the arrow y. If the angular speed to of the auxiliary pendulum F is considered as positive, when the some turns in the above mentioned direction, it follows that I seen from the positive side of the V axis,

deflects in the direction of the hands of a clock.

In the following will now be shown that the moments M and M in each Instance 5 will have such a value as will. he required for preserving the pcrpendlcular equllibrium of the main pendulum A.

The os latmg movements of the ship 111 it sca es as is "Well known, consist(l) in 10 rolling, that is, the swinging around the diving movement, that means the swinging of the Whole ships'hody in a vertical d1rection. In very largennd heavy ships, such as armored bottle ships (for which the described device is intended) the diving move ment is, as a rule very small in comparison with the oscillations of the rolling and stamping movements; this divin move ment may therefore be entirely le t out in the discourse, as it is of very little consequence as compared to the magnitude of the oscillations of the rolling and stamping movements. The stamping movement may also be left out of the reckoning as it is, in the ships in question, comparatively insignificant and also causes very small turning of the ship, 'i'vhich in the aimingcf the 111s scarcely has any disturbing influence. s it furthfirn'iore would not he difficult to'comiu'insatc for the influence of this stamping movement, in describing this device it will be pii'acticully sullicicnt to consider the ad justmcnt for the influence of the rolling movement only. ln the following, it will therefore be supposed that the ship only rolls.

Ships having very large moments of inertia. uud comparatively small moments 'of stability, such il'or instance as armored hatt-le ships, will roll in u sea-way lmost according to the some low in calm water; that they oscillate with. the closest approximaiion like an ordinary pendulum. It therefore the angle in which the ship defleets ii'oi'n its middle position during the time I? culledro, and o the largest value o'F 9 and the constant duration of the compleiej oscillation: the. following equation may he written according to the law of the peudul1unln Fi the position of the s point oi the main pendulum A is m, that means the position of the inn.

bearing stands B around this i,

spun-"ion I denoted by 1 tions of the axes of the trunnions c withthe ship in its middle position; the position of the same point, vvlr ship is swung around the oscillation e drawn through the point e unfaiuglo con to c during the rolling. It'w'ill'ntm he i: 1 posed that the turning angle of the s in in. its rolling movement is very small (less then 10). In this case it can be supposed that 75 the point m moves approximately in a. straight line 'm/-b, which stands pei'pen. dicular to the straight line (e -m o d th its total acceleration p is appri i equal to the tangential accelem eis i dc

when Z denotes the distance mh -r m from the oscillating then the equation (3) we obtain P: o' Bin. it or if we put l ,11 I I "p0 sin. in (5 The gun turret B may he s'wuu int angular position. That posit-ion ehou considered as the main position oi. lulu nu turret, in which the axis of the is parallel to the oscillating em. o. drawn through the point 0, Fi ship and the pendulum A at gulur position of the gun turret n denoted by the same angle" 12,, formed between the of the ti. and the oscillating axis, ivlii th the pendulum A are at rest.

If the main pendulum A new perpendicular during the es l. ship, the frame C of the unive must generally oscillate both i in the main pendulum A around the u trunnions a as well as in relation t trunnions-c", with any angular p s the gun turret. Calling the a which the frame C is turned from position during its oscillation urour axis of the trunnions a during and calling the angle o in which (1 turns from its middle position oscillation around the axis of the ill 0 during the same len 'th of the. lowing equations may he Written greatest approximation as ohtainin the angles $1 or @2 and q I'OSPt'ECtl'W, 5,, i

will casil; be evident in" so small a voice around the axis going through i gravity, and through the suspend:

and

50 z (,0 sin. n'

pendulum have the some acceleration, namely the acceleration g) of the suspension point on.

A three-axial cobrdinate system X Y 2, Figs. 5 and 6 may be considered to be arranged with thesuspension point in as starting point, in which the Z-axis is always vertical and the X-nxis and Y-axis always parallel to the direction respectively which the longitudinal and. transverse axes, drawn through the center, of gravity of the ship, will take when the latteris in its equilibrium. The Z-axis coincides in the above -mentioned' movement of the pendulum A with the axis-going through the center of gravity and througlithe point on; while the X'ZtXlS and the. Y-axis always make an angle a, Fig. 6, with the axis of the auxiliary pendulums F or J, that means with the U-axis or the V-axis respectively. during the arti ular position a: of the turret B.

