0139-自定中心振動(dòng)篩設(shè)計(jì)

0139-自定中心振動(dòng)篩設(shè)計(jì),自定中心振動(dòng)篩,設(shè)計(jì) 南昌航空大學(xué)科技學(xué)院學(xué)士學(xué)位論文 低能耗機(jī)器人懸浮機(jī)構(gòu)的應(yīng)用 摘要 （文檔摘要） 本文給出一種采用懸浮裝置直接驅(qū)動(dòng)機(jī)器人手臂來(lái)操縱重型物體的低能量操縱方法?？紤]到在水平面內(nèi)懸吊工具的操作，利用懸吊在水平面內(nèi)的工具的動(dòng)態(tài)行為給出了混合位置/力跟蹤計(jì)劃的運(yùn)算法則，為了垂直操縱懸浮機(jī)器人手臂,由考慮到彈簧秤的重力補(bǔ)償，這種混合位置/力的動(dòng)力學(xué)模型已經(jīng)發(fā)展。為了顯示應(yīng)用于工業(yè)的可能性，這種模型在倒角作業(yè)領(lǐng)域已經(jīng)展開(kāi)。模擬和實(shí)驗(yàn)證明了此擬議系統(tǒng)的可行性。 文本全文?(5295個(gè)字) 著作權(quán)MCB UP Limited (MCB) 2000截至2000小型斷路器有限公司(簡(jiǎn)稱MCB) Mohammad Jashim Uddin: 博士, 山形大學(xué)系統(tǒng)和信息工程系, 日立 4-3-16, 日本Yonezawa 992-8510,電話: +81 238 26 3237; 傳真: +81 238 26 3205. Yasuo Nasu:山形大學(xué)機(jī)械系統(tǒng)工程部教授,日立 4-3-16, 日本Yonezawa 992-8510, Kazuhisa Mitobe: 副教授, 山形大學(xué)機(jī)械系統(tǒng)工程部教授,日立 4-3-16, 日本Yonezawa 992-8510, Kou Yamada: 副研究員, 山形大學(xué)電子及信息工程系, 日立 4-3-16, 日本Yonezawa 992-8510, 鳴謝: 在此作者真誠(chéng)的感謝Yoshihiro Ishihara先生, Yoshiyasu Hariu先生, Hidekazu Satou先生, 及 Kazuo Abe先生在機(jī)器人的制作和控制軟件的執(zhí)行中所做出的努力Mohammad Jashim Uddin還將感謝教育部，科學(xué)會(huì)，運(yùn)動(dòng)商及(MONBUSHO)給出的獎(jiǎng)學(xué)金, Japan. Received: 5 January 2000 Accepted: 7 February 2000 1. 簡(jiǎn)介： 在水平的運(yùn)動(dòng)中，工具重量在連接摩擦上有相當(dāng)大的影響，它直接地影響推進(jìn)時(shí)的轉(zhuǎn)動(dòng)力矩。在垂直的運(yùn)動(dòng)中，地心引力效果在操作體的動(dòng)力學(xué)上有相當(dāng)大的影響。機(jī)器人的操縱應(yīng)該在推進(jìn)轉(zhuǎn)力矩的可允許極限和力量感應(yīng)器的能力里面。懸浮工具系統(tǒng)(STS)是一種新提議的橫向操縱重型工具的處理策略，懸吊機(jī)器人手臂系統(tǒng)(SRAS)是一種新提議的機(jī)器人手臂用在垂直面實(shí)現(xiàn)低功率驅(qū)動(dòng)和小容量感應(yīng)器的操作方法。由于和傳統(tǒng)的系統(tǒng)比起來(lái)具有很多優(yōu)點(diǎn)，懸浮工具系統(tǒng)和懸吊機(jī)器人手臂系統(tǒng)已經(jīng)成為工業(yè)應(yīng)用領(lǐng)域越來(lái)越感興趣的話題。 當(dāng)需要結(jié)構(gòu)的堅(jiān)硬性和高性能動(dòng)態(tài)的時(shí)候，并聯(lián)操作結(jié)構(gòu)與現(xiàn)有的機(jī)器人系列相比，提供了許多明顯的優(yōu)點(diǎn)。因此, 這種機(jī)制在過(guò)去二十年受到了一定的關(guān)注(自1983). 一般說(shuō)來(lái)，直接驅(qū)動(dòng)式機(jī)械手, ,容易出現(xiàn)過(guò)快的操作幅度, 然而其輸出動(dòng)力卻很小。為了使其能拿起物體，在多個(gè)機(jī)械手的協(xié)調(diào)性控制方面做了很多研究(Schneider and Cannon, 1992; Walker et al., 1988). 當(dāng)兩個(gè)或更多機(jī)器人手臂用來(lái)完成一單一的任務(wù)時(shí)，其承載、處理、操縱能力會(huì)得到增強(qiáng)。 然而, 一個(gè)單一的機(jī)械手不能操縱重物，因?yàn)槠潋?qū)動(dòng)轉(zhuǎn)矩滯留在一個(gè)固定的極限。當(dāng)前，許多工業(yè)機(jī)器人被用于研磨作業(yè)。大部分的研磨機(jī)器人操作受限于環(huán)境. 許多研究人員開(kāi)展了工業(yè)機(jī)器人的力量控制(Kashiwagi et al., 1990; Whitney and Brown, 1987). 然而, 在那些系統(tǒng)中,研墨工具以傳統(tǒng)的方式直接裝在機(jī)器人手臂上，而且需要一個(gè)很大的驅(qū)動(dòng)力，雖然對(duì)有關(guān)在垂直面內(nèi)機(jī)器人手臂的操作有所研究 (Nemec, 1994), 但沒(méi)考慮到重力的補(bǔ)償，一般，由一個(gè)或多個(gè)機(jī)械手完成一個(gè)任務(wù)的可能性取決于其運(yùn)動(dòng)學(xué)和動(dòng)態(tài)的能力。 自動(dòng)化機(jī)器人的修邊已經(jīng)在(Her and Kazerooni, 1991)被描述。在惠特尼等地報(bào)道，美洲獅 560 機(jī)器人的機(jī)械手焊珠研磨系統(tǒng)已經(jīng)具有視覺(jué)系統(tǒng) (1990). 在所有先前的修邊或研磨的研究中,大功率驅(qū)動(dòng)器被應(yīng)用于機(jī)器人系統(tǒng)。在垂直面內(nèi)，由于機(jī)械手的巨大的重力的影響，研磨加工過(guò)程變得非常困難，尤其是當(dāng)驅(qū)動(dòng)器的轉(zhuǎn)矩極限小于重力的影響范圍。 機(jī)器人系統(tǒng)通常應(yīng)用于一個(gè)受約束的環(huán)境，所以，要控制最終受力器在自由方向的位置和在被約束方向的觸點(diǎn)壓力 。由Raibert 和Craig (1981)提出的混合位置/力控制方案在別的現(xiàn)存的控制方案上擁有相當(dāng)大的聲望。 