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南京理工大學泰州科技學院 畢業(yè)設計 論文 外文資料翻譯 學院 系 機械學院 專 業(yè) 機械工程及自動化 姓 名 張廣濟 學 號 1201010160 外文出處 Mechatronics 24 2014 1223 1230 附 件 1 外文資料翻譯譯文 2 外文原 文 指導教師評語 簽名 年 月 日 注 請將該封面與附件裝訂成冊 分布式驅(qū)動機器人機械手的設計與控制機制 摘要 本文提出了一種基于分布式驅(qū)動原理的設計方法 目的是實現(xiàn)一個具有高性 能的機器人 驅(qū)動點的空間運動提供了幾個優(yōu)點如高負載能力 高效率和輕重量 結(jié)構(gòu)的機器人機械臂 在分析的基礎上 分布式驅(qū)動機制為提出的機械臂采用了 單一滑塊 一個有兩個自由度的機械臂雛形作為一個例子可被開發(fā)和控制 實驗 驗證了所提出的方法的有效性 關鍵詞 分布式驅(qū)動機制 機械手 機械臂 高載荷 輕型臂 1 引言 機器人一般采用高容量的執(zhí)行器增強各種性能特點 如有效載荷和運動速度 然而 在實 踐中 執(zhí)行器和減速器經(jīng)常導致機械手很笨重 因此 為高性能和緊湊的設計 在這些想法中 必然會想要有一個權(quán)衡 為了解決這些沖突的設計目標 有各種各樣的方法 在提高傳統(tǒng)機械臂的性能時使用大容 量的電機是有利的 這樣會使結(jié)構(gòu)變化少 液壓作動器對產(chǎn)生大扭矩很有用 電機的電液冷卻 系統(tǒng)有效地提高了短時工作的峰值扭矩 此外 并聯(lián)機械手往往被用在結(jié)構(gòu)剛度要求高并有動 態(tài)能力的應用中 此外 機械臂結(jié)構(gòu)的優(yōu)化可能需要減少機器人的重量 降低了執(zhí)行器功率要 求 并減少機器人系統(tǒng)所需的空間 最近提出的一個低體重的機器人手臂被稱為是最有效的設 計之一 對機械臂的機械結(jié)構(gòu)和電機進行了優(yōu)化設計 將導致一個負載的重量比為 1 總系統(tǒng) 重量不到 15 公斤 和 1 5 米的工作區(qū) 上述研究中的操縱 在旋轉(zhuǎn)執(zhí)行器被放置在相鄰連接 的機械臂上利用了聯(lián)合驅(qū)動拓撲 這種關節(jié)驅(qū)動機構(gòu)在簡單的結(jié)構(gòu)和易于控制方面是有優(yōu)勢的 然而 它不好的地方在于需要沉重的機械組件 以承擔的集中載荷的關節(jié) 換句話說 齒輪或 諧波傳動裝置應用于減速和扭矩的提高 這將導致在實踐中的重型機械手出現(xiàn) 此外 齒輪與 高速的減速比 不可避免地降低了機械手的效率 出于這些困難 我們采用分布式驅(qū)動機制 提出了一種輕量級但高效的機械手設計 分布 式驅(qū)動原理為了迫使點與鏈接最大限度地提高指尖的力量在空間上優(yōu)化了位置 由于工作點的 位置能被改變 可以在他們的最佳位置進一步提高機器人手指的輸出力 分布式驅(qū)動原理的可 行性確認了小機器人手指是由超聲電機或無刷直流電機驅(qū)動的 在本文中 我們提出了一個機器人操縱器在分布式驅(qū)動機制的應用下 具有輸出轉(zhuǎn)矩大 效率高 但重量輕的特點 從 提出的機械手的設計的不同視角 符合一個系統(tǒng)的設計過程 此外 機器人操縱器的控制是新提出來的 作為結(jié)果 本文提到的機械手 預計將是一種有效 的替代 并能夠在其他領域中使用 例如 移動機器人平臺 論文組織如下 在第 2 節(jié) 從機械臂設計的角度對分布式驅(qū)動原理進行了簡要的回顧和分 析 在第 3 節(jié) 機器人設計和實驗結(jié)果在列 最后 結(jié)論如下在 4 節(jié) 2 分布式驅(qū)動機械臂 2 1 分布式驅(qū)動機制研究綜述 一般情況下 機械手是由關節(jié)驅(qū)動機制驅(qū)動的 例如 在工業(yè)機器人中一個電機齒輪組件 是被放置在兩個鏈接的關節(jié)處 此外 一個液壓執(zhí)行器通常是固定在挖掘機的關節(jié) 與上述相反 分布式驅(qū)動機制通過把滑塊沿鏈接 由剛性桿連接 在關節(jié)處產(chǎn)生了力矩 如圖 1 所示 該滑塊由滾珠絲杠與電機驅(qū)動 分布式驅(qū)動的雙滑塊的一個典型特征是將工作點 使關節(jié)力矩的變化取決于他們的位置的自由 這是一個額外的自由度 以最大限度地提高聯(lián)合 扭矩 在中 這可能不是一個主要問題 因為小尺寸的執(zhí)行器只是偶爾使用 1 1 2 2 建議致動機構(gòu) 在這一小節(jié)中 我們將分布式驅(qū)動機制擴展到一個具有高負載能力的輕型機械臂的設計中 例如 超過 10 公斤 為此 我們專注于幾個通用的分布式驅(qū)動機制 是以前沒有在文獻中 研究過的 為了減少執(zhí)行器的數(shù)量 只有一個滑塊可以通過從接頭固定在一定的距離移動 即 X1 固定 如圖 2 所示 同時 鏈接有一個角度偏移 即 hoffset 有了這個配置 在 2 1 節(jié)中解 決的滑塊位置的冗余不能持續(xù) 但致動器的位置仍然保持有效的變量 換句話說 在關節(jié)處所 產(chǎn)生的力矩取決于移動滑塊的位置 即 X2 此外 通過調(diào)整 X1 fixed h2 Lrod 和 offset 的尺寸 轉(zhuǎn)矩可以保持為比所需扭矩較大 用于操縱有效載荷過工作區(qū) 為了證明這一點 使用該機制 的運動學 讓我們考慮產(chǎn)生的轉(zhuǎn)矩 是關節(jié)角度 并且 F2 是移動連接的滑 塊推力 所產(chǎn)生的轉(zhuǎn)矩變化通過驅(qū)動點 X2 的位置 并且其外形取決于設計參數(shù)例如在第 3 節(jié)中將 被優(yōu)化的 X1 fixed h2 Lrod 和 offset 特別是 它指出 offset 確實在一定程度上在工作區(qū)內(nèi)的扭 矩分布發(fā)揮重要作用 為了說明它 所產(chǎn)生的轉(zhuǎn)矩計算和不對于相同的其他設計參數(shù)對 offset 夾雜 X1 fixed h2 Lrod 如圖 3 所示 所述扭矩曲線移動到左側(cè)當 offset 8 這樣生成的扭 矩總是比要求轉(zhuǎn)矩大 用于通過整個 的工作空間操縱 13 公斤力的有效載荷 應當注意 所 需的轉(zhuǎn)矩是通過考慮即將在第 3 小節(jié)開發(fā)的有效載荷和重量的機械臂的原型來計算的 建議的 機制與一個單一的滑塊不提供冗余的滑塊位置 需要最大限度地提高輸出轉(zhuǎn)矩 然而 這個問 題可以通過優(yōu)化的結(jié)構(gòu)參數(shù) 考慮在工作區(qū)內(nèi)的性能規(guī)格來緩解 圖 1 分布式驅(qū)動機制的概念 圖 2 機器人機械手的關節(jié)模型 圖 3 關節(jié) 1 處角度 offset 的影響 圖 4 關節(jié)驅(qū)動 a 或者分布式驅(qū)動 b 對單自由度 機械手的虛擬設計 該機制和常規(guī)聯(lián)合驅(qū)動有幾點不同 首先 