fhe main pendulum A is influenced besides by the gravity and by the two moments M and M from the two revolving disk systems, also by a'moment which is generated by the inductors c a? and b c. The moments generated by the inductors a f and a i are not here taken into account as they depend on forces, which may be considered as inner forces relative to the main pendulum. Theinductor c a exercises a moment on the main pendulum, the vector of which falls in the direction of the U-axis This moment will be. called mu and considered positive,

when its vector points in the direction of the positive side of the ll-exis. The in doctor (2" b exercises the moment m the vector of which falls in the axis of trunnions c. This axis moves during the swinging of the ship, when the main pendulum hangs perpendicular, in a vertical plane through the V-axis, and forms with the TaXl S a very small. almost constant angle e, [compare equation (6)]. With regard to the vertical equilibrium of the main pendulum that horizontal component of the moment-vector will only be considered that falls in the direction of the V-axis and possesses the magnitude of m, cos. 4),. small as theengle n; cos. c, may be put down as approximately equal to 1. It may therefore be supposed with great approximation that the inductor o 7) will producea mo memo-enter. which falls inthe direction of the Vaxis, and has a magnitude that will 'as the clock runs.

As the angle 4 is inst as he cre and considered as positive, when it points toword the positive side of. the V- axis.

It we now examine whet conditions have in. be fulfilied whereby the main pendulum A, during the oscillation of the ship, will always retain its perpendicular equilibrium, it will be found, by using for instance the principle of dAlsznbert, snotn,%* cos. so; one. a sin. 5pm.. 8 and i ln'these equations the signs denote: g the acceleration of gravity, G the weight of the main pendulum (coinorising allthe difierent parts thereon), s the distance of its center of gravity from the suspension point m (compare Fig. 7) and G the angle, which the straight line ire-- Fig. 5, forms with the Ysxis. it ,will furthermore vbe supposed that the angle 0; from the port of the Xexis which is absolutely considered as positive, and which in Fig. 6 has been indicated by an arrow, will'be, counted as positive in the direction in which the clock runs; and that the positive part or" the U-exis must be turned QQ as the clock runs, in orderto make-it coincide with the positive part of theV-exis as is the case in thesrrsngernent selected for the drawing, Fig. 6. it is furthermore supposed can the angle o from the line o-me, Fig. 5, locked at from the positive sideof the X-axis, will be read as positive in the same direction as the clock runs. It will now only be necessary to further develop two principal equations (8 and 9). It will then be supposed that the anguler deflection of the auxiliary pendulums F and 3, which will be denoted as q and A? respectively, as seen from the positive side oi the U-axis or the V-axis, will be read as positive, from the middle position of the auxiliary pendulums, in the same direction It will furthermore be supposed that, at the instant under consideration, which would be determined by the time if, both the ship and the two auxiliary pendulums turn in the positive direction and that the angies o, ll) and d have simultaneously positive values. The angular position of the gun turret will be selected, as shown in Fig. 6, so that as will be a positive acute angle.

For the circuit/1 f N 72 that direction of the current will be established as positive,

in which the current runs in the positive di- "iecti'on as regards the U-exis, in the part of the (in-nature winding (i which lies below the npper'pole-piece of the magnet stand 0 that means in looking rt ig. 1, that the cur-' rent-runs toward the spe ator. It will also be supposed that the current has a positive direction as regards the clcctioinotoric forces generated in tho inductors 0, a and l l hcu the hip has turned out of its middlc position, in the smuc direction as the c ck runs, the angle at" q, the frame C has sunultuncously thmclh i-clutivc to tho main pendulum A. (which has to he considered hanging continuously pol'pcndicular) around the axis of the .trunnions o inthe' some direction, on anglc o -cp cos. outcompoi'c equation 6). An OlQCtl'OlllOtOllC fOlCB E will thci'chy be generated in the inductor c l u 'hioh forcepnopoitionutc with the hold power oil tho inductor, the number of tin-hr; of tho miniature Wiiu'liug o and the migului" velocity i 'ifi iii If the product of the field force, tho mun-- her of tut is oi thc oruiutui'c Winding a and the proportimmtc factor were summed up the (constant) quantity N, one would obtain 51S [Lit'QSillll :l'orthc elcctromotoiricforce the expression i I (it E llci l cos. a: cos it (10) The quantity wmld he considered posic'oonc'l to tho quantity l, neglecting the sign A i dz The quantity u should ho considered as positive, according to the sign rulcfor N, when the upper pole of" the magnet frame a, is a north pole, as is indicated in Fig. 1 by the direction of the arrow of the exciting czurrcnt; and should be considered as negative, when the upper pole is a south pole. With A positive value of ll, as indicated in Fig. 1., ond. tho ac'ccptcd moving condition of the auxiliary pendulum F. owill have negati e dirvction, under the supposition thut tho ui'n'mtuic windings u f are con ncc'icd in such :1 u'iunnc that :1 current runs in the posit I to du'cction oi th ll-fl? if such jut is ung in the [H'ibl'tllt (.lllljfjlilfill Glowing oxoression'will. be obtained both in the part of the armature winding: j which 15 situated below the uppcr polo pllfl'll 4 of the magnet stand a and in tho port of tho tcd i-t tho armature WlllLlll'lg c which is below the upper pole piece of the may stand 0 Should on. the other hunii armature windings of andf he councc that :1 current going in tho posilivc ll} in the part of the armature winding 1 lies beneath the upper pole piece of the 11mg: nct stand a, run in the ncgativc direction of the U-oxis, then 0 will huvc positivc di-- rection with a, positive value of it. o how therefore to Write, taking the signs into iron-- sidcrution,

