Title of Invention

TRANSMISSION

Technical Field

[0001] The present invention relates to a transmission that changes the speed of the power (e.g., rotary motion or linear motion) at the input side and outputs the changed speed of the power at the output side.

Background Art

[0002] A transmission is applied to wide-variety of machines and usages, such as robots, office machines, medical devices, and music instruments, and is frequently used in a limited space as cases such as a displaying mechanism of an analoo clock or an electric vehicle. Available examples of a coaxial accelerator (rotary transmission) in the market, which is one type of transmission, are a planetary gear decelerator, strain wave gearing, a Cyclo-drive decelerates (registered mark), and a bail-type spired reducer. A coaxial decelerator (Japanese Patent No. 3166057) and a crown gear device (Japanese Patent No. 6100044) have been proposed.

[0003] Requiring complex structure such as a planetary gear mechanism, an eccentric rotating member and a rotating shaft thereof, or a mechanism to extract output rotation from a revolving element 'which are acc.ompanied by a large number of parts, the above conventional coaxial deceierators have difficulty in reducing the sites and the production cost. In addition, in the cases of a coaxial decelerator which utilizes large elastic deformation of a member being used or which transmits power only at limi ed part of the circu ference of the rotating shaft, the stiffness of the decelerator would decline. Furthermore, a decelerator, such as strain wave gearing, has technological difficulty in achieving a small reduction ratio. Not only rotary transmissions, but also linear-motion transmissions commonly have the same problems.

Summary of Invention

Technical Problem

[0004] With foregoing problems in view, one of the objects of the present embodiments is to provide a transmission that is simple in structure, consisting of a small number of elements, but not requiring large elastic deformation, high in stiffness, low in production cost, and wide in reduction ratio range.

Solution to Problem

[0005] (1) There is provided a transmission that changes a speed of an input from a driving source and outputs the input having the changed speed including: an inputting shaft that is connected to an output part on a side of the driving source and that includes an inpu waveform face having a predetermined input waveform on a circumference thereof; an outputting shaft that is coaxially arranged with the inputting shaft and that includes an output waveform face having an output waveform with a different number of waves from that of the input waveform; three or more synchronisers that are in contact with the input waveform face and the output waveform face and that forcibly make the phase of the output waveform at contact positions of the synchronizers with the output waveform face coincide with the phase of the input waveform at contact positions of the synchronizers with the input waveform face; a guide that supports each of the synchronizers such that the synchronizer is able to move only in each amplitude direction of the input waveform and the output waveform at points where the phase of the input waveform coincides with the phase of the output waveform; and a restricting mechanism that restricts the inputting shaft and the outputting shaft to being rotatable relative- to each other and also restricts the relative positional relationship between the inputting shaft and the outputting shaft in an axis direction .

[0006] (2) As a preferable feature, the inputting shaft and the outputting shafft may rotate in a same direction.

[0007] (3) As another preferable feature, the inputting shaft and the outputting shaft may rotate in respective opposite di rect ions .

[0000] (4) As an additional preferable feature, the input waveform face and the output waveform face may be arranged so as to face each other; and the amplitude direction of the input waveform and the amplitude direction of the output waveform may coincide with axis directions of the inputting shaft and the outputting shaft, respectively.

[0009] (5) As a further preferable feature, the restricting mechanism may include a pressurizing mechanism that presses each of the synchronizers agains the input waveform face and the output waveform face,

[0010] (6) As a still further preferable feature, the input waveform and the output waveform may be triangle waves.

[0011] (7) As a still further preferable feature, each of the synchronizers may be a rotating element.

[0012] (ø} In case of above (2), each of the synchronizers

20 may include two rot ting elements tha are arr nged in contact with each amplitude direction of the input waveform face and the output waveform face and that are rotatable independently of each othier .

[0013] (3) Otherwise, as a still further preferable feature, each of the synchronizers may foe configured to foe slidable at the contact positions with the input waveform face and the output wave foran £ace .

Advantageous Effects of Invention

DU [0014] The structure disclosed herein can achieve a

transmission that is simple in st ucture, including a small number of elements but not requiring large elastic deformation, high in stiffness, low in production cost, and wide in reduction ratio range.