本文中, 將闡述具有一種懸吊工具系統(tǒng)的機(jī)械手混合位置/力控制方案?？紤]到懸浮工具在水平面內(nèi)的動(dòng)態(tài)性能，我們將延伸說(shuō)明到混合控制方案的基本原理。在垂直的運(yùn)動(dòng)中,討論由彈簧秤引起的重力補(bǔ)償?shù)膭?dòng)態(tài)性能。 2. 系統(tǒng)描述： Asada和Ro (1985) 設(shè)計(jì)了直接驅(qū)動(dòng)五桿并聯(lián)機(jī)器人,具有如下許多優(yōu)點(diǎn)：沒(méi)有后沖，微小的摩擦，高機(jī)械硬度以及精確的運(yùn)動(dòng)。這種實(shí)驗(yàn)裝置系統(tǒng)包含一個(gè)兩自由度機(jī)器人，具有一個(gè)五桿連接結(jié)構(gòu)和懸架系統(tǒng)。圖1和圖2展示了機(jī)器人結(jié)構(gòu)的計(jì)算機(jī)輔助設(shè)計(jì)，在水平面和豎直面內(nèi)分別附帶一個(gè)彈簧平衡器。表一顯示了五桿連接機(jī)制的一些重要性能。 2.1. 運(yùn)動(dòng)學(xué)和動(dòng)力學(xué)方程： 本節(jié)討論的連接結(jié)構(gòu)是一個(gè)五桿閉環(huán)連桿機(jī)構(gòu)，如圖3。有兩個(gè)輸出環(huán)節(jié)，分別由兩個(gè)獨(dú)立的直驅(qū)馬達(dá)驅(qū)動(dòng)，兩個(gè)馬達(dá)安裝在底架上， 1，2，3，4桿的長(zhǎng)度分別由[sub]1,\ l[sub]2,\ l[sub]3,\ & l[sub]4表示。輸入桿的角度由q[sub]1 和 q[sub]2表示，從Y軸測(cè)量所得。終點(diǎn)坐標(biāo)(見(jiàn)方程式1)(見(jiàn)方程式2)，從方程 (1)和 (2)得該機(jī)器人的反轉(zhuǎn)運(yùn)動(dòng)學(xué)為：(見(jiàn)方程式3)( 見(jiàn)方程式4)，工作空間是一個(gè)Jacobian矩陣2×2矩陣,可以表示為：(見(jiàn)方程式5)，機(jī)器人手臂的慣量矩陣是一個(gè)2 x 2 矩陣，可以表示為 (見(jiàn)方程式6) A=I[sub]1+m[sub]1l[sup]2[sub]C1+I[sub]3+m[sub]3l[sup]2[sub]C3+m[sub]4l[sup]2[sub]1 B m= (m[sub]3l[sub]2l[sub]C3+m[sub]4l[sub]1l[sub]C4)cos(q[sub]1-q[sub]2) C m= (m[sub]3l[sub]2l[sub]C3+m[sub]4l[sub]1l[sub]C4)cos (q[sub]1-q[sub]2) Dm=I[sub]2+m[sub]2l[sup]2[sub]C2+I[sub]4+m[sub]4l[sup]2[sub]C4+m[sub]3l[sup]2[sub]2 科里奧利公式和向心力矩陣是一個(gè) 2 x 1 矩陣，可表達(dá)為:(見(jiàn)方程式 7)(見(jiàn)方程式 8)，重利矩陣是一個(gè)2 x 1矩陣，可以表示為：( (見(jiàn)方程式9)( (見(jiàn)方程式10)，g是由重力引起的重力加速度。 2.2.硬件描述： 控制系統(tǒng)的一個(gè)硬件示意圖如圖4，一部奔騰微型計(jì)算機(jī), 133 兆赫, 被用來(lái)控制此系統(tǒng)。輸入（A/D）和輸出（D/A）轉(zhuǎn)換具有八條通道和12字節(jié)的處理能力。伺服系統(tǒng)驅(qū)動(dòng)器有三種控制模式：位置控制模式速度控制模式和轉(zhuǎn)矩控制模式。此計(jì)算機(jī)主板具有三個(gè)端口和24字節(jié)脈沖處理。一個(gè)低容量的三軸力傳感器 (逐漸校正到19.62 N) 裝在機(jī)器人手臂頂端和氣動(dòng)夾子之間。運(yùn)算放大器與一個(gè)低通濾過(guò)器設(shè)計(jì)在一起，以消除預(yù)想不到的噪音，表2顯示了直驅(qū)馬達(dá)的一些重要性能。 2.3. 工作空間與異常： 對(duì)于一個(gè)給定的末端受動(dòng)器位置，反轉(zhuǎn)運(yùn)動(dòng)學(xué)一般具有兩個(gè)可行的解決方案。異常的結(jié)構(gòu)會(huì)分開(kāi)這兩種解決方案，在異常的結(jié)構(gòu)中，操縱器的最終受動(dòng)器不能在一個(gè)特定的方向移動(dòng)。異常分為兩種：固定異常和不定異常。一個(gè)閉環(huán)操縱器可能既有固定異常又有不定異常，在一個(gè)靜止的異常中, Jacobian 點(diǎn)陣具有零決定因素，然而在一個(gè)不定異常中，Jacobian點(diǎn)陣的決定因素為無(wú)窮大。Ting (1992) 、 Asada和 Ro (1985) 指出了五桿閉環(huán)連桿機(jī)構(gòu)的異常問(wèn)題。 對(duì)于五連桿結(jié)構(gòu)，Jacobian 矩陣的決定因素J被定義為(見(jiàn)方程式11)；對(duì)于五連桿機(jī)構(gòu)，當(dāng)( 見(jiàn)方程式12)的情況時(shí)，固定異常存在。由方程式 (10)知,固定異常發(fā)生在工作空間的邊界，所以，籍由選擇鏈環(huán)尺寸來(lái)獲得一個(gè)自由空間的寬闊異常。機(jī)器人手臂的笛卡爾工作空間是最終受力器的總電子掃頻量，同時(shí)機(jī)器人手臂執(zhí)行所有的可行的動(dòng)作，最終受力器伴有一種特殊的力，即法向力和切向力。 迪卡爾工作空間受限于機(jī)器人手臂的幾何學(xué)分析和鉸鏈的機(jī)械約束以及驅(qū)動(dòng)器的旋轉(zhuǎn)極限。力量工作空間受限于最終受力器的發(fā)向力和切向力。實(shí)際上，力量工作空間是機(jī)械人手臂的一個(gè)笛卡爾工作空間的子集。 當(dāng)驅(qū)動(dòng)器的旋轉(zhuǎn)力矩在如下范圍內(nèi)時(shí)：0[sup]- <= q[sub]1\ <=180[sup]- & 0[sup]- <= q[sub]2 <=180[sup]-.圖5展示了五連桿機(jī)構(gòu)在水平面內(nèi)的模擬卡迪爾工作空間。笛卡爾總工作空間應(yīng)付 5.0 N 的力量工作空間，在10.0 N的力量工作空間情況下是卡迪爾工作空間的一個(gè)子集。當(dāng)彈簧秤的提升力設(shè)為9.81 N 和驅(qū)動(dòng)器的旋轉(zhuǎn)力在以下范圍時(shí)：0[sup]- <= q[sub]1 <=180[sup]- and 180[sup]- <= q[sub]2 <=360[sup]-.