wherein the upon sign has to be taken for the first name connection and the latter sign for the last numccl connection of the armature windings a and f For the sake of brevity, it will, in the following, be said as regards the first named connection, that the uriuuturc windings are similarly con-- nectcd, and as regards the latter connection that they are oppositely connected. If the resistance of the circuit a" f N p is called q,

We will, fol the current force 2' have the expi'cssion i t i cos. a cos. 4MP d9 The moment wt, exercised by thcinductor a" a outhe printipul pendulum is pi opon tionatc with the cxprcssion Ni, and the factor of proportion, which in the following will he called c, isindecd dc endent on the selected unity of measure, Vhen the moment acts in thefsomc direction as the clock runs and consequently has to be considered as positive, when N and i have positive values, and also changes its sign simultanc ously with ll and in, than the following cqum (ion is obtained m Ni (12) from which the following eqiiiitiou will ho cvolvocl when the valucof t, given in cqura u r u w tion (ll) 16 inserted In order to further develop the above equation the movement of the auxiliary pendulum BRdescribed by the angle '11 has first-to he decided. The acceleration 1) (com pare equation 4) will influence this moyenoeee'zo force will, at the instant under considerawill therefore he grew by :cni. The tion, have negative direction, under the sup components of the soelefition 79' falling in position on which the calculation is based. the direction of the axis ofsoscil'lation, that. is Should 2' at the sonic time be positive, the in the direction of the U-exis, do evidently so a current and the electromotive force will. con not at. all come under consideration fo the sequently have opposite signs (as in an elecmovement of the auxiliary pendulum F. tromotor). The moment. caused by the in- Even the component falling in the direct on ductor acts therefore in the direction of the the Z-anis may be neglected, es the die movement v,o-f the auxiliary pendulum. end flections h Fig. 7 of the auxiliary pendulum 35 has consequently to be taken as positive duron account of the supposed considerable ing the supposed condition oi movement of damping, may beconsidered as small and the auxiliary pendulum. Should the sigrr' consequently the factor 9,, of the Z compochange of one or the other of the quantities nent of p comprisin the iactor will generate z and n, the sign. of the moment will then a moment as roger s the axis of the nuxil- 4o change simultaneously. "With the armature iary pendulum which moment contains the windings a and f continuously connected, small quantity o sin. all of the second order. the term +cm' then expresses the magnitude The component falling in the direction of and sign of the moment. Are, on the other the V-axis need therefore only be taken into hand, the armature windings a and f oppo-- the reckoning, namely 4 2O sitely connected, the moment exercised on e the auxiliary pendulum, will reversely be exp 3) cos. ,8 cos. a 13., cos. ,8 cos. a sin. It pressed as to magnitude and sign by -cn, which will be readily understood. lVith e- For the movements of the auxiliary pengard to the manner of connection of the duluni F is consequently obtained by using so armature Winding, the moment, exercised by for instance the principle of dAlemhert, the

the inductor a f on the auxiliary pendulum,- diflerential equation 'k%+G s $cni= cos. fiGag-cos. a sin li in which is the moment of inertia, re-