Brief Description OJ 'rawings [0015] The nature of this invention, as well as other objects and advantages thereof, will be explained in the following with reference to the accompanying drawings, in which like reference characters designate the same or similar parts throughout the figures and wherein:

[0016] FIG. 1 is an axis-direction sectional view of a rotary transmission serving as a transmission according to an embodi ent ;

FIG. 2 is a graph describing an action of a rotary transmission serving as a transmission of an embodiment;

FIG. 3(a) is a schematic diagram illustrating the structure of a rotating transmission by same-direction synchronization, and FIG. 3 (b) is a schematic diagram illustrating the structure of a rotating transmission by opposifee-direction sy chronizat ion ?

FIG. 4 is an axis-direction sectional view of a rotary transmission of same-direct ion synchronisation according to a first modification;

FIG. 5 is an axis--direction. sectional view of a ro ary transmission according to a second modification;

FIG. 6 is an axis-direction sectional view of a rotary transmission according to a third modification;

FIG, 7 is an axis-direction sectional view of a rotary t ansmission according to a fourth modification; and

FIG. 8 is an radial-direction sectional view of a rotary transmission according to a fifth modification.

Descript ion of Embodi.ments

[0017] Hereinafter, description will now be made in relation to a transmission according to an embodiment with reference to the accompanying drawings. This description assumes that the transmission is a rotar transmission. The embodiment to be described below is an example and does not intend to exclude various modifications and application of techniques that are not detailed in the following embodiment. Various changes and modifications to the present embodiment can be suggested without departing the scope thereof. The respective structures of the present embodiment can be selected, omitted, or combined appropriately according to the requirement.

[1. Structure]

[0018] FIG. 1 is a sectional view of a rotary transmission 10 (hereinafter, referred to as the "transmission 10") of the present embodiment. The transmission 10 is connected with a rotati g shaft (output part, not illustrated) of a driving source (not illustrated) , which the rotating shaft is coaxially arranged to the transmission 10. The rotating shaft is disposed at an upstream position on a power transmission path from the transmission 10. The transmission 10 changes the speed of an input (rotation) from the driving source and outputs the rotation having the changed speed. The embodiment assumes that the transmission 10 is a decelerator. Alterna ively, a transmission may have an acceleration function in place of the deceleration function .

[0019] As illustrated in FIG. 1, the transmission 10 of the present embodiment includes an inputting shaft 1, an outputting shaft 2, three or more synchronizers 3, a guide 4, a casing 5, and a restricting mechanism 6. The inputting shaft 1 is connected to the rotating shaf 11 on the side of the driving source and has an input waveform face la having a predetermined input waveform formed on its circumference. The outputting shaft 2 is coaxially arranged with the inputting shaft 1 and has an output waveform face 2a having an output waveform with a different number of waves from that of the input waveform face la. The input 'waveform face la and the output waveform face 2a of the present embodiment are arranged so as to face each other. The two waveform faces la and 2a are sat i sfactor! iy arranged to have the same amplitude and the same vibrating direction, but do not have to face each other.

[0020] The present embodiment assumes that the difference (wave number difference) between the input 'waveform and the cutout waveform of the transmission 10 i md the output waveform has waves more than those of the input waveform. In n the present embodiment, the input waveform and the output waveform both exhibit triangle waves. Here, peaks and bottoms of each triangle wave are formed into angle portion formed by combining the two curves. In the transmission 10, the amplitude direction of the input waveform and the amplitude direction of the output waveform are set to coincide with the axis direction of the inputting shaft 1 and the axis direction of the outputting shaft 2, respectively , In other words, the input waveform face la ana the output waveform face 2a are formed on the end faces extending in the radius direction of the inputting shaft 1 and the outputting shaft.2, respectively. The inputting shaft 1 and the outputting shaft 2 are formed into stepped bars having end faces facing each other and to nave larger sizes in the radius direction.

[0021] Each synchronizer 3 comes into contact both with the input waveform face la and the output waveform face 2a, and forcibly makes the phase of the output waveform at contact positions of the synchronizers 3 with the output waveform face 2a coincide with a phase of the input waveform at contact positions of the synchronizers 3 with the input waveform face la. In the present embodiment, each synchronizer 3 is formed of a single rotating element. In the illustrated example, each rotating element is a bail (spherical member), but

alternatively may be a roller.