圖6展示展示了五連桿機(jī)構(gòu)在豎直面內(nèi)的模擬卡迪爾工作空間。笛卡爾總工作空間應(yīng)付 5.0 N 的力量工作空間，在10.0 N的力量工作空間情況下是卡迪爾工作空間的一個(gè)子集。 3. 懸浮動(dòng)態(tài) 懸浮工具系統(tǒng)和懸浮機(jī)器人手臂系統(tǒng)的模型分別如圖7圖8 所示。 彈簧秤的性能參數(shù)見(jiàn)表III 。在懸浮系統(tǒng)中, [phi]是旋轉(zhuǎn)角度, [psi] 是方位角。為了將懸浮系統(tǒng)形象化，我們考慮做如下假設(shè)：高架鐵路的彈性變形，鋼索的質(zhì)量，滾動(dòng)阻力，風(fēng)力以及忽略噪音。最終受力器的卡迪爾坐標(biāo)定義如下： (見(jiàn)方程式13)( 見(jiàn)方程式14)，有效的提升力F[sub]取決于彈簧秤的設(shè)置，與懸浮的質(zhì)量有關(guān)而不是鋼絲繩的長(zhǎng)度變化。在懸浮工具上的有效力被定義為： (見(jiàn)方程式15)( 見(jiàn)方程式16)?，F(xiàn)在，水平面內(nèi)的懸浮力為：(見(jiàn)方程式17)。在豎直面內(nèi)的有效力F[sub]vy和 F[sub]vz 被定義為：(見(jiàn)方程式18)( 見(jiàn)方程式19)。此時(shí)，在豎直面內(nèi)來(lái)自彈簧秤的補(bǔ)償力可被定義為：(見(jiàn)方程式20) 4. 系統(tǒng)動(dòng)力學(xué) 混合位置/力控制方案以一個(gè)工作空間的直角分解為基礎(chǔ)。在平面運(yùn)動(dòng)中，考慮到懸浮工具的動(dòng)態(tài)影響，我們討論位置/力控制模型 。在這部分中，豎直面中的混合位置/力控制模型從彈簧秤的重力補(bǔ)償方面來(lái)描述。 5. 仿真結(jié)果 為了探討機(jī)器人手臂在橫向和縱向面內(nèi)的執(zhí)行性能，利用前面章節(jié)的MATLAB仿真程序進(jìn)行了動(dòng)態(tài)模型模擬，仿真框圖如圖10。軌跡發(fā)生器,運(yùn)動(dòng)器,控制器,操作器動(dòng)力, 以及約束條件都在MATLAB函數(shù)中被描述了。端口用來(lái)連接標(biāo)量或矢量信號(hào)匯集成一個(gè)更大的矢量信號(hào)。轉(zhuǎn)換器用來(lái)選擇輸出矢量的有用信號(hào)。 5.1.水平面內(nèi) 為顯示工具重力的影響，利用混合位置/力模擬以實(shí)現(xiàn)水平面運(yùn)動(dòng)。在模擬過(guò)程中，總操作時(shí)間為10秒，混合的時(shí)間為0.5秒，要求速度為0.02米/秒。最終受力器的軌跡在一個(gè)被約束的表面，從(0.0, 0.3) 到 (0.2, 0.3) 。模型工具的重量是2.0 kg 。 假設(shè)是特制鋼，彈簧秤的提升力看作是19.62 N ，所需的力為5.0 N 。從圖11可看出, 與傳統(tǒng)的工具系統(tǒng)相比，由于特制鋼工具系統(tǒng)具有更小的連接摩擦，故其位置誤差更小。 此外，從圖12可看出，由于小的懸浮力作用于此懸浮工具系統(tǒng)，故其引起力的誤差更小。 5.2. 豎直面內(nèi) 在豎直面內(nèi)，當(dāng)驅(qū)動(dòng)器力矩極限在重力影響范圍之內(nèi)時(shí)，彈簧秤的提升力是必要的，用以補(bǔ)償重力。一個(gè)特征曲線圖用來(lái)說(shuō)明提升力的必要性以使機(jī)械手在力矩的極限內(nèi)保持在一個(gè)預(yù)設(shè)的速度。圖13表示了在速度為0.01米/秒時(shí)彈簧秤的提升力和馬達(dá)的驅(qū)動(dòng)力矩之間的關(guān)系F[sub]b。 在此特征曲線圖里，提升力達(dá)到5.0 N ，由于假想摩擦力的影響（方向力河切向力），馬達(dá)驅(qū)動(dòng)力保持不變。此時(shí)，由于受到提升力的影響，馬達(dá)的驅(qū)動(dòng)力將增加。從此特征圖可以看出，當(dāng)提升力從5.2 N變到16.5 N時(shí)，在驅(qū)動(dòng)力極限內(nèi)機(jī)器人手臂能夠被操作。 我們進(jìn)行了懸浮機(jī)器人手臂操作的混合位置/力控制模擬實(shí)驗(yàn)。在模擬實(shí)驗(yàn)中，總操作時(shí)間為10秒，混合的時(shí)間為0.5秒，最大速度為0.01米/秒，從特征曲線圖可知，提升力設(shè)定為9.81 N ，要求的力是5.0 N。在垂直向上的運(yùn)動(dòng)中，機(jī)械手的軌跡在一個(gè)被約束的表面，從(0.3, 0.0) 到(0.3, 0.1) 。圖14 展示了機(jī)械手的有效的提升力和重力 。在豎直面的運(yùn)動(dòng)，彈簧秤的提升力是補(bǔ)償重力的主要部分，以及有效力非常小。圖15和圖16分別展示了位置軌跡和力的軌跡。輸出的位置軌跡與要求的位置軌跡之間存在一個(gè)小的固定誤差以及力的輸出與要求的力輸出有一個(gè)小的時(shí)間滯后。 6. 實(shí)驗(yàn)結(jié)果 為了證明以上系統(tǒng)地有效性和正確性，我們?cè)谒矫婧拓Q直面都進(jìn)行了實(shí)驗(yàn)，實(shí)驗(yàn)結(jié)果如下部分所示。 6.1. 靜力 圖17和圖18分別展示了在靜態(tài)時(shí)沿X軸和Y軸的有效力F[sub]hx 和F[sub]hy。很明顯， 當(dāng)機(jī)器人手臂抓住懸浮工具時(shí)，有效的靜態(tài)力大小接近最佳，但是當(dāng)機(jī)器人手臂抓住工具而沒(méi)有懸浮時(shí)，由于工具自身重量的影響，有效力將非常高。由于工具自身重量，機(jī)械手頂端會(huì)偏離引起位置誤差。有效的靜態(tài)力造成連接摩擦影響驅(qū)動(dòng)器的驅(qū)動(dòng)力矩。 6.2.水平運(yùn)動(dòng) 在本實(shí)驗(yàn)中，機(jī)械手抓取一個(gè)2.0千克的懸浮工具的運(yùn)動(dòng)軌跡在一條從(0.1, 0.34) 到 (0.2, 0.34)的線上。速度指令為0.02米/秒，所需的力是10.0牛。從彈簧秤上懸吊起工具所需的力為19.62 N 。在實(shí)驗(yàn)開(kāi)始之前，最終受力器與一個(gè)被約束的表面接觸，圖19展示了本實(shí)驗(yàn)的位置軌跡，圖20展示了力的軌跡。實(shí)際的位置軌跡與所需的位置軌跡存在一個(gè)穩(wěn)定的小誤差，以及實(shí)際力與要求的力輸出有一個(gè)小的時(shí)間滯后。 