the parts F Fhfroln the axis of the suxduced' to the e-xis of the auxiliary pendulum, 3 P P of all the oscillating parts of the revolving i the Value -fp we @qufitwn i di k system 1) E th t means f th t 15 inserted in the above cufierentiel equation, E D D d d F F F ,1; h fagtor f the equation will take the following :ipnesrping,G the Weight of the parts F F F and Mice afielisevei'al deli-fictions 65 s, the distance of the center of gravity of 2 cos. a 2? k G,s,= -25 cos. e6 8, 0% T sin. or; The phase displacing-angle 7 found in the above equation is here givenns tgf. ig 14 cos. ,QgGw, g

The solution of the dilierential equation here only will he considered, is follows as regards the state of permanence, which cos. 7

cos. a

2, ,112}, cos. 7 E

sin. 6 sin. (.lt Fr -rl) (15} The )hase'dis ilacin angle 6 will be deso follows that l l b r, i

cided through the equation If now the condition is selected so that- L01 PI cos. y

we. (EH57) is wesmo the dillerentiation of the above velocity to f theznjmilimsy pen rlulmn I will be obtemed 4 sin. (it F-r) (19} tie enove'velue Ol -3:193 inserted 1R equation (13) we obtain on? cos. y

m3 from equation (1) with regard to equation (19).

" 2 289; (303 M3 C03. 5' g "i new be evident that the foregoing will be identically satisfied by v "st main condition for the equiliben in equation (8) will therefore he i M when A and N have the valuesdeiined "by the above equations (23) and irrespective of What value Zfiaqv and'g in. an equally simple manner it can he moved that the second main condition set i by equation (9) for maintaining the mlgmlihrlum of the main pendulum has been I iuliilled. The quantities corresponding to tiw quantities N n E e z and g for thein- "t rs W 0 and a i? Will be desigmited n? E o z" and cg -With regard to is for N n E e and i the some n ll hold good 'as before as to the diion of the some. The armature wind- 323 0 and will furthermore be designated E llIQIBtUJi OIE, as Similarly or oppositely consin. (it

generated in the inductor .7) c of ted aceording to how the currents flow in some or the opposite direction to each I tained from equation are inserted in equation (8) and the letter equetionie divided by cos. a the following will be obtained. 15

v 12: cos. flGs sin. it cos. 7 g

p Nlt Gi iarmature winding other in the p it of the or pole iece of the lying underneeththe up magnet stands o" 31K (1.". L1 ewlse, as everywhere heretofore, when in the following equations simultaneously a plus or minus sign given, the upper sign refer to the first kind and. the lower sign to the second kind of emineetion of the armature Winding-i \Vhile the ship has turned during the time t from its equilibrium an angle o in the same dir tion as the clock runs, the frame C has also turned in the some direction around the axis of the trunnion 0 an angle I i [compare equation from its middle position force will then be T) l. An electromotoric i E n- N (ZCZ'Z E: Nrp l sin. 1! cos. it

Simultaneonelv will he enerated. in the a I i m 0 t i luetor a r an electromotoric tome 1 U F ihelein filui positinn 01% its was 01? revelutlon "1W pendul um Cmnparing 3415251011 (23 with aqua-.1011 j Ab 11% an .lum J in whiuh and. 71: have 1 alum J when 01+9O") H muw! aim he perceiwd that equation \xiu Hm smzae dirs ction will (10 '01- m Mum Q h shbstitutcd b}; 4 90 90 that iw equation will he:

'n accord-aim .CNQ *2 i sin. 11. a 60s. it? 1 g" m. "I U sin. (ii-$7") (29) s 'ur-thfifnwre, in wool-dance with m H above yalue of M and file oxpmsmm m, given in wgnution is; imam-1m in vqmziizm {9), @Kpresdng the $000111! and i 11min mmfiitiun 1 0-1 Um: nminl zxinizlg 0! NW 1 wwHHn-ium01 1110mainpcnduimn: L110 Yo]- lwwingg eqlmiinn wiil he obtained 11 ilw whole m 'miinn dividud by M sin. 2:

mat-ion 1 i and N have the j the angular posit-ion of the gun turret desix noted by the angle 0:; nor on the amount of the rolling motion denoted by an (if (9 only lies below the above given limits of about 10). As it furthermore does not de end on tho magnitude of q and g, the equi ihrium of the main pendulum will he maintained, when and :3" is permitted. to he of infinite magnitude ythatmeans as regards the maintenance of the cquili rium [of the main pendulum, that it is indifferent whether the circuits a f N p and 0* 1' r? N are open of closed. As cquatio'ns '(23) and show, it is furthermore of noconsequencc whether the armature windings a and f as-Well as c and i are connected similarly or oppo sitely, as long-as the signs of N and n, as

well. as N and a have been corrcctl selected. Of the greatest importanceis, however, (1}- that the two conditions of syn chronism determined by equations (17) and (28) are fulfilled, (2 that foreachrevolw ing disk system the irection of rotation of the revolving disk has. been so selected, looking at the system. from that side from which the beveled. Wheel sector, arranged on the shaft of the auxiliary pendulum, appears to he situated behind the axis of oscillation of If in accordance with the equation l3 taken that the equation for i will be transformed into t=AD 00s. a sin. (lt+e) Similarly will be foundthat -a' aaaan. aw 34.

the revolving disk frame; that the right-- hand revolving disk will run, in the same direction as theclock, if seen from above, (3) that thepnumber of revolutions and the moment of inertia of the revolving disk is selected for each disk system, so that the kinetic moment of each semi-ate revolving disk takes the value-determmed by equations (9i) and (31) respectively; and (4) that thevquantitles N and n as well as N and n will satisfy equations- (23) or (30) respecvalue gfdetermined by equation (19), the

cos [3 cos. a (einfllti following is obtained after several tran sfor motions of the equation:

00s. it) n? cos. Bil s and in accordance with equation (33) will. be determined by equation:

i 2 no; 2 f G8 g 0053. E"

The currents i and i serve to cxcite the enerators P p and R 1". As has already een said the motor T fed by the enerator R 1' must always steer the part '0 the uni-l versal hearing of. the platform corres ond iug tothc frame 0, so that said part a ways turns the same angle as the frame C (around the axis of thel trunnions c) as regards the gun turret actuated by the rolling movement of the ship. The angle in which each part has been turned as regards the gun turret, counted from the middle position, by means of the motor '1 during the time 6 will be called E. As the exciting current 1"- of: the generator It ain accordance-with aqua-- .21 rrm'xgement (fog instance fem; itseif regzurds he m ins always at rest asihe disc Lian (34;) :i s'perie-iically eme gfeebi new be evident, that else ii w ill be periedigards the we may conseoscillation 611 ,up in cordanare w th equatmn (3%) quentiy Write 5 9% sin.

Herein B stands regards its si'm is: tio'n 0i i and motor; and z fiepen lent net only" {L1 field ;.wive1' and the mum}: acting on the armature 9f the meter, as well the nun tions 0% the angle urmmu which g phzise'ue regmfds By phase reguator) it may new The ratio nmy fuxhthexzmare be an that .Bfl

, u it io ewb than that hr-1t the O 1* me pied in; the G, will be in gun turret by means 01' the n ameunt as $119 frame {3. It else be ShGWN in a simifim' manner; the: the plat "peak 0? the smiversai bearing ihfit eon spon-zie m the frame (I, may" be mm'ed by the mmor the qeme amount the main pendnhnn EL z EOfifld the axis 015 the trnnnions a in regard in The frame C. The plaiferm as We as the main penduhu'n A, will *iherefnre always YC- main in equi'ifln-iun'l during; the uscidutiol'l efthe ship.

\Vith 1:0, the auxiiiary pendulum J reclosed. and also the equafinn shows, i te the mean pendulum A; so th fewoiving disk system G H remains cm of uctmn. F01 thxs' reason, the revolving (hsk system G might be left out eniirely. when the :1: pendulum suspem in a. gun u l'e't but nth-er .pemied in T0001 that vloa .ne: turn r013 U in i the:

which had in he p'zaflei with Zhe lengitudiv mil axis @510 s if however, the main pendulum has; be 2.1 suspended in universal bem'in e and prams C. with a sesame. revolvieg dis de the arranqement of I system b. 2:

' isk eye em G H, this second system may be utilized to iuelece 0f the stamping This is not abjecrolling movement hitbxto been considered.