由于 三角形 連接桿的閉環(huán)結(jié)構(gòu)封閉回路的 結(jié)構(gòu)剛度顯著增加 由于外部負載所產(chǎn)生的彎曲力矩可以被連接桿的排斥力所支撐 減少撓度 和最大彎矩 此外 不同于 JM 造成滾珠絲杠的變形幾乎可以忽略不計 因為滾珠絲杠的剛 度是很高的 因此 盡管機器人的重量輕 該提出的機制具有顯著的結(jié)構(gòu)剛度 允許質(zhì)量重的 對象來進行處理 其次 通過采用滾珠絲杠系統(tǒng)驅(qū)動線性滑塊 我們可以在轉(zhuǎn)矩 力轉(zhuǎn)換過程中效果顯著的 得到高速減速比 與那些傳統(tǒng)的由一個行星齒輪和一個諧波傳動 傳輸效率低于 70 的減速 器相比 滾珠絲杠系統(tǒng)具有大約 95 的效率 并且 如此這樣 這將需要更小的致動器 同 時保持機械手所需要的輸出功率 此功能也有利于建立一個輕量機械手系統(tǒng) 為了證明擬議的機械手的有效性 我們幾乎設計了 2 個不同的機械手 如圖 4 所示 一個 是使用標準的聯(lián)合常規(guī)單自由度機械手驅(qū)動機構(gòu) JM 另一種是單自由度機械手提出的分布 式驅(qū)動機制 DM 對于這兩種情況 設計的目標是實現(xiàn)在 0 7 米外展的 13 公斤有效載荷能 力 輸出功率約為 110W 此外 對于數(shù)據(jù)挖掘 假設 X1 fixed h2 Lrod 和 offset 分別是 230 毫 米 145 毫米 38 毫米和 8 度 這也是在 3 節(jié)中使用的硬件設計的參數(shù) 詳細描述見表 1 電機 減速器 由諧波傳動和行星齒輪組成 和一個滾珠絲桿都是在市售的組件中 在接頭處 有類似的輸出 即關節(jié)力矩和速度 設計可能不是最佳的 但這是最好的試驗和誤差的方法 首先 一個更大的電機采用 JM 因為諧波傳動效率低約 70 另一方面 在 DM 的情況下 滾 珠絲桿的效率約為 95 所以可以使用較小的和更輕的電機 此外 滾珠絲杠比 JM 減速機輕 得多 因此 DM 是明顯輕于 JM 同時保持類似的輸出功率 值得注意的是 DM 的工作范圍 是小于 JM 的 這可能是一個缺點 然而 這可能不是一個關鍵問題 如果數(shù)據(jù)挖掘的任務是 在有限的工作范圍內(nèi) 例如 一個爆炸軍械處理 EOD 機械手 一個碼垛機械手等 此外 DM 由于比 JM 較高的剛度具有結(jié)構(gòu)優(yōu)勢 它指出 在表 1 DM 的關節(jié)僵值四 119 kNm 弧度 幾乎是 JM 得 2 倍 表一 比較結(jié)果 設計結(jié)果和主要規(guī)格 項目 1 項目 2 子項目 JM 設計 DM 設計 主要部件 a 電機 模型 EC 45 EC60 flat 功率 164w 111w 速度 9290 轉(zhuǎn) 3740 轉(zhuǎn) 重量 850g 470g 諧波傳動 模型 CSG32 160 1 重量 890 g 行星齒輪 模型 GP42C 6 1 質(zhì)量 260 g 滾珠絲桿 模型 MDK 1002 質(zhì)量 200 g 框架 b 質(zhì)量 1526g 1450g 設計結(jié)果 聯(lián)合輸出 c 扭矩 114 Nm 111 Nm 速度 1 01 rad s 0 93 rad s 節(jié)點剛度 41 kNm rad 119 kNm rad 固有頻率 d 1 2 kHz 2 1 kHz 最大撓度 鏈接 497 lrad 415 lrad 減速器 776 lrad 29 lrad 效率 70 95 工作范圍 0 360 30 120 總重量 3526 g 2120 g a 制造商 1 電機與行星齒輪 maxon 電機公司 2 諧波傳動滾珠絲杠 THK b 鏈接提示的最大撓度在 13 千克最大有效載荷下要比 500 小 c 轉(zhuǎn)矩和速度的值是平均值 d 是以 13 公斤的有效載荷為標準計算的 with Soohyun methodology the The high ics and bulky goals robotic systems 9 12 A low weight robot arm was recently pro posed in 13 and is known to be one of the most efficient designs The mechanical structure and motors of the robot arm were opti mized which results in a load to weight ratio of 1 a total system weight of less than 15 kg and a workspace of 1 5 m The manipulators in the aforementioned studies utilize a joint actuation topology under which rotary actuators are placed at the joints of adjacent manipulator links 14 23 This joint actua s validated for a or BLDC r that possesses high output torque and efficiency but light weight thanks use of a distributed actuation mechanism Different perspectives from 24 are presented for the robot manipulator design allowsforasystematicdesignprocess Also thecontroloftherobot manipulator is newly presented As a result the proposed robot manipulator is expected to be an effective alternative that may be used in several fields e g mobile robot platforms 26 28 The paper is organized as follows In Section 2 the distributed actuation principle is briefly revisited and analyzed from the per spective of a manipulator design In Section 3 the robot design Corresponding author Tel 82 42 350 3047 E mail address kyungsookim kaist ac kr K S Kim Mechatronics 24 2014 1223 1230 Contents lists available applications requiring high structural rigidity