JPS62218087A - Reduction gear for industrial robot - Google Patents
Reduction gear for industrial robotInfo
- Publication number
- JPS62218087A JPS62218087A JP61061636A JP6163686A JPS62218087A JP S62218087 A JPS62218087 A JP S62218087A JP 61061636 A JP61061636 A JP 61061636A JP 6163686 A JP6163686 A JP 6163686A JP S62218087 A JPS62218087 A JP S62218087A
- Authority
- JP
- Japan
- Prior art keywords
- reduction
- gear
- speed
- stage
- robot
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
- 239000003638 chemical reducing agent Substances 0.000 description 37
- 230000001133 acceleration Effects 0.000 description 6
- 238000010586 diagram Methods 0.000 description 6
- 238000002474 experimental method Methods 0.000 description 6
- 230000000052 comparative effect Effects 0.000 description 5
- 230000000694 effects Effects 0.000 description 4
- 239000006096 absorbing agent Substances 0.000 description 3
- 230000005284 excitation Effects 0.000 description 3
- 238000000034 method Methods 0.000 description 3
- 230000007935 neutral effect Effects 0.000 description 3
- 230000010355 oscillation Effects 0.000 description 3
- 238000005259 measurement Methods 0.000 description 2
- 230000002093 peripheral effect Effects 0.000 description 2
- 230000001186 cumulative effect Effects 0.000 description 1
- 238000000605 extraction Methods 0.000 description 1
- 238000003754 machining Methods 0.000 description 1
- 239000004575 stone Substances 0.000 description 1
Classifications
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
- Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
- Y02E60/10—Energy storage using batteries
Landscapes
- Manipulator (AREA)
Abstract
(57)【要約】本公報は電子出願前の出願データであるた
め要約のデータは記録されません。(57) [Summary] This bulletin contains application data before electronic filing, so abstract data is not recorded.
Description
【発明の詳細な説明】
（産業上の利用分野）
本発明は産業ロボット制御系の電動モータの回転数を減
速する減速装置に関する。DETAILED DESCRIPTION OF THE INVENTION (Field of Industrial Application) The present invention relates to a speed reduction device that reduces the rotational speed of an electric motor in an industrial robot control system.
（従来の技術）
産業ロボットにおいては、一般に、作業に適した出力ト
ルクを得るため、アーム等の駆動系（あるいは制御系と
いう）には電動サーボモータまたは電動パルスモータと
この出力を低速高トルクに変換する：ｌｊｉ速装置とを
用いている。(Prior art) In industrial robots, in order to obtain an output torque suitable for the work, the drive system (or control system) of the arm, etc. is generally equipped with an electric servo motor or an electric pulse motor, and this output is controlled at low speed and high torque. Convert: using a lji speed device.
また、産業ロボットに用いる減速装置は、例えば、減速
比１／１２０程度の大減速比を有していること、また、
歯車間のガタ、すなわち、いわゆるバックラッシュが小
さいこと、さらに、慣性を小さくするため軽量であるこ
と等が要求される。Further, the reduction gear used for industrial robots must have a large reduction ratio of about 1/120, for example, and
It is required that there is little play between gears, that is, so-called backlash, and that it is lightweight to reduce inertia.
これらの要求を満たすために、従来の産業ロボットは１
段の減速で大減速比が得られ、また、累積バックラッシ
ュが小さく、さらに、小型軽量として減速装置が使用さ
れている。このような、従来の減速装置としては、例え
ば、特開昭５９−１９０５４１号公報に係る調和歯車装
置および特開昭５９−１０６７４４号公報に係る偏心揺
動型遊星差動歯車装置がある。In order to meet these demands, conventional industrial robots have 1
The speed reduction device is used because a large speed reduction ratio can be obtained through stage speed reduction, cumulative backlash is small, and the speed reduction device is small and lightweight. Examples of such conventional speed reduction devices include a harmonic gear device disclosed in Japanese Patent Application Laid-open No. 59-190541 and an eccentric oscillation type planetary differential gear device disclosed in Japanese Patent Application Laid-open No. 59-106744.
従来、ロボットの制御系においては、前記電動モータと
前記減速装置との組合せが用いられているが、例えば、
ロボットの本体の第１アームに前記電動サーボモータが
取付けられ、電動サーボモータの出力が、前記偏心揺動
型遊星差動歯車装置を介してロボットの第２アームに連
結される。Conventionally, a combination of the electric motor and the speed reduction device has been used in a robot control system.
The electric servo motor is attached to the first arm of the robot body, and the output of the electric servo motor is connected to the second arm of the robot via the eccentric oscillating planetary differential gear.
電動サーボモータの回転数は減速装置で大幅に減速され
、得られた低速高トルクの回転力を有する出力が第２ア
ームを回動し、作業する。一般に、ロボットアーム自体
は剛性が高いためその固有振動数は高い。しかしながら
、ロボット全体として見たとき、回動部近辺のロボット
固有振動数は一般に剛性の低い減速装置で決まり、減速
装置と同程度に低い。したがって、制御系全体の固有ね
じり振動数ｆ０は一般に数ヘルツと低くなり減速装置に
人力する電動モータの回転数が低い領域で、減速装置と
ロボットの第２アームとが共振を起こし、第２アームに
よる正確な作業ができない等の問題点が起こる。共振が
生じる理由は、制御系（電動モータ、減速装置およびロ
ボットアームから構成される系）の固有ねじり振動数ｆ
０と、歯切の加工誤差等に起因して振動する減速装置の
振動周波数とが、電動モータの低回転数域で一致するた
めと考えられていた。The rotational speed of the electric servo motor is significantly reduced by a reduction gear, and the resulting output having low speed, high torque rotational force rotates the second arm to perform work. Generally, the robot arm itself has high rigidity, so its natural frequency is high. However, when looking at the robot as a whole, the robot's natural frequency near the rotating part is generally determined by the reduction gear with low rigidity, and is as low as the reduction gear. Therefore, the natural torsional frequency f0 of the entire control system is generally as low as several hertz, and in the region where the rotational speed of the electric motor that manually powers the reduction gear is low, the reduction gear and the second arm of the robot cause resonance, and the second arm Problems such as not being able to perform accurate work may occur. The reason why resonance occurs is due to the natural torsional frequency f of the control system (system consisting of an electric motor, reduction gear, and robot arm).