6.3. 豎直運(yùn)動(dòng) 在豎直平面內(nèi)，當(dāng)驅(qū)動(dòng)器的驅(qū)動(dòng)力矩極限在重力影響范圍之內(nèi)時(shí)，機(jī)器人手臂不能進(jìn)行自動(dòng)操作。在本實(shí)驗(yàn)中，彈簧秤的提升力設(shè)定為15.0 N，足夠?qū)⒃诘退龠\(yùn)行的機(jī)器人手臂懸吊起來(lái)。機(jī)械手的軌跡在一個(gè)從(0.28, 0.22) 到 (0.28, 0.26)的被約束表面上。指令速度為0.005米/秒，所需的力為2.0牛 。圖21和圖22分別展示了位置軌跡和力的軌跡。實(shí)際的位置軌跡與要求的位置軌跡之間存在一個(gè)小的固定誤差以及實(shí)際的力的與所需的力軌跡有一個(gè)小的時(shí)間滯后。圖23 說(shuō)明了所需的驅(qū)動(dòng)力矩，此力矩在驅(qū)動(dòng)器的最大極限之內(nèi)。 7.工業(yè)應(yīng)用 為證實(shí)上述被應(yīng)用于工業(yè)的機(jī)器人系統(tǒng)的低能耗，倒角作業(yè)已經(jīng)實(shí)行。圖24 展示了在豎直平面內(nèi)的實(shí)驗(yàn)裝備，在傳統(tǒng)的系統(tǒng)中，用旋轉(zhuǎn)的鐵碳銼刀修毛刺的結(jié)果顯示，在304不銹鋼上用0.88牛的解點(diǎn)壓力和0.01米/秒的速度可生成一個(gè)可令人接受的倒角。 在上述被提議的機(jī)器人手臂系統(tǒng)中，已經(jīng)應(yīng)用于SS400倒角作業(yè)。懸吊此低能耗機(jī)器人手臂的提升力為15.0牛。用一個(gè)重0.13千克（直徑為16 mm）的氣動(dòng)砂輪以最大旋轉(zhuǎn)速度為每秒30000轉(zhuǎn)的速度進(jìn)行銑削 ，倒角表面的照片如圖25所示，圖26 顯示了在勻速為0.01米/秒的法向摩擦力f[sub]n及切向磨削力f[sub]t。法向磨削力保持在所需的大小2.0牛，因?yàn)樵诿鞒叽缰袥](méi)有大的變化。切向力大約是法向力的一半，圖27展示了通過(guò)一次單一的磨削倒角表面的剖切圖。倒角結(jié)果顯示了倒角面的寬度0.36 +- 0.07 mm ，此結(jié)果在公差范圍內(nèi)。 8. 結(jié)論 上述提議的懸浮系統(tǒng)的主要目標(biāo)是用能耗操作器完成中午的作業(yè)。在水平面和豎直面內(nèi)都已經(jīng)討論過(guò)。在水平運(yùn)動(dòng)中，懸浮系統(tǒng)具有一些優(yōu)點(diǎn)，當(dāng)重型工具超出驅(qū)動(dòng)器的驅(qū)動(dòng)力矩極限時(shí)，它可以利用彈簧秤的提升力進(jìn)行操作。此系統(tǒng)的連接摩擦力小于傳統(tǒng)的系統(tǒng)，在橈腕關(guān)節(jié)產(chǎn)生的阻力更小，這對(duì)小容量的力傳感器來(lái)說(shuō)更是一大益處。此外，在豎直運(yùn)動(dòng)中，懸浮力補(bǔ)償了作用在操作器上的重力。 懸浮工具的動(dòng)態(tài)模型和懸浮機(jī)器人手臂系統(tǒng)已經(jīng)發(fā)展和執(zhí)行，利用當(dāng)前的動(dòng)力學(xué)公式，開(kāi)展了模擬和實(shí)驗(yàn)以證明上述提議的系統(tǒng)的有效性。在豎直平面內(nèi)，倒角作業(yè)已經(jīng)開(kāi)展了。在豎直平面內(nèi)操作機(jī)器人手臂需要一個(gè)大力矩驅(qū)動(dòng)的驅(qū)動(dòng)器以克服重力。彈簧秤的提升力補(bǔ)償了工具在豎直平面內(nèi)的重力。倒角表面的結(jié)果證明了懸浮機(jī)器人手臂的自動(dòng)磨削系統(tǒng)可以以低功率驅(qū)動(dòng)力傳感器和低能量驅(qū)動(dòng)器在大尺寸的金屬切削過(guò)程中具有廣泛的可應(yīng)用性。 Application of suspension mechanisms for low powered robot tasks Abstract: The manipulation methods of a low powered direct-drive robot-arm for heavy object manipulation using a suspension device are presented. Manipulation of a suspended tool in the horizontal plane is considered. The algorithm is presented of the hybrid position/force tracking scheme with respect to the dynamic behavior of suspended tools in the horizontal plane. To manipulate the suspended robot-arm vertically, the hybrid position/force dynamic model has been developed by considering the gravity compensation of the spring balancer. In order to show the possible industrial applications chamfering operations have been carried out. Simulations and experiments demonstrate the feasibility of the proposed systems. Introduction Copyright MCB UP Limited (MCB) 2000 Mohammad Jashim Uddin: PhD student, Department of Systems and Information Engineering, Yamagata University, Jonan 4-3-16, Yonezawa 992-8510, Japan. Tel: +81 238 26 3237; Fax: +81 238 26 3205. Yasuo Nasu: Professor, Department of Mechanical Systems Engineering, Yamagata University, Jonan 4-3-16, Yonezawa 992-8510, Japan. Kazuhisa Mitobe: Associate Professor, Department of Mechanical Systems Engineering, Yamagata University, Jonan 4-3-16, Yonezawa 992-8510, Japan. Kou Yamada: Research Associate, Department of Electrical and Information Engineering, Yamagata University, Jonan 4-3-16, Yonezawa 992-8510, Japan. ACKNOWLEDGMENT: The authors gratefully acknowledge Mr Yoshihiro Ishihara, Mr Yoshiyasu Hariu, Mr Hidekazu Satou, and Mr Kazuo Abe's efforts during fabrication of the robot and implementation of the control software. Mohammad Jashim Uddin would like to acknowledge his scholarship by the Ministry of Education, Science, Sports, and Culture (MONBUSHO), Japan. Received: 5 January 2000 Accepted: 7 February 2000 1. Introduction In horizontal motion, tool weight has a considerable effect on joint friction. It affects directly the driving torque. In vertical motion, the gravity effect has a considerable influence on the dynamics of the manipulator. Robotic manipulation should be within the allowable limits of the driving torque and capacity of the force sensors. Suspended tool system (STS) is a newly proposed object handling strategy to manipulate heavy tools horizontally and suspended robot-arm system (SRAS) is a newly proposed robot-arm manipulation method in the vertical plane using low power actuators and small capacity force sensors. Due to their many advantages compared to conventional systems, STS and SRAS have become topics of growing interest for applications in industry. Parallel manipulators offer significant advantages over current serial manipulators when structural stiffness and high-performance dynamic properties are required. Therefore, such mechanisms have received some attention over the last two decades (Hunt, 1983). Direct-drive arms, in general, tend to have excessively fast operating ranges, whereas the output forces are extremely small (Asada and Ro, 1985). For object handling, there are many researches on the coordinated control of multiple robot-arms (Schneider and Cannon, 1992; Walker et al., 1988). When two or more robot-arms are used to perform a single task, an increased load carrying, handling, and manipulating capability can be achieved. However, a single manipulator cannot manipulate a heavy object because the actuator torque stays within a fixed limit. Many industrial robots are currently used in automated grinding operations. Most of the grinding robots operate in a constrained environment. Force controlled grinding robots for industrial uses are developed by many researchers (Kashiwagi et al., 1990; Whitney and Brown, 1987). However, in those systems, the grinding tool is directly mounted on the robot-arm in a conventional way and requires a large actuator power. There are some researches on robot-arm manipulation in the vertical plane (Nemec, 1994), but compensation for gravity was not considered. In general, the feasibility of a task to be performed by one or more arms depends on both the kinematic and