and dynamic capa bilities 9 12 In addition the manipulator structure optimization may be needed to minimize the weight of robot reduce the actua tor power requirements and decrease the space needed for the bility of the distributed actuation principle wa tiny robot finger actuated by ultrasonic motors 24 25 In this paper we propose a robot manipulato http dx doi org 10 1016 j mechatronics 2014 09 015 0957 4158 C211 2014 Elsevier Ltd All rights reserved motors a to the which ous approaches The use of high capacity motors is advantageous in increasing the performance of conventional manipulators with less structural changes 1 3 Hydraulic actuators are useful to generate large torques 4 7 A liquid cooling system of electric motors effectively enhances the peak torque in short time opera tion 8 Moreover the parallel manipulator is often used in the ation mechanism proposed in 24 to obtain a light but highly effi cient manipulator design The distributed actuation principle spatially optimizes the locations of forcing points along with links for maximizing the fingertip force 24 Because the location of actuating points can be changed the output force of the robot fin ger can be further enhanced at their optimal locations The feasi 1 Introduction Robotmanipulators generally employ enhance various performance characterist speed of movement However in practice speed reducers often lead to heavy so thus there exists an inevitable trade off for high performance and compact design To resolve these conflicting design capacity actuatorsto such as payload and the actuators and the manipulators and between the desires there have been vari tion mechanism is advantageous in terms of the simplicity of the structure and the ease of control However it suffers from the need for heavy mechanical components to bear the concentrated load at the joints In other words gears or harmonic drives should be used for speed reduction and torque enhancement which leads to heavy manipulators in practice Moreover gears with high speed reduc tion ratios inevitably decrease the efficiency of a manipulator Motivated by these difficulties we adopt the distributed actu High payloads Light weight arm Design and control of robot manipulator mechanism Sung Hwan Kim Young June Shin Kyung Soo Kim Department of Mechanical Engineering KAIST 291 Daehak ro Yuseong gu Daejeon 305 701 article info Article history Received 24 February 2014 Accepted 29 September 2014 Available online 19 October 2014 Keywords Distributed actuation mechanism Robot manipulator Robot arm abstract This paper presents a design performance robot manipulator such as high payload capacity ulator Based on the analysis proposed manipulator A prototype controlled as an example Mechatron journal homepage www elsevi a distributed actuation Kim Republic of Korea based on the distributed actuation principle to achieve a high Spatial movement of the actuation points provides several advantages high efficiency and a light weight structure for the proposed robot manip distributed actuation mechanism using a single slider is adopted for the