0 and the vibration frequency of the reduction gear, which vibrates due to machining errors in gear cutting, etc., were thought to be the same in the low rotational speed range of the electric motor.
このような問題点に対し、特開昭５８−２１１８８１号
公報には、発生した振動を打ち消すように電動モータの
速度指令信号を変化させる電気的制御方式が提案されて
いる。しかしながら、このような方式においてはフィー
ドハックゲインを大きくすると系が不安定となり、特に
剛性の低いロボット駆動系においては、逆に発振し易く
なるという問題を生じるため、ゲインを大きくできず、
したがって、充分な振動打ち消し効果を得られない。ま
た、特開昭５９−１７５９８６号公報には高張力を与え
たタイミングベルトで減速機を駆動し、該ベルトで振動
を吸収する方式のものが提案されている。しかしながら
、この方式においてはタイミングベルトが破断するとい
う危険がある。To address these problems, Japanese Patent Laid-Open No. 58-211881 proposes an electrical control method that changes the speed command signal of the electric motor so as to cancel out the generated vibrations. However, in such a system, increasing the feed hack gain causes the system to become unstable, which causes the problem that oscillations are more likely to occur, especially in robot drive systems with low rigidity, so it is not possible to increase the gain.
Therefore, a sufficient vibration canceling effect cannot be obtained. Further, Japanese Patent Application Laid-Open No. 59-175986 proposes a system in which a reduction gear is driven by a timing belt with high tension and vibrations are absorbed by the belt. However, in this method there is a risk that the timing belt will break.
また、特開昭５９−１１５１８９号公報には減速機の主
軸にばねとおもりから成る吸振器を取り付ける方式が提
案されている。しかし、この方式においては遠心力によ
り吸振器が破損したり、ロボットの負荷荷重に対応して
おもり等を調整しなければならないという問題点がある
。Furthermore, Japanese Patent Application Laid-Open No. 59-115189 proposes a system in which a vibration absorber consisting of a spring and a weight is attached to the main shaft of a speed reducer. However, this method has problems such as damage to the vibration absorber due to centrifugal force and the need to adjust weights and the like according to the load applied to the robot.
（発明の目的）
そこで、本発明は、ロボット制御系において、吸振装置
等を設けなくとも、電動モータ等の駆動部の通常の制御
回転数の範囲内で減速装置とロボットとの共振が起きな
い減速装置を提供することを目的とする。(Objective of the Invention) Therefore, the present invention provides a robot control system in which resonance between the speed reducer and the robot does not occur within the normal control rotational speed range of the drive unit such as the electric motor, even without providing a vibration absorber or the like. The purpose is to provide a speed reduction device.
（発明の構成）
発明者らは、ロボットアームの関節装置に用いる減速機
のばね定数、固有ねじり振動数、トルク変動等と共振現
象との関係につき種々研究を行った。(Structure of the Invention) The inventors conducted various studies on the relationship between the resonance phenomenon and the spring constant, natural torsional frequency, torque fluctuation, etc. of the reducer used in the joint device of the robot arm.
先ず、中立位置付近（いわゆるコストモーション位置）
の回転ばね定数ＫＥの高い減速機をロボットアームの関
節装置に用いることによりロボットの駆動系の固有ねじ
り振動数ｆ。を実用域から外すことが可能か否かについ
て試算した。しかし、減速機の中立位置付近の回転ばね
定数ＫＪは、大きなものでもロボットアーム自体の回転
ばね定数ＫｒのＩ／１０〜１１５であるため、駆動系全
体のばね定数に＝Ｋｌ−Ｋｒ／ （Ｋ！！＋Ｋｒ）は大
して大きくできず、その結果、駆動系の固をねしり振動
数ｆ、＝１／２π・石「−アコ７（ここに、Ｊは駆動系
の慣性モーメント）も大して大きくできない。したがっ
て、減速機の中立位置付近のばね定数Ｋ ｌを高めるこ
と、すなわち剛性を高めることによっては、駆動系の固
有ねじり振動数ｆ。を実用域から外すことは不可能であ
るとの結論に達した。First, near the neutral position (so-called cost motion position)
By using a reducer with a high rotational spring constant KE in the joint device of the robot arm, the natural torsional frequency f of the robot drive system can be reduced. A trial calculation was made to determine whether it is possible to remove this from the practical range. However, the rotational spring constant KJ near the neutral position of the reducer is I/10 to 115 of the rotational spring constant Kr of the robot arm itself, even if it is large, so the spring constant of the entire drive system is = Kl - Kr / (K !!+Kr) cannot be made very large, and as a result, the vibration frequency f, = 1/2π・stone of the drive system cannot be made very large (here, J is the moment of inertia of the drive system). Therefore, it was concluded that by increasing the spring constant K l near the neutral position of the reducer, that is, by increasing the rigidity, it is impossible to remove the natural torsional frequency f of the drive system from the practical range. Reached.
そこで、発明者等は、振動発生の原因である減速機のト
ルク変動を無くすことを試みた。具体的には偏心揺動型
の遊星歯車減速機を用い、トルク変動を阻止ないし減す
るよう、この減速機の内歯歯車と外歯歯車の歯に高精度
の仕上げ加工を施し、かつ、トルク変動が生じてもこれ
を吸収するよう、偏心入力軸の軸受部やトルク取出ビン
の軸支部等に環状溝を設け、該溝にゴムリングを装着し
た。Therefore, the inventors attempted to eliminate torque fluctuations in the reducer, which are the cause of vibrations. Specifically, an eccentric oscillating planetary gear reducer is used, and the teeth of the internal gear and external gear of this reducer are finished with high precision to prevent or reduce torque fluctuations. In order to absorb fluctuations even if they occur, an annular groove was provided in the bearing part of the eccentric input shaft, the shaft support of the torque extraction bottle, etc., and a rubber ring was attached to the groove.
しかしながら、このような対策を施しても実用域での共
振を防ぐことはできず、しかも、共振が生じる時の電動
モータ回転数は、そのような対策を施さない場合とほと
んど同じであることがわかった。However, even if such measures are taken, it is not possible to prevent resonance in the practical area, and furthermore, the electric motor rotation speed when resonance occurs is almost the same as when no such measures are taken. Understood.