dynamic abilities of the manipulators. Automated robotic deburring has been described in (Her and Kazerooni, 1991). Robotic weld bead grinding system by PUMA 560 robot with vision system has been reported in Whitney et al. (1990). In all the previous deburring or grinding researches, big power actuators were used in the robot system. In the vertical plane, the grinding process is very difficult due to the enormous gravity effects of the manipulator, especially when the actuator torque limit is beyond the range of the gravity effects. Robotic systems usually operate in a constrained environment. So, it is necessary to control the position of the end-effector in the free direction and the contact force in the constrained direction. The hybrid position/force control scheme proposed by Raibert and Craig (1981) has gained considerable popularity over the other existing force control schemes. In this paper, hybrid position/force control scheme of robot-arm with a suspended tool system is described. We extend the basis of hybrid control scheme by considering the dynamics of the suspended tool system in horizontal motion. In vertical motion, the dynamics of gravity compensation by spring balancer is discussed. 2. System description Asada and Ro (1985) designed a direct-drive five-bar parallel drive manipulator, which has many advantages such as: no backlash, small friction, high mechanical stiffness, and accuracy of motion. The experimental system consists of a robot with two degrees of freedom (DOF) having a five-bar link configuration and a suspension system. Figures 1 and Figure 2 show the CAD design of the robot configuration with a spring balancer in the horizontal and vertical plane, respectively. Table I shows some important properties of the five-bar link mechanism. 2.1. Kinematic and dynamic equations The link mechanism discussed in this section is a closed-loop five-bar link mechanism as shown in Figure 3. There are two input links that are driven by two independent direct-drive motors. Both motors are fixed to the base frame. The length of links 1, 2, 3, and 4 are denoted by l[sub]1,\ l[sub]2,\ l[sub]3,\ & l[sub]4, respectively. The angles of the input links are denoted by q[sub]1 and q[sub]2 measured from Y-axis. The end point coordinates are given by:(see equation 1)(see equation 2)From equations (1) and (2) the inverse kinematics of the manipulator is obtained as:(see equation 3)(see equation 4)The task space Jacobian matrix is a 2 x 2 matrix and can be expressed as:(see equation 5)The inertia matrix of the robot-arm is a 2 x 2 matrix and can be expressed as:(see equation 6)where A = I[sub]1+m[sub]1l[sup]2[sub]C1+I[sub]3+m[sub]3l[sup]2[sub]C3+m[sub]4l[sup]2[sub]1 B m= (m[sub]3l[sub]2l[sub]C3+m[sub]4l[sub]1l[sub]C4)cos(q[sub]1-q[sub]2) C m= (m[sub]3l[sub]2l[sub]C3+m[sub]4l[sub]1l[sub]C4)cos (q[sub]1-q[sub]2) D m= I[sub]2+m[sub]2l[sup]2[sub]C2+I[sub]4+m[sub]4l[sup]2[sub]C4+m[sub]3l[sup]2[sub]2 The Coriolis and centripetal forces matrix is a 2 x 1 matrix and can be expressed as:(see equation 7)(see equation 8)The gravity matrix is a 2 x 1 matrix and can be expressed as:(see equation 9)(see equation 10)where g is the acceleration due to gravity. 