[0022] The guide 4 supports each synchronizer 3 such that the synchronizer .3 can move only in each amplitude direction of the input waveform and the output waveform (in the present embodiment, he axis direction) t points where the phase of the input waveform coincides with the phase of the output waveform. This means that, when the rotation of the inputting shaft 1 changes the phase of the input waveform at a point where the phase of the input waveform has coincide with that of the output waveform, the guide 4 moves each synchronizer 3 to the amplitude direction of the waveform to conform with the change of the phase, and further makes the phase of the output waveform forcibly coincide with the phase of the input waveform to thereby rotate the outputting shaft 2.

[0023] The guide 4 of the present embodiment has a plate 4a fixed to the inner circumference face of the cylindrical casing 5 at an intermediate point of the casing 5 with respect to the axis direction, and guide holes 4b placed on the plate 4a. The plate 4a has the same shape as the radius-direction cross section of the casing 5, and in the present embodiment, is integrated with the casing 5. The guide holes 4b of the present embodiment are cylindrical penetrating holes extending along the axis direction. Each synchroniser 3 is arranged in the corresponding guide hole 4b so as to be movable in the axis direc ion. The casing 5 accommodates at least the

synchronisers 3 and the guide 4. The casing 5 of the present embodiment takes the form of a cylinder having both ends are opened and also accommodates the end portions of the inputting shaft 1 and the outputting shaft 2, the end portions facing each other .

[0024] The restricting mechanism 6 restricts the inputting shaft 1 and the out utting shaft 2 o being rotatable relative to each other and also restricts the relative positional relationship between the inputting shaft 1 and the outputting shaft 2. The restricting raechanisri 6 of the present embodiment i attached to the casing 5 and formed of an input-side restricting part 6a attached to input-side end face of the casing 5, an output-side restric ng part 6b attached to an output-side end face of the casing 5, and two bearings 6c rotatably supporting the inputting shaft 1 and the outputting shaft 2. The restricting mechanism 6 of the pr sent embodiment presses each synchronizer 3 toward the input waveform face la and the output waveform face 2a by means of the respective two restricting parts 6a and 6b. Namely, the restricting parts 6a and 6b serve as a pressurizing mechanism having a function of pressurizing the synchronizers 3.

[0025] Here, description will now be made in relation to the principle of the transmission 10 with reference to FIG. 2. The number of input waveforms and the number of output waveforms are represented by p and q, respectively. The example of FIG.

2 is p-1 and q-4. The outputting shaft 2 can be rotated in the same direction as the inputting shaft 1. Hereinafter, this manner of rotation is referred to as "sarae-direction synchronization" . in contrast, the outputting shaft 2 can be rotated in the opposite direction to the inputting shaft 1. Hereinafter:, this manner of rotation is referred to as "opposi te-direction synchro i zation" . In o posite-di rection synchronization, the output waveform proceeds with a direction from large to small rotation angle in FIG, 2, i.e., opposite to the input waveform. In other words, the phase of the input waveform and the phase of the output waveform have the relationship of mirror symmetry to each other.

[0026] In cases of the same-direction sy chro ization, points at which the input waveform and the output waveform are synchronized with each other are as many as the difference (in the number of waveforms) between p and q exist on the circumference. For example, as shown by the bl ck circles in FIG. 2, the input and output waveforms in cases of the same-direction synchronization (SDS) are synchronized with each other at the three points at the rotating angle of the inputting shaft 1 of 60°, 180°, and 300 ^c . In contrast, in cases of the opposite-direction synchronization, points at which the input waveform and the output waveform are synchronised with each other tire as many as the sum (of the number of waveforms) of p and q exist on the circumference . For: example, as shown by the white circles in FIG. 2, the input and output waveforms in cases of the opposite-direction synchronization (ODS) are synchronized with each other at the five points at the rotating angle of the inputting shaft 1 of 0°, 72 ^* , 114°, 16*, and 288 ^* .