このような実験結果から、一定の機構の減速機であれば
、はぼ一定のトルク変動特性、すなわちロボ７）の駆動
系に対する加振周波数特性ををするとの結論が導かれた
。また、斯かる結論から、ロボット駆動系に組み込む減
速装置の機構を変更することによりトルク変動特性を実
用域外に置くことができるとの仮説の下に種々の実験を
行った。From these experimental results, it was concluded that a reduction gear with a fixed mechanism would have a nearly constant torque fluctuation characteristic, that is, an excitation frequency characteristic for the drive system of the robot 7). In addition, based on this conclusion, various experiments were conducted under the hypothesis that the torque fluctuation characteristics could be brought out of the practical range by changing the mechanism of the reduction gear incorporated in the robot drive system.
これらの実験の内容および結果については後述するが、
これらの実験結果から仮説は実証され、下記の結論に到
達した。The content and results of these experiments will be discussed later, but
The hypothesis was verified from these experimental results, and the following conclusions were reached.
従来の常識では全く考えられなかった構成、すなわち、
偏心揺動型の遊星歯車減速機は、内歯歯車と外歯歯車の
歯数差が１であって、単独でも１／２００程度の減速比
にてきるが、この減速比を数十分の一程度とし、これに
所定範囲の減速比を有する前段（第１段）減速比をわざ
わざ設けて歯車装置を構成し、これをロボットアームの
駆動系に組み込むという構成により共振現象の生じる範
囲を電動モータの実用域から外すことができる。A configuration that was completely unthinkable according to conventional common sense, that is,
In an eccentric oscillating planetary gear reducer, the difference in the number of teeth between the internal gear and the external gear is 1, and even when used alone, it can achieve a reduction ratio of about 1/200, but this reduction ratio can be increased to several tens of minutes. The range where the resonance phenomenon occurs can be reduced by electric power, and the gear system is constructed by intentionally providing a front stage (first stage) reduction ratio with a reduction ratio within a predetermined range, and this is incorporated into the drive system of the robot arm. It can be removed from the practical range of motors.
なお、偏心揺動型の遊星歯車減速機に前段減速機を設け
た減速装置は、米国特許４．３４８．９１８号明細書に
開示されているようにクローラ車両の走行装置等に採用
されている。しかしながら、そのような走行装置等は採
用する減速機の重量、バックラッシュ等の問題をほとん
ど考慮しなくともよい。Incidentally, a speed reduction device in which an eccentric oscillating planetary gear speed reduction gear is provided with a front speed reduction device is used in a crawler vehicle traveling device, etc., as disclosed in U.S. Pat. No. 4.348.918. . However, in such a traveling device, there is little need to consider problems such as the weight of the speed reducer used and backlash.
したがって、単に減速機の縮減速比の変更を容易にする
ため、あるいは単に低速大トルクを出力するため、前段
減速機を設けているのである。これに対し、高速性、位
置精度等を要求され、且つ、全体構造の剛性が低いロボ
ットにおいては、減速機の重量、バックラッシュを小さ
くすることが重要であるため、関節部に、減速辻占たり
の重量が調和歯車装置より大きい偏心揺動型の遊星歯車
減速機を用い、さらに重量、バンクラッシュを増大させ
る要素となる前段減速機をわざわざ設けることは従来考
えられなかったのである。Therefore, the pre-stage reduction gear is provided simply to facilitate changing the reduction/reduction ratio of the reduction gear or simply to output low-speed large torque. On the other hand, in robots that require high speed, positional accuracy, etc. and have low rigidity of the overall structure, it is important to reduce the weight and backlash of the reducer. Conventionally, it was unthinkable to use an eccentric oscillating planetary gear reducer, which weighs more than a harmonic gear unit, and to take the trouble to include a front-stage reducer, which would increase the weight and bank lash.
発明者らはさらに種々研究を重ねた結果、下記の構成を
存する本発明に到達した。As a result of further various studies, the inventors have arrived at the present invention having the following configuration.
本発明に係る産業ロボットの減速装置は、ロボットの第
１部材に一体的に取り付けられた駆動部の回転数を減速
してロボットの第２部材を回動させる減速装置において
、駆動部の回転数を減速する第１段減速部と、第１段減
速部に連結され、回転数を更に減速して前記第２部材に
出力する第２段減速部と、を備え、前記第２段減速部が
内歯歯車と、内歯歯車に噛み合い内歯歯車の歯数より１
つだけ少ない歯数を有する外歯歯車と、外歯歯車に係合
して外歯歯車を揺動回転させる入力クランク軸と、を有
する偏心揺動型遊星差動歯車装置によって構成し、前記
第１段減速部の減速比が１／２〜１１５および前記第２
段減速部の減速比が１／２５〜１／６０であることを特
徴としている。The speed reduction device for an industrial robot according to the present invention is a speed reduction device that rotates a second member of the robot by reducing the rotation speed of a drive portion integrally attached to a first member of the robot. a first-stage deceleration section that decelerates the rotational speed; and a second-stage deceleration section that is connected to the first-stage deceleration section and further decelerates the rotational speed and outputs it to the second member, and the second-stage deceleration section 1 from the number of teeth of the internal gear that meshes with the internal gear
an eccentric oscillating planetary differential gear device having an external gear having a number of teeth as small as 1, and an input crankshaft that engages with the external gear to oscillately rotate the external gear; The reduction ratio of the first stage reduction section is 1/2 to 115 and the second
It is characterized in that the reduction ratio of the stage reduction section is 1/25 to 1/60.
（実施例）
以下、本発明に係る産業ロボットの減速装置を図面に基
づいて説明する。第１図ないし第３図は本発明の一実施
例を示す図である。(Example) Hereinafter, a reduction gear device for an industrial robot according to the present invention will be explained based on the drawings. 1 to 3 are diagrams showing one embodiment of the present invention.