2.2. Hardware description A hardware schematic diagram of the control system is shown in Figure 4. A Pentium based microcomputer, 133 MHz, is used to control the system. The A/D and D/A converter has eight channels and 12-bit resolution. The servo driver has three control modes: position control mode, velocity control mode, and torque control mode. The counter board has three ports and 24-bit pulse resolution. A low capacity three-axis force sensor (calibrated to work up to 19.62 N) is mounted between the robot-arm tip and the pneumatic gripper. The operational amplifier is designed with a low pass filter to eliminate unexpected noise. Table II shows some important properties of direct-drive motors. 2.3. Work space and singularity For a given end-effector position, there are in general two possible solutions to the inverse kinematics. The singular configuration separates these two solutions. At the singular configuration, the manipulator end-effector cannot move in certain directions. There are two types of singularities, stationary singularity and uncertainty singularity. A closed-loop manipulator may have both stationary and uncertainty singularities. At a stationary singularity, the Jacobian matrix has zero determinant, whereas at an uncertainty singularity, the determinant of Jacobian matrix is infinity. Ting (1992) and Asada and Ro (1985) pointed out the singularity problem for the five-bar closed link manipulator. For the five-bar link configuration, the determinant of Jacobian matrix, J, is defined as follows:(see equation 11)For five-bar link configuration the stationary singularity will exist when:(see equation 12)From equation (10), the stationary singularity occurs on the boundary of the workspace. Thus, by selecting link dimensions, a wide singularity free workspace can be obtained. The Cartesian workspace of a robot-arm is the total volume swept out by the end-effector as the robot-arm executes all possible motions. The force workspace of a robot-arm is the total volume swept out by the end-effector as the robot-arm executes all possible motions with a specific force at the end-effector, normal force and tangential force. The Cartesian workspace is constrained by the geometry of the robot-arm as well as mechanical constraints of the joints and the limit of the actuator's rotation. The force workspace is constrained by the normal and tangential force applied at the end-effector. Actually, the force workspace is a subset of Cartesian workspace of a robot-arm. Figure 5 shows the simulated Cartesian workspace of the five-bar link mechanism in the horizontal plane when the actuator rotation is limited within the following ranges: 