[0027] The transmission 10 arranges the synchronizers 3 at the points represented by above black circles for the same-direction synchronization and arranges the synchronizers

3 at the points represented by above white circles for the opposite-direction synchronization. This means that three synchronizers 3 are arranged for the former case and five synchronizers 3 are arranged for the latter: case. With this arrangement, when the phase of the input waveform changes, being accompanied by the rotation, the synchronizers 3 forcibly synchronize the phase of the output waveform with that of the input phase and thereby achieves deceleration at the ratio of p:q. For the same-direct ion synchronization, the number p can foe arbitrarily determined and the number q can also foe arbitrarily determined as far as the difference between p and q is three or more. For the opposite-direct ion synchronization, the numbers p and q can be arbitrarily determined as far as the numbers are different from each other. This makes it possible to achieve wide range of reduction ratio such as p:q-ll : 14 and p:q ^~ 3:100. Setting the number q to a larger number than the number p makes it possible to use the transmission 10 as an accelerator.

[0028] FIGs. 3(a) and 3(b) are schematic diagram illustrating a case where the wavefor is a triangle wave, p-1, q=4, and the synchronizers 3 each has circular section. FIG. 3(a) illustrates a case of the same-direction synchronization and FIG. 3(b) illustrates a case of the opposite-direction synchronization. As illustrated in FIG. 3(a), when the input waveform of the inputting shaft 1 moves from left to right as indica ed by the upper black arrow, the synchronizer 3 positioned at the rotating angle 120° is pushed down by the input waveform face la and therefore contributes to driving the output waveform face 2a. Hereinafter, a synchronizer 3 that contribu es to driving is referred to as "driving sy chroni er 3". Here, the output waveform of the outputting shaft 2 moves from left to right as indicated by the lower blac arrow.

[0029] The synchronizer 3 positioned at the otciting angle

240° is pushed up by the output waveform face 2a, which means that the synchronizer 3 simply follows the input waveform face la and does not contribute to driving the output waveform face 2a. Hereinafter, a synchronizer 3 that follows the input waveform face la is referred to as a ''following synchronizer 3" . In addition, a synchronizer 3 that does not correspond to JL iU the driving synchroniser 3 and the following synchroniser 3 is referred to as a "dead point synchronizer 3". The transmission 10 can be achieved by arranging the synchronizer s 3 such that at least one driving synchroniser 3 and at least one following synchronizer 3 always exist even when the input waveform has any phase and any rotating direction. The transmission 10 of FIG. 3(a) has three synchronizers 3 and may alternatively have more than three synchronizers 3. For the same-direction synchronization, the number of synchronizers 3 can be set to three or more and also set to an arbitrary number of the difference between the wave number of input waveform and the output waveform or less.

[0030] As illustrated in FIG. 3(b), when the input waveform of the inputting shaft 1 moves from left to right as indicated by the upper black arrow, the synchronizers 3 positioned at the rotating angles 192° and 264° are pushed down by the input waveform face la and contribute to driving the output waveform face 2a. Thereby, the output waveform of the outputting shaft

2 moves from right to left (i e . , the opposite direction to that. of the input waveform) as indicated by the lower black arrow.

The following synchronizers 3 positioned at the rotating angles -24° and 48° are pushed up by the output waveform face 2a and follows the input waveform face la. A dead point synchronizer

3 is positioned at the rotating angle 120 ^a . The number of synchronizers 3 for the opposite-direct io synchroni zat ion can be set to three or more and also to an arbitrary value of the sum of the wave number of the input waveform and the wave number of the output wa eform or less. The synchronizers 3 within the above range can achieve a rotary transmission likewise the transmission 10 of FIG. 1. For both the same-direct ion synchronization and the opposite-direction synchronization, it is satisfactory that at least one driving synchronizer 3 and at least one following synchronizer 3 exist regardless of the phase and the rotating direction of the input waveform.

[2. Effects]

G 00311 (15 The above transmission 10 can achieve a wide range of transmission ratio with a simple structure consisting of the input waveform face la, the output waveform face 2a, the synchronizers 3, the guide 4 , and the restricting mechanism 6. For the above, the transmission 10 can be mass-produced at a low manufacturing cost and can have enhanced commercial value. Differently from a conventional rotary transmission that requires large elastic deformation or transmits power at only part on the circumference of the rotary shaft, he transmission 10 can be free fro deterioration in stiffness.

[0032] {2} As shown in FIG. 3(a), the trans.miss.ion 10 of the same-direction synchronicat ion can rotate the inputting shaft 1 and the outputting shaft 2 in the same direction.

[0033] (3) In contrast, since the transmission 10 of the opposite-direction synchroni zat ion as shown in. FIG. 3(b) car- rotate the inputting shaft 1 and the outputting shaft 2 in the opposite directions to each other and also the input waveform face la and the output waveform face 2a that are in contact with the synchroni zers 3 rotate in the same direction, the friction can be further reduced.