まず、構成について説明する。第１図は本発明に係る産
業ロボットの減速装置を用いたロボットの制御系の全体
概略説明図である。１は産業ロボットの駆動部、すなわ
ち、電動モータであり、電動モータ１のフランジ２は本
発明に係る減速装置３の筒体４に固定されている。筒体
４はロボットの第１アーム５の先端部５ａに固定されて
いる。First, the configuration will be explained. FIG. 1 is an overall schematic explanatory diagram of a robot control system using an industrial robot deceleration device according to the present invention. Reference numeral 1 denotes a drive unit of the industrial robot, that is, an electric motor, and a flange 2 of the electric motor 1 is fixed to a cylinder 4 of a speed reduction device 3 according to the present invention. The cylinder 4 is fixed to the tip 5a of the first arm 5 of the robot.
電動モータ１の出力の回転軸７は減速装置３の入力回転
輪８に連結され、減速装置３の出力は軸１０に伝達され
軸１０の先端は円筒体１１の中心を貫通し、ロボットの
被駆動部１２、すなわち、第２アームに固定されている
。第２アーム１２の基部の筒状体１３と第１アーム５の
先端部５ａの下面から下方に突出する円筒型の突出体１
５との間には一対のベアリング１６が介装されている。The rotary shaft 7 of the output of the electric motor 1 is connected to the input rotary wheel 8 of the speed reducer 3, and the output of the speed reducer 3 is transmitted to the shaft 10. It is fixed to the drive unit 12, that is, the second arm. A cylindrical protrusion 1 protrudes downward from the lower surface of the cylindrical body 13 at the base of the second arm 12 and the tip 5a of the first arm 5
A pair of bearings 16 are interposed between the bearings 5 and 5.
突出体１５の内周面と円筒体１１の中央部の外周面との
間には一対のベアリング１７が介装されている。円筒体
１１の上部および下部の内面と軸１０との間にはそれぞ
れ一対のベアリング１８が介装されている。したがって
、減速装置３は駆動部１の回転数を減速してロボットの
被駆動部すなわち第２アーム１２を回動させる。A pair of bearings 17 are interposed between the inner peripheral surface of the protruding body 15 and the outer peripheral surface of the central portion of the cylindrical body 11. A pair of bearings 18 are interposed between the upper and lower inner surfaces of the cylindrical body 11 and the shaft 10, respectively. Therefore, the speed reducer 3 reduces the rotational speed of the drive unit 1 and rotates the driven part of the robot, that is, the second arm 12.
減速装置３は第２図および第３図に示すように、第１段
減速部２０と第２段減速部２１とから構成され、駆動部
１の回転数を減速する第１段減速部２０と、第１段減速
部２０に連結され、回転数をさらに減速する第２段減速
部２１と、を備えている。第２段減速部２１は固定して
いる内歯歯車２２と内歯歯車２２に噛み合う外歯歯車２
３と、外歯歯車２３に嵌合して外歯歯車２３を揺動回転
させる入力クランク軸２４と、を有する偏心揺動型遊星
差動歯車装置によって構成されている。また、内歯歯車
２２はピン歯２６を用いたビン歯車２７で構成され、か
つ外歯歯車２３の歯数より１つだけ多い歯数を有してい
る。また、第１段減速部は通常の平歯歯車により構成さ
れている。As shown in FIGS. 2 and 3, the speed reduction device 3 is composed of a first stage speed reduction section 20 and a second stage speed reduction section 21. The first stage speed reduction section 20 reduces the rotation speed of the drive section 1 and , and a second stage reduction section 21 that is connected to the first stage reduction section 20 and further reduces the rotation speed. The second stage reduction section 21 includes a fixed internal gear 22 and an external gear 2 that meshes with the internal gear 22.
3, and an input crankshaft 24 that fits into the external gear 23 and rotates the external gear 23 in an oscillating manner. Further, the internal gear 22 is composed of a pin gear 27 using pin teeth 26, and has one more tooth than the external gear 23. Further, the first stage reduction section is constituted by a normal spur gear.
第１段減速部２０の減速比と第２段減速部２１の減速比
とは電動モータ１の通常制御回転数の範囲内でロボット
すなわち、第１アーム５および第２アーム１２と、第２
段減速部２１との共振が起きないように選択している。The reduction ratio of the first stage reduction section 20 and the reduction ratio of the second stage reduction section 21 are defined as the reduction ratio of the first stage reduction section 20 and the second stage reduction section 21.
It is selected so that resonance with the stage reduction section 21 does not occur.
この実施例においては、電動モータｌの通常制御回転数
がＯ〜１１０００ｒｐ、 第１ （前）段減速部２０の
減速比が１／２〜１１５および第２ （後）段減速部２
１の減速比は１／２５〜１／６０であり、減速装置３の
全体の減速比は１／１２０になるよう選択されている。In this embodiment, the normally controlled rotational speed of the electric motor l is 0 to 11000 rpm, the reduction ratio of the first (front) stage reduction section 20 is 1/2 to 115, and the second (rear) stage reduction section 2
1 has a reduction ratio of 1/25 to 1/60, and the overall reduction ratio of the reduction gear device 3 is selected to be 1/120.
前段減速機２０の減速比１１が１１５未満（分母が大き
くなることを意味する。以下同じ）または後段減速機２
１の減速比１２が１／２５を超える（分母が小さくなる
ことを意味する。以下同じ）と、前段減速機２０に構造
の簡単な平行軸減速機を採用して１／１２０の終減速比
ｉを得ることは困難となるので、設計的経済的に不利と
なる。また、後段減速機２１の減速比１２が１／６０未
満または前段減速機２０の減速比１１が１／２を超えて
１／１２０の終減速比ｉを得る場合は、電動モータ１の
実用域において、前段減速ａ２０の毎秒光たり回転数が
ロボットの駆動系の固有ねじり振動数ｆｏ近辺あるいは
それ以上となるので、共振を防ぐ効果が少ない。The reduction ratio 11 of the front stage reducer 20 is less than 115 (meaning that the denominator becomes larger. The same applies hereinafter) or the rear stage reducer 2
When the reduction ratio 12 of 1 exceeds 1/25 (meaning that the denominator becomes smaller; the same applies hereinafter), a parallel shaft reduction gear with a simple structure is adopted as the front stage reduction gear 20, and the final reduction ratio of 1/120 is achieved. Since it is difficult to obtain i, this is disadvantageous in terms of design and economics. In addition, when the reduction ratio 12 of the rear stage reduction gear 21 is less than 1/60 or the reduction ratio 11 of the front stage reduction gear 20 exceeds 1/2 to obtain a final reduction ratio i of 1/120, the electric motor 1 is within the practical range. In this case, the rotation speed per second of the first stage deceleration a20 is close to or higher than the natural torsional frequency fo of the drive system of the robot, so that the effect of preventing resonance is small.