of the manipulator with two degrees of freedom is developed and efficacy of the proposed approach is verified experimentally C211 2014 Elsevier Ltd All rights reserved at ScienceDirect ics and experimental results are presented Finally the conclusion fol lows in Section 4 2 Manipulator with distributed actuation 2 1 Review of distributed actuation mechanisms Generally robot manipulators are driven by joint actuation mechanisms For example a motor gear assembly is placed at the joint of two links in the case of industrial robots 29 31 In addition a hydraulic actuator is often fixed at the joint for excava tors 32 33 In contrast to the above the distributed actuation mechanism generates the torque at a joint by thrusting the sliders connected by a rigid rod along the links as shown in Fig 1 The slider is actu ated by a ball screw with a motor A typical feature of the distrib uted actuation with dual sliders is the freedom to move the several generic features of the distributed actuation mechanism needed to maximize the output torque However this issue can be mitigated by optimizing the structural parameters considering the performance specifications within the workspace 1224 S H Kim et al Mechatronics 24 2014 1223 1230 that has not been previously investigated in literature To reduce the number of actuators needed only one slider is allowed to move by fixing the other at a certain distance i e x 1 fixed from the joint as shown in Fig 2 Also the link has an angle offset i e h offset With this configuration the redundancy of the slider locations addressed in Section 2 1 cannot be sustained but the actuator location remains effectively variable In other words the torque generated at the joint varies depending on the location of the moving slider i e x 2 Furthermore by adjusting the dimen sions of x 1 fixed h 2 L rod and h offset the torque can be maintained to be actuating points so that the joint torque varies depending on their locations which is an additional degree of freedom DOF to max imize the joint torque In 24 the fingertip force of a robot finger with three joints is significantly increased by optimizing the slider locations On the other hand the increasing number of actuators is a dis advantage as the number of joints increases i e two actuators per a joint are needed for the distributed actuation For small scale applications such as the robot finger in 24 this may not be a major issue because actuators of small size are only utilized 2 2 Proposed actuation mechanism In this subsection we extend the distributed actuation mecha nism to the design of a light weight manipulator with a high pay load capacity e g exceeding 10 kg To this end we focus on Fig 1 The concept of a distributed actuation mechanism larger than the required torque for manipulating the payload over the workspace To demonstrate this using the kinematics of the mechanism let us consider the generated torque s F 2 x 1 fixed sin h h offset C0h 2 x 2 C0 x 1 fixed cos h h offset x 2 h 2 C18C19 1 where h cos C01 x 1 fixed 2 x 2 2 h 2 2 C0L 2 rod 2 x 2 1 fixed x 2 2 h 2 2 q 0 1 A tan