0[sup]- <= q[sub]1\ <=180[sup]- & 0[sup]- <= q[sub]2 <=180[sup]-. The total Cartesian workspace copes with 5.0 N force workspace, where the 10.0 N force workspace is a subset of Cartesian workspace. Figure 6 shows the simulated Cartesian workspace of the five-bar link mechanism in the vertical plane when the lifting force of the spring balancer is set to a force of 9.81 N and the actuator rotation is limited within the following ranges: 0[sup]- <= q[sub]1 <=180[sup]- and 180[sup]- <= q[sub]2 <=360[sup]-. The total Cartesian workspace copes with 5.0 N force workspace, where the 10.0 N force workspace is a subset of Cartesian workspace. 3. Suspension dynamics The models of the suspended tool system and the suspended robot-arm system are shown in Figure 7 and Figure 8, respectively. The properties of the spring balancer are shown in Table III. In the suspension system, [phi] is swing angle, and [psi] is orientation angle. In order to simplify the suspension system, the following assumptions are considered. The elastic deformation of the overhead rail, the mass of the wire rope, rolling resistance, wind forces, and noise are neglected. The Cartesian coordinates of the end-effector are defined as follows:(see equation 13)(see equation 14)The active lifting force, F[sub]b, in the wire rope depends on the setting of the spring balancer, which is related to the suspended mass but independent of the variation of the rope length. The active forces on the suspended tool are defined as follows:(see equation 15)(see equation 16)Now, the suspension force in the horizontal plane is:(see equation 17)The effective forces F[sub]vy, and F[sub]vz in the vertical plane are defined as follows:(see equation 18)(see equation 19)Then, the compensation force from the spring balancer in the vertical plane can be defined as follows:(see equation 20) 4. System dynamics The hybrid position/force control scheme is based on an orthogonal decomposition of task space. The hybrid position/force control model is discussed for planar motion by considering the dynamic effect of the suspended tool. In this section, hybrid position/force control model for vertical motion is described by gravity compensation of the spring balancer. 5. Simulation results In order to investigate the performance of robot-arm in the horizontal and vertical planes, simulations have been carried out using the dynamic models developed in the preceding sections by MATLAB Simulink program. The Simulink block diagram is shown in Figure 10. The trajectory generator, kinematics, controller, manipulator dynamics, and constraint conditions are described in MATLAB functions. The ports are used to combine scalar or vector signals into a larger vector. The switches are used to select the desired signals of the output vector. 5.1. The horizontal plane Hybrid position/force simulation is carried out for horizontal motion to show the effect of tool weight. In simulation, total manip