第２アーム１２の軸１０を中心としたねじりのバネ定数
は約３７．５ｋ ｇ−ｍ／分である（ここに、分とは１
度の１７６０の角度のことである。）次に作用について
説明する。The torsional spring constant of the second arm 12 about the axis 10 is approximately 37.5 kg-m/min (where min is 1
It is an angle of 1760 degrees. ) Next, the effect will be explained.
ただし、電動モータ１、減速装置３、および第２アーム
１２を含んで構成される駆動系の固有ねじり振動数ｆＯ
は、後述する実験例における駆動系の固有ねじり振動数
「０と同様、８．４ Ｈｚであるものとして以下説明す
る。この８．４Ｈｚは共振ピーク点における電動モータ
１の回転数および本発明に係る減速装置について後述す
るトルク変動特性から算出される。電動モータ１をＯ〜
１１０００ｒｐの通常回転数で回転させると、減速比ｉ
、が１／３の前段減速機２０の出力回転数はＯ〜３３３
ｒｐｍとなり、減速比１２がｌ／４０の後段減速機２１
の出力回転数は０〜８．３ｒｐｍとなり、この範囲では
共振現象が生じない。共振は実用域外、すなわち電動モ
ータ１の出力回転数が１５０Ｏｒｐｍ近辺（このときの
前段減速機２０の出力回転数は１５００ｒｐｍ Ｘ １
／ ３ ＝ ５０Ｏｒｐｍ近辺、遊星歯車減速機２１
の出力回転数は１５００ｒｐｍ Ｘ １ ／ ３ Ｘ
１ ／４０＝１２．５ｒｐｍ近辺）で生じる。However, the natural torsional frequency fO of the drive system including the electric motor 1, reduction gear 3, and second arm 12
will be explained below assuming that the natural torsional frequency of the drive system in the experimental example described later is 8.4 Hz, which is the same as 0. This 8.4 Hz is the rotational speed of the electric motor 1 at the resonance peak point and the present invention. It is calculated from the torque fluctuation characteristics described later for such a reduction gear.The electric motor 1 is
When rotating at the normal rotation speed of 11000 rpm, the reduction ratio i
, is 1/3, the output rotation speed of the front stage reducer 20 is O~333
rpm, and the rear stage reducer 21 has a reduction ratio 12 of l/40.
The output rotation speed is 0 to 8.3 rpm, and no resonance phenomenon occurs in this range. The resonance is outside the practical range, that is, the output rotation speed of the electric motor 1 is around 150 rpm (at this time, the output rotation speed of the front speed reducer 20 is 1500 rpm x 1
/ 3 = around 50Orpm, planetary gear reducer 21
The output rotation speed is 1500rpm x 1/3 x
1/40 = around 12.5 rpm).
このように共振現象が電動モータ１の実用域外で生じる
理由は明らかではないが、実験結果から推定すると上記
実施例のように内歯歯車と外歯歯車の歯数差が１の遊星
差動歯車装置は入力軸（クランク軸２４）の１回転当た
り１のトルク変動が生じ、したがって、これに減速比ｉ
Ｉが１／３の前段減速機２０を取り付けると電動モータ
１の回転数が実用域外である１５００ｒｐｍを中心とし
た付近で１５００ Ｘ（１／３） Ｘ １ ＝ ５００
程度の毎分光たりトルク変動が生じ、このトルク変動数
が駆動系の固有振動数８．４ヘルツ（５００振動／分）
にほぼ一致して共振を起こすものと考えられる。Although it is not clear why the resonance phenomenon occurs outside the practical range of the electric motor 1, it is estimated from the experimental results that the planetary differential gear in which the difference in the number of teeth between the internal gear and the external gear is 1 as in the above embodiment The device generates a torque fluctuation of 1 per revolution of the input shaft (crankshaft 24), and therefore the reduction ratio i
When the front speed reducer 20 with I of 1/3 is installed, the rotation speed of the electric motor 1 will be around 1500 rpm, which is outside the practical range, at 1500 x (1/3) x 1 = 500.
Torque fluctuations occur every minute, and this torque fluctuation frequency is the natural frequency of the drive system, 8.4 Hz (500 vibrations/min).
It is thought that resonance occurs almost in agreement with .
これに対し、内歯と外歯の歯数差が２の調和歯車装置の
場合は、実験結果から推定すると、入力軸（ウェーブジ
ェネレータ）の１回転当たり２のトルク変動が生じ、し
たがって、これに減速比１／３の前段減速機を取り付け
ると、電動モータの回転数が７５０ｒｐｍ付近で７５０
Ｘ １ ／３ ｘ ２ ＝ ５００の毎分当たりトルク
変動が生じ、駆動系の固有振動数ｒＯが上記実施例と同
様８．４ヘルツ（５００振動／毎分）であるならば電動
モータの回転数が実用域内である７５０ｒｐｍ付近で共
振が生じるものと考えられる。この場合、毎分当たり加
振数がおおよそ５００のときに共振が生じるのであるか
ら、調和歯車減速機に減速比ｔ＋＝１／６程度の前段減
速機を設けることにより共振時の電動モータの回転数を
実用域外である１５００ｒｐｍを中心とする付近にまで
上げることも考えられる。しかし、調和歯車減速機の減
速比はｉｚは最小でも１／８０程であるから、総減速比
ｉは最小でも１ ／４８０となり、１〜１１０００ｒｐ
を実用域とする電動モータが一般に必要とする減速比ｉ
（１／１２０程度）を満足できないため、実用できない
ことになる。On the other hand, in the case of a harmonic gear device in which the difference in the number of teeth between internal and external teeth is 2, it is estimated from the experimental results that a torque fluctuation of 2 occurs per revolution of the input shaft (wave generator), and therefore, When a front stage reducer with a reduction ratio of 1/3 is installed, the rotation speed of the electric motor will be 750 rpm at around 750 rpm.