C01 h2 x 2 C16C17 C0 h offset is the joint angle and F 2 is the thrust force of the slider in the moving link The generated torque changes through the position of the actu ation point x 2 and its profile depends on the design parameters such as L rod h 2 x 1 fixed and h offset which will be optimized in Section 3 In particular it is noted that h offset does play an important role to shift the torque profile to some extent within the workspace To illustrate it the generated torques are computed with and without the inclusion of h offset for the same other design parameters of L rod h 2 x 1 fixed as shown in Fig 3 The torque profile is shifted to the left hand side when h offset 8 C14 so that the generated torque is always larger than the required torque for manipulating the 13 kgf payload through the entire workspace of h It is noted that the required torque is calculated by considering the payload and the weight of two links of the prototype of a manipulator which will be developed in Section 3 The proposed mechanism with a single slider does not provide the redundancy of slider positions Fig 2 The joint model of the proposed robot manipulator Fig 3 The effect of angle offset h offset at joint 1 The proposed mechanism has several features different from the conventional joint actuation First the structural stiffness increases significantly because of the triangular closed loop structure featuring the connecting rod The bending moment due to the external load can be supported by the repulsive force of with the conventional speed reducers which are composed of a planetary gear and a harmonic drive having a transmission effi ciency lower than 70 the ball screw system has the efficiency of approximately95 and sothus itwouldrequireasmalleractuator while maintaining the desired output power of the manipulator This feature is also advantageous to build up a light manipulator system To demonstrate the effectiveness of the proposed manipulator we virtually design two different manipulators as shown in Fig 4 One is a conventional 1 DOF manipulator using the standard joint actuation mechanism JM and the other is the proposed 1 DOF manipulator with the distributed actuation mechanism DM For both cases the design targets are to achieve the payload capacity of 13 kgf at the 0 7 m outreach and an output power of about 110 W Also for DM it is assumed that L rod x 1 fixed h 2 and h offset are 230 mm 145 mm 38 mm and 8 C14 respectively which are also the parameters used for the hardware design in Section 3 The detailed descriptions are summarized in Table 1 The motor the speed reducer composedof a harmonicdrive and a planetarygear and a ball screw are all selected among commercially available components to have the similar outputs at the joint i e the joint torque and speed The designs may not be optimal but best in the trial and error approach First a larger motor is adopted for JM because the efficiency of the harmonic drive is low as about 70 On the other hand in the case of DM the efficiency of ball screw is about 95 so that a smaller and lighter motor can be