[0034] (4) The structure of the transmission 10 can be further simplified by arranging the two waveform faces la and 2a so as to face each other and thereby setting the amplitude directions of the respective waveforms to coincide with the axis direction of the shafts 1 and 2.

[0035] (5) In the above transmission 10, the driving synchronizer 3 and the following synchronizer 3 always function, and when the rotating direction of the inputting shaft 1 is changed ( i . e . , switched to rotating in the opposite direction) , the driving synchronizer 3 and the following synchronizer 3 immediately exchange their .functions. Since multiple synchronizers 3 are always in contact with the input waveform face la and the output waveform; face 2a, pressurizing the s nchronizers 3 by the pressurizing mechanism of the

restricting mechanism 6 can avoid backlash and enhance the stiffness of the transmission.

[0036] (6) Since the input waveform and the output waveform are both triangle waves, the structure of the transmission 10 can be simplified and the contact angle of each synchronizer 3 with the input waveform face la or the output waveform face 2a can be kept constant.

[0037] (7} Since each synchronizer 3 is an independent rotating element (e.g., a bail or a roller), the transmission 10 can have a further simplified structure and the friction drag when the sliding starts can be abated.

[3. Modifications]

[0038] The above structure of the transmission 10 is one example and should by no means be li ited to this. Hereinafter , description will now be made in relation to first to fif h modifications. Like reference number used in the above embodiment and the following modifications designate same or the substantially same elements and parts ana repetitious description will be omitted here.

[0039] FIG. 4 is an axis-direction sectional view of a rotary transmission 10A of the same-direction synchronization according to the first modification. The rotary transmission 10A is different only in structure of a synchronizer 3A from the transmission 10 of the above embodiment . As illustrated in FIG. 4, each synchronizer 3A is formed of two rotating elements (in this example, spherical elements such as balls) that are arranged in contact with each amplitude direction of the input waveform face la and the output waveform face 2a and that are rotatable independently from each other. This structure makes the respective rotating directions of the two rotating elements coincide with the rotating directions of the corresponding waveform faces la and 2a being in contact as shown by the arrows in the drawing, so that the friction can be further abated. If transmission of large torque is required, rollers may be used in place of the balls.

[0040] FIGs . 5 and 6 are axis-direction sectional views of rotary transmissions 10B and 10C according to the second and third modifications, respecti ely. The rotary transmissions 108 and 10C are different only in structure of synchronizers ru

3B and 3C fro the transmission 10 of the above embodiment. As illustrated in FIGs. 5 and 6, the synch roni zero 3B and 3C are configured so as to be slidable at contact portions with the input waveform face la and the output waveform face 2a,

[0041] The synchronizer 3B in FIG. 5 is formed into a shape { e . g . , an e11 iptical shape extendi.ng 1 n the axis di ect ion ) being contacted with the input waveform face la, the output waveform face 2a, and the guide 4 by means of sliding friction. This configuration makes it possible to reduce the production cost and enlarge the amplitudes of the input and output waveforms. The synchronizer 3C in FIG. 6 is provided with rolling-element bearings and/or sliding bearings that slide on entire or part of the input waveform face la, the output waveform face 2a, and guide 4, This configuration can reduce the friction loss and can thereby achieve a large output and a high transmission efficiency.

[0042] FIG. ? is an axis-direction sectional view illustrating a rotary transmission 10D according to the fourth modification. The rotary transmission 10D is different only in the structures of waveform faces la and 2a from the transmission 10 of the above embodiment. The waveform faces la and 2a of the above embodiment are both triangle waves having peaks and bottoms of each triangle 'wave formed into angle portions. Alternatively, the bottoms of the triangle wave may be formed into a shape conforming to the shape of each synchroniser 3. For example, as shown in FIG, 7, if the sectional shape of each synchronizer 3 is a circle, the shape of each bottom can be formed into an arc (curved shape! when seen from the side.