If a torque fluctuation of X 1 /3 x 2 = 500 per minute occurs and the natural frequency rO of the drive system is 8.4 hertz (500 vibrations/minute) as in the above example, then the rotational speed of the electric motor is It is thought that resonance occurs around 750 rpm, which is within the practical range. In this case, resonance occurs when the number of excitations per minute is approximately 500, so by providing a pre-stage reducer with a reduction ratio of approximately t+=1/6 in the harmonic gear reducer, the rotation of the electric motor during resonance is reduced. It is also conceivable to increase the number to around 1500 rpm, which is outside the practical range. However, since the reduction ratio iz of the harmonic gear reducer is at least about 1/80, the total reduction ratio i is at least 1/480, and from 1 to 11000 rpm.
The reduction ratio i generally required for an electric motor with a practical range of
(approximately 1/120), it cannot be put to practical use.
なお、電動モータ１および前段減速４１２０の振動は駆
動系の発振に影響を及ぼさない。これはこれらの振動は
小さいこと、後段部２１を介することにより吸収される
こと等によるものと考えられる。Note that the vibrations of the electric motor 1 and the pre-stage reduction gear 4120 do not affect the oscillation of the drive system. This is thought to be due to the fact that these vibrations are small and are absorbed through the rear stage section 21.
方駅凱
次に、減速装置の種類を変えた場合、減速装置とロボッ
トとの共振の発生状態について実験した。Kai Hoeki Next, we conducted an experiment to determine the state of resonance between the speed reducer and the robot when the type of speed reducer was changed.
別表において、比較した減速装置は前述の実施例の減速
装置のほかに比較例１〜３に示す減速装置である。ただ
し、前述の実施例を含めサイクロ減速機は、クランク軸
および外歯歯車の揺動によるアンバランスを防ぐため、
実開昭５９−１２７９５１号公報に開示されているよう
に外歯歯車を２枚としこれらを１８０度の位相差をもっ
て組付けたもので、かつ、内歯歯車が外歯歯車の歯数よ
り１つ多い歯数を有するものを用いた。また、調和歯車
減速機は内歯歯車が外歯歯車の歯数より２つ多い歯数を
有するものを用いた。それぞれの減速装置の減速段数、
減速比１１．１２、ねじりばね定数に、および慣性モー
メンｌ−Ｊは別表に示しである。In the attached table, the speed reduction devices compared are the speed reduction devices shown in Comparative Examples 1 to 3 in addition to the speed reduction devices of the above-mentioned embodiments. However, in the cyclo reducer including the above-mentioned embodiment, in order to prevent unbalance due to swinging of the crankshaft and external gear
As disclosed in Japanese Utility Model Application Publication No. 59-127951, two external gears are assembled with a phase difference of 180 degrees, and the internal gear has one more teeth than the external gear. A type with a large number of teeth was used. Further, the harmonic gear reducer used has an internal gear having two more teeth than an external gear. The number of reduction stages of each reduction gear,
The reduction ratio 11.12, torsional spring constant, and moment of inertia l-J are shown in the attached table.
実験は第５図に示す全体構成図によって実施した。すな
わち、電動サーボモータ３１の出力軸３１ｂに減速装置
３２を取付け、減速装置３２の出力軸３２ａにロボット
の被駆動部（第２アーム）の慣性モーメントに相当する
慣性負荷としてフライホイール３３が取付けられた。ロ
ボットの第２アームの長さに相当するフライホイール側
面３３ａの半径上の位置に、円周方向の加速度および振
幅を測定できる圧電素子を利用した加速度ピックアップ
３４を取り付ける。この加速度ピックアップ３４の出力
はインジケータ３６に連結されている。電動モータの回
転数を変化させて、その時のフライホイールの加速度の
大きさ、および振幅を測定した。測定はフライホイール
３３が定速度で約１回転する範囲で行った。測定結果は
第４図に示す。横軸は電動サーボモータ３１の回転数（
すなわち、減速装置３２の入力軸の回転数）であり、縦
軸はフライホイール３３の加速度ピンクアップ３４に表
れる円周方向の加速度（すなわち、振動）の大きさく単
位、Ｇ）を示す。The experiment was conducted using the overall configuration diagram shown in FIG. That is, the reduction gear 32 is attached to the output shaft 31b of the electric servo motor 31, and the flywheel 33 is attached to the output shaft 32a of the reduction gear 32 as an inertial load corresponding to the moment of inertia of the driven part (second arm) of the robot. Ta. An acceleration pickup 34 using a piezoelectric element capable of measuring acceleration and amplitude in the circumferential direction is attached to a position on the radius of the flywheel side surface 33a corresponding to the length of the second arm of the robot. The output of this acceleration pickup 34 is coupled to an indicator 36. The rotational speed of the electric motor was varied and the magnitude and amplitude of the acceleration of the flywheel at that time were measured. The measurement was performed within a range in which the flywheel 33 rotated approximately one rotation at a constant speed. The measurement results are shown in Figure 4. The horizontal axis is the rotation speed of the electric servo motor 31 (
That is, the rotation speed of the input shaft of the reduction gear 32), and the vertical axis indicates the magnitude unit (G) of the circumferential acceleration (that is, vibration) appearing in the acceleration pink-up 34 of the flywheel 33.
比較例１、比較例２および比較例３においては、共振の
ピークはそれぞれ、電動モータ３１の回転数において、
７００ｒｐｍ、５００ｒｐｍおよび２５０ｒｐｍのとき
であり、電動モータ３１の通常制御回転数Ｏ〜１１００
０ｒｐの範囲で共振が起こっている。しかしながら、本
発明に係る減速装置を用いた実施例の場合には、前述の
説明のように、共振時の電動モータ回転数は極めて高＜
、１５００ｒｐｍとなっている。In Comparative Example 1, Comparative Example 2, and Comparative Example 3, the resonance peak was at the rotation speed of the electric motor 31, respectively.
700 rpm, 500 rpm, and 250 rpm, and the normal control rotation speed of the electric motor 31 is O to 1100.
Resonance occurs in the 0rp range. However, in the case of the embodiment using the speed reducer according to the present invention, as explained above, the rotational speed of the electric motor at the time of resonance is extremely high.
, 1500 rpm.