' 1 1's been ezmeuied 2 escixliziion of dime t0 the sinehe penduhnn A. 1m? with 'rea'ecorreet' devise, the oscilmpficete kin-:1 is can the same laws which alane he" iii; ium 01 $89 1111;,

sear

M.- device for A maintaining cqnilibrium of a x: 51in penduhm'l. said device he A 1 u iversa] bearing for aid main peradumm, t 0 revclving diek sgetems indep nient ofeacs-h other and we}; comprispair 0f .cinuting frames dud a pair 01" revolv'ing Cusks mounted?!) rotate. in said frames; said rave? mgdisk systems udilpced to influence said main pendulum and to gen erate mom-mute the veetore of which fall ap-' proximately in ihe direction of the axes of seic} universe hearing. A fievice f0? mainiaining the equiatrium of a penrhzim'n ,,ended fa'em an rver neieliseessed fine pensaid main I oscillutlng movement ll'i synchronism with 10- lihrium of a main pendulum suspended from on oscillating body, said device coin arising frame mounted. on said pendulum and a revolving disk mounted to rotate in said frame; said revolving disk 5 stems being adapted to influence said pen ulum and to generate moments, the vectorsof which essentially fall in the directions of the axes of said universal hearing, and means for uu'toumticnlly imparting to said frames on the oscilletion of said body from which the pendulum is sus icnded.

A device or maintaining the equilihriurn of a main )endulum euspen ded from an oscillating loo y, scid device having a universal hearing for seid main pendulum two revolving dish. nystonls independent 0 each other and each comprising an csoillat ing frame mounted on said main pendulum end a revolving dialmounted to rotate in said frame; said revolving disk systems being adapted to influence said main pendulum and to generate moments, the vectors of which essentially fellin the directions ofthe axes of snid'universal" bearing, two auxiliary pphduluxns mounted on the main ndu lum, the axes of said auxiliary en ulums res ect-ively being. parallel with t e axes of said universal hear ng ivhen said oscillating body is in itsmiddle osition, and damping arrangements for sci, jimxiliary endulums, the length of the 'auxiliiiry pendu lu'ms being so determined that the, per od of their free vibration is essentially the some as that of the oscillution'of saidbod from which the 1 main pendulum is susp'en ed.

6, A, device for muintnining the equian oscillating frame mounted on sai mam pendulum, a revolving disk, hearings in said frame for said revolving disk, an auxiliary pendulum, damping arrangement for said auxiliary pendulum, menus establishing positive connection between said auxiliary pendulum and said frame, said auxiliary pendulum having a length so detetmined that the periodof its free vibriition is essentlall" the same as that ofthe oscillzttion of said body from which the main pendulum is suspended, on inductor actuated by means of the movement of said auxiliary pendulum to generate an clectroniotoric force being two revolving disk proportionate to the angular velocity of the auxiliary pendulum another inductor actuated by means of the movement of the main pendulum relative to its bearing to generutelan electromotoric force, proportionateto the angular velocity of said movement, and an electric circuit connecting said inductors.

7r A device for maintaining the equilibrium, of a main endulum suspended from an oscillating b y, said device having a universal hearing or said main pendulum, systems independent of each other and each comprisi an oscillating frame a revolving disk mounted to rotate in said frame; sald revolving disk systems being adapted to influence said main pendulum and to generate moments, the vectors 0! which essentially fall in the directions 01 the axesof said universal bearing, two auxiliary pendulums mounted on the zen;

dulum, the axes of said auxiliary e axes of res ctively being parallel with t sai universal bearing when said oacillotin body is'in its middle position, the length to the auxiliary pendulums being so deteb mined thatvthe period of their free vibrations is essential y the some on that of the oscillation of said bod from the min pendulum is suspen ed, two pairs of in dudtors, each pair com rising an inductor, not ated by means of t a movement of one of aid auxiliary pendulums totgenerate an ele tromctoric force lproportionate to the an gu. 1r velocity of t e auxiliary endulum up ertaining thereto and a oecon inductor actuated by means of the relative urning of th main pgadulum around that axis of said un fiersail ring which'is urallel with the axis of the auxiliary p'en lum actuating said first-namedinductor H to generate an electromotoric force, roportionato to the an gular velocity; of sai relative turning,'nnd electric circuits connecting the inductors of each pair of inductors. v

The foregoing specification signed at Barmen, Germany, this 12th day of February,

WILHEQM LUYKEN. 1,. 5;

In presence of-- HELEN NUFER, ALBERT F Norma.

mounted on saidpen ulum and

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