[0043] The input waveform and the output waveform may be various shapes . For example, assuming that the synchronizers 3 are designed to move along a sine wave, the shapes of the input and output waveforms are satisfactorily set so as circumscribe about the trajectories in the inpu ting shaft 1 side and the outputting shaf 2 side when the synchroni er 3 moves along the sine wave as depicted in FIG. 7. Furthermore, when large torque is to be transmitted using bails as the synchronizers 3, grooves conforming to the a cs of the bails are formed on the input and output waveform faces such that the contact pressures between the bails and waveform faces are low. These alternative configurations bring the same effects as those of the above embodime t .

[0041] FIG . 8 is a radial -direction sectional view illustrating a rotary transmission 10E according to the fifth modification. The rotary transmission 10E is different from the transmission 10 of the above embodiment in the point that each amplitude direction of the input waveform and the output waveform is set to be the radius direction of the rotary transmission IDE. In other words, the rotary transmission 10E has a structure that the end portion of the inputting shaft IE and the end portion of the outputting shaft 2S overlap in the radius direction; one end portion is arranged outward of the other end portion; and the input waveform face lEa and the output waveform face 2Ea are arranged on their circumference faces. The rotary transmission 10E includes a guide 4E that can move the synchronizers 3E only in the radial direction of the rotary transmission 10E (i.e. the amplitude direction of each waveform) .

[0045] FIG. 8 exemplary illustrates the rotary transmission 10E in which a triangle wave of the input waveform p=l is formed on the circumference (outer circumference) of the inputting shaft IE arranged on inward of t e radial di ection and another triangle wave of output waveform q-12 is formed on the circumference (inner circumference) of the outputting shaft 2E arranged on the outward of the radius direction. The rotary transmission 10E of FIG. 8 can be likened to an analog clock display. Namely, in the rotary transmission 10E, each time the inputting shaft IE corresponding to ''minutes" of an analog clock makes one revolution, the outputting shaft 2E

corresponding to "hours" is driven by 1/12 revolution.

Accordingly, this structure brings the same effects as those of the above embodiment. Here, the numeric letters XII, III, VI, and IX and the long and short hands are illustrated to associate with an analog clock in FIG. 8.

[0046] In cases where the inputting shaft and the outputting shaft preferably rot te in the same direction to be applied to, for example, a turning peg of an ukulele and an analog clock shown in FIG, 8, the same-direction synchronization can be selected. In contrast, in cases where the inputting shaft may rotate in the opposite direction to that of the outputting shaft and transmission of large torque is required, otherwise, in cases where a transmission ratio of, for example, 1:2 is desired to be selected, the opposite-direction synchronization can be selected because of its large degree of freedom in selecting p and q and capability to accommodate more synchronizers.

[4. Others]

[0047] The synchronizers 3 shown in FIG. 1 may foe lubricated so as to smoothly slide on the input waveform face la, the output wavefor face 2a, and guide 4 or smooth sliding may be achieved by selecting appropriate materials for the respective parts. Likewise, the rotary transmission 10E of FIG. 8 may also be treated by, for example, lubrication. The shapes of the guide 4, the casing 5, and the restricting mechanism 6 are merely example and are not limited to those described above. For example, the restricting mechanism 6 may penetrate through the shafts 1 and 2 in the axis direction in place of being attached to the casing 5. Furthermore, the pressurizing mechanism can be omitted from the restricting mechanism 6.

[0048] The transmission 10 and the like of the above embodiment and modifications can be applied to, for example, robots, office machines, medical devices, music instruments, display mechanisms of analog clocks, wheel hub motors for electric vehicles, and in particular, are effectively used as a rotary t ransmission for a limited space.

[0049] The above structure can be applied to not only a rotary transmission that changes the speed of rotation of the inputting shaft and outputs the changed rotation, but also to a linear-motion transmission. This means that, apparently fro FXGs, 3 and 1, it is possible to use only the circumference directions obtained by infinitely enlarging the radii of the inputting shaft and the outputting shaft, and the linear motion transmission is expected to be appl ied to manipulators for fine oper such s a surgical ope:

Reference Sings List

[0050]

1 inputting shaft

la,lEa input waveform face

2 outpu11 ing sha ff.

£a,2Ea output waveform face

3, 3A, 3B, 30, 3E synchronizer

4,4E guide

3 casing

6 restricting mechan a.sm

6a input-side restricting part (oressu izing mechanism}

6fo output-side restricting part (pressurizing mechanism)1 10.A, 10B, 10C, 10D, IDE rroottaarryy tt raannssmiisssiioonn ( transmission)