したがって、通常制御回転数の範囲では共振は起きない
。Therefore, resonance does not occur within the normal control rotational speed range.
別表の実施例と比較例１において、慣性モーメンＪおよ
びねじりばね定数に１は殆ど同じであるが、負荷が発振
するときの電動モータの回転数に大きな差異があり、そ
の差は第１段減速比と反比例している。この理由は、第
２段減速部の加振周波数と負荷の固有ねじり振動数が一
敗したとき、すなわち、電動モータの回転数が１５０Ｏ
ｒｐｍのとき発振するからである。In the example and comparative example 1 in the attached table, the moment of inertia J and the torsional spring constant 1 are almost the same, but there is a large difference in the rotational speed of the electric motor when the load oscillates, and the difference is due to the first stage deceleration. It is inversely proportional to the ratio. The reason for this is that when the excitation frequency of the second stage reduction section and the natural torsional vibration frequency of the load are lost, that is, the rotational speed of the electric motor is 150
This is because it oscillates at rpm.
なお、このような実験結果から前述のように各減速機の
トルク変動特性が指定され、かかる指定を用いて実験装
置の固有ねじり振動数ｆｏを逆算すると、実験で用いた
減速機のいずれを組込んだ場合も約８．４ ｆｉｚとな
る。これは、共振が駆動系のＩ’Ｊ：１１性が最も低い
時、即ち、負荷状態が減速機のいわゆるロストモーショ
ンの範囲内にある時に生じ、その時のロストモーション
ばね定数Ｋｆが 実験で用いたいずれの減速機の場合も
おおよそ等しいためと考えられる。Furthermore, from these experimental results, the torque fluctuation characteristics of each reducer are specified as mentioned above, and when the natural torsional frequency fo of the experimental equipment is calculated backwards using this specification, it is possible to determine which of the reducers used in the experiment is assembled. Even if it is included, it will be about 8.4 fiz. This occurs when resonance occurs when the I'J:11 characteristic of the drive system is at its lowest, that is, when the load condition is within the so-called lost motion range of the reducer, and the lost motion spring constant Kf at that time is the one used in the experiment. This is thought to be because the values are approximately the same for all speed reducers.
（発明の効果）
以上説明したように、本発明によれば、ロボット制御系
において、減速装置とロボットとの共振が生ずるときも
、共振が生ずるときの電動モータの回転数が極めて高く
なり、電動モータ駆動部の通常制御回転数の範囲内での
ロボットと減速装置との共振を生じなくすることができ
る。(Effects of the Invention) As explained above, according to the present invention, even when resonance occurs between the reduction gear and the robot in the robot control system, the rotational speed of the electric motor at the time of resonance becomes extremely high, and the electric motor It is possible to prevent resonance between the robot and the speed reduction device within the normal control rotational speed range of the motor drive unit.
第１図反型第５図は本発明に係る産業ロボットの減速装
置の１実施例を説明する図であり、第１図はその全体概
略説明図、第２図はその要部断面図、第３図は第２図の
Ｉ−Ｉ［［矢視断面図、第４図は本発明に係る産業ロボ
ットの減速装置の実施例および比較例の性能を説明する
図、第５図は第４図に係る実験例の全体構成図である。
■・・・・・・駆動部（電動モータ）、３・・・・・・
減速装置、
５・・・・・・第１アーム、
１２・・・・・・被駆動部（ロボットの第２アーム）、
２０・・・・・・第１段減速部、
２１・・・・・・第２段減速部、
２２・・・・・・内歯歯車、
２３・・・・・・外歯歯車、
２４・・・・・・人力クランク、
２７・・・・・・ピン歯車。1 and 5 are diagrams for explaining one embodiment of the speed reduction device for an industrial robot according to the present invention, in which FIG. 1 is an overall schematic explanatory diagram, FIG. 3 is a sectional view taken along the line I-I [[ of FIG. 2, FIG. FIG. 2 is an overall configuration diagram of an experimental example according to the present invention. ■... Drive unit (electric motor), 3...
Reduction device, 5...First arm, 12... Driven part (second arm of robot),
20...First stage reduction section, 21...Second stage reduction section, 22...Internal gear, 23...External gear, 24. ...Human crank, 27...Pin gear.
Claims (1)
回転数を減速してロボットの第２部材を回動させる減速
装置において、駆動部の回転数を減速する第１段減速部
と、第１段減速部に連結され、回転数を更に減速して前
記第２部材に出力する第２段減速部と、を備え、前記第
２段減速部が内歯歯車と、内歯歯車に噛み合い内歯歯車
の歯数より１つだけ少ない歯数を有する外歯歯車と、外
歯歯車に係合して外歯歯車を揺動回転させる入力クラン
ク軸と、を有する偏心揺動型遊星差動歯車装置によって
構成し、前記第１段減速部の減速比が１／２〜１／５お
よび前記第２段減速部の減速比が１／２５〜１／６０で
あることを特徴とする産業ロボットの減速装置。A speed reduction device that rotates a second member of the robot by reducing the rotation speed of a drive section that is integrally attached to a first member of the robot includes a first stage reduction section that reduces the rotation speed of the drive section; a second stage reduction part connected to the first stage reduction part to further reduce the rotational speed and output it to the second member, the second stage reduction part meshing with the internal gear and the internal gear; An eccentric oscillating planetary differential gear having an external gear having one fewer tooth than the number of teeth of the gear, and an input crankshaft that engages with the external gear and rotates the external gear in an oscillating manner. An industrial robot comprising a device, wherein the first stage reduction section has a reduction ratio of 1/2 to 1/5, and the second stage reduction section has a reduction ratio of 1/25 to 1/60. Reduction device.
Priority Applications (2)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP61061636A JPS62218087A (en) | 1985-01-18 | 1986-03-18 | Reduction gear for industrial robot |
| JP10304728A JPH11198086A (en) | 1985-01-18 | 1998-10-13 | Speed reduction gear for revolt joint driving of industrial robot |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP61061636A JPS62218087A (en) | 1985-01-18 | 1986-03-18 | Reduction gear for industrial robot |
Related Child Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| JP10304728A Division JPH11198086A (en) | 1985-01-18 | 1998-10-13 | Speed reduction gear for revolt joint driving of industrial robot |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| JPS62218087A true JPS62218087A (en) | 1987-09-25 |
| JPH0513794B2 JPH0513794B2 (en) | 1993-02-23 |
Family
ID=13176882
Family Applications (2)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| JP61061636A Granted JPS62218087A (en) | 1985-01-18 | 1986-03-18 | Reduction gear for industrial robot |
| JP10304728A Pending JPH11198086A (en) | 1985-01-18 | 1998-10-13 | Speed reduction gear for revolt joint driving of industrial robot |
Family Applications After (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| JP10304728A Pending JPH11198086A (en) | 1985-01-18 | 1998-10-13 | Speed reduction gear for revolt joint driving of industrial robot |
Country Status (1)
| Country | Link |
|---|---|
| JP (2) | JPS62218087A (en) |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2007086476A1 (en) | 2006-01-26 | 2007-08-02 | Nabtesco Corporation | Speed reducer |
| WO2007125835A1 (en) | 2006-04-28 | 2007-11-08 | Nabtesco Corporation | Reduction gear mechanism, and its manufacturing method |
| US8435149B2 (en) | 2006-02-07 | 2013-05-07 | Nabtesco Corporation | Reduction gear device |
Families Citing this family (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| KR20070044008A (en) * | 2004-08-11 | 2007-04-26 | 나부테스코 가부시키가이샤 | Speed reducer installed at articulation of industrial robot |
| JP4820310B2 (en) * | 2007-02-02 | 2011-11-24 | ナブテスコ株式会社 | Reduction gear |
| JP5348182B2 (en) * | 2011-06-07 | 2013-11-20 | 株式会社安川電機 | Motor with reduction gear |
Citations (12)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| GB927684A (en) * | 1960-10-20 | 1963-06-06 | Merritt & Company Engineering | Epicyclic gearing |
| US3129611A (en) * | 1960-10-14 | 1964-04-21 | Lee Engineering Company | Speed reducers |
| JPS5639341A (en) * | 1979-08-31 | 1981-04-15 | Teijin Seiki Co Ltd | Reduction gear |
| JPS56152594A (en) * | 1980-04-25 | 1981-11-26 | Meidensha Electric Mfg Co Ltd | Reduction gear for manipulator |
| JPS57121490A (en) * | 1980-12-19 | 1982-07-28 | Kuka Shiyubuaisuanraagen Unto | Gearing for hinge head coupled with jib of manipulator |
| JPS58211881A (en) * | 1982-06-02 | 1983-12-09 | 松下電器産業株式会社 | Industrial robot |
| JPS59106744A (en) * | 1982-12-07 | 1984-06-20 | Sumitomo Heavy Ind Ltd | Method and device for installing eccentric body in planetary gear mechanism |
| JPS59115189A (en) * | 1982-12-20 | 1984-07-03 | 松下電器産業株式会社 | Joint device for robot |
| JPS59124093U (en) * | 1983-02-04 | 1984-08-21 | 株式会社神戸製鋼所 | Wrist mechanisms for industrial robots, etc. |
| JPS607856A (en) * | 1983-06-27 | 1985-01-16 | 株式会社クラレ | Anionic body fluid treating membrane |
| JPS607856Y2 (en) * | 1981-03-31 | 1985-03-18 | 日立造船株式会社 | Precision punching equipment for thin plates |
| JPS618760A (en) * | 1984-06-20 | 1986-01-16 | Mitsubishi Electric Corp | Tracking error detection |
-
1986
- 1986-03-18 JP JP61061636A patent/JPS62218087A/en active Granted
-
1998
- 1998-10-13 JP JP10304728A patent/JPH11198086A/en active Pending
Patent Citations (12)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US3129611A (en) * | 1960-10-14 | 1964-04-21 | Lee Engineering Company | Speed reducers |
| GB927684A (en) * | 1960-10-20 | 1963-06-06 | Merritt & Company Engineering | Epicyclic gearing |
| JPS5639341A (en) * | 1979-08-31 | 1981-04-15 | Teijin Seiki Co Ltd | Reduction gear |
| JPS56152594A (en) * | 1980-04-25 | 1981-11-26 | Meidensha Electric Mfg Co Ltd | Reduction gear for manipulator |
| JPS57121490A (en) * | 1980-12-19 | 1982-07-28 | Kuka Shiyubuaisuanraagen Unto | Gearing for hinge head coupled with jib of manipulator |
| JPS607856Y2 (en) * | 1981-03-31 | 1985-03-18 | 日立造船株式会社 | Precision punching equipment for thin plates |
| JPS58211881A (en) * | 1982-06-02 | 1983-12-09 | 松下電器産業株式会社 | Industrial robot |
| JPS59106744A (en) * | 1982-12-07 | 1984-06-20 | Sumitomo Heavy Ind Ltd | Method and device for installing eccentric body in planetary gear mechanism |
| JPS59115189A (en) * | 1982-12-20 | 1984-07-03 | 松下電器産業株式会社 | Joint device for robot |
| JPS59124093U (en) * | 1983-02-04 | 1984-08-21 | 株式会社神戸製鋼所 | Wrist mechanisms for industrial robots, etc. |
| JPS607856A (en) * | 1983-06-27 | 1985-01-16 | 株式会社クラレ | Anionic body fluid treating membrane |
| JPS618760A (en) * | 1984-06-20 | 1986-01-16 | Mitsubishi Electric Corp | Tracking error detection |
Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2007086476A1 (en) | 2006-01-26 | 2007-08-02 | Nabtesco Corporation | Speed reducer |
| EP2357380A1 (en) | 2006-01-26 | 2011-08-17 | Nabtesco Corporation | Reduction gear box |
| US8162789B2 (en) | 2006-01-26 | 2012-04-24 | Nabtesco Corporation | Reduction gear box |
| US8435149B2 (en) | 2006-02-07 | 2013-05-07 | Nabtesco Corporation | Reduction gear device |
| WO2007125835A1 (en) | 2006-04-28 | 2007-11-08 | Nabtesco Corporation | Reduction gear mechanism, and its manufacturing method |
Also Published As
| Publication number | Publication date |
|---|---|
| JPH0513794B2 (en) | 1993-02-23 |
| JPH11198086A (en) | 1999-07-27 |
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