utilized Moreover the ball screw is much lighter than that of the speed Fig 4 The virtual design of 1 DOF manipulator with the joint actuation a or the distributed actuation b S H Kim et al Mechatronics 24 2014 1223 1230 1225 the connecting rod which decreases the deflection and maximum bending moment In addition different from JM the deflection caused by ball screw is almost negligible because the stiffness of ball screw is significantly high Therefore despite the light weight of the robot the proposed mechanism has significant structural stiffness allowing heavy objects to be handled Second byadoptingaball screwsystemtoactuatethelinearsli der wecan achievethehighspeed reductionratio withremarkably high efficiency in the torque force conversion process Compared Table 1 Comparison result design results and major specifications Item 1 Item 2 Sub items Major parts a Motor Model Power Speed Weight Harmonic drive Model Weight Planetary gear Model Weight Ball screw Model Weight Frame b Weight Design result Output at joint c Torque Speed Joint stiffness Natural frequency d Max deflection Link Speed reducer Efficiency Operating range Total weight a Manufacturers i motor and planetary gear maxon motor AG ii ball screw and b For the maximal deflection of the link tip to be smaller than 500lrad at the maximum c The values of torque and velocity of DM are average values d The values are calculated with the 13 kgf payload reducer of JM As a result DM is significantly lighter than JM while keeping the similar output power to it It is noted that the working range of DM is smaller than that of JM which may be a drawback However this may not be a critical issue if the task of DM is limited inside the working range e g an explosive ordnance disposal EOD manipulator a palletizing manipulator and etc Besides DM has structural advantages thanks to higher stiffness than that of JM It is noted that in Table 1 the joint stiffness of DM is 119 kNm rad that is almost 2 times larger than that of JM Design with JM Design with DM EC 45 EC 60 flat 164 W 111 W 9290 rpm 3740 rpm 850 g 470 g CSG32 160 1 890 g GP42C 6 1 260 g MDK 1002 200 g 1526 g 1450 g 114 Nm 111 Nm 1 01 rad s 0 93 rad s 41 kNm rad 119 kNm rad 1 2 kHz 2 1 kHz 497lrad 415lrad 776 lrad 29 lrad 70 95 0 360 C14 30 120 C14 3526 g 2120 g harmonic drive THK payload of 13 kgf Fig 5 The design procedure of proposed manipulator Table 2 The detailed specification of the proposed 2 DOF manipulator Spec Joint 1 Joint 2 Motor torque 284 mNm 284 mNm Motor speed 3740 rpm 3740 rpm Length of x 1 fixed 145 mm 130 mm Length of L rod 230 mm 230 mm Link length L 360 mm 393 mm Offset from slider h 2 38 mm 38 mm Operating range 30 120 C14 30 120 C14 Lead of ball screw 2 mm 2 mm Max thrust force 839 N 839 N Output torque a 112 2 Nm 100 3 Nm Joint velocity a 0 93 rad s 1 04 rad s Angle offset b 8 C14 0 C14 Maximum payload c 13 0 kg Maximum reach 0 65 m Weight 4 2 kg Efficiency 95 a The values of torque and velocity are average values b At joint 2 the angle offset isn t considered to simplify the design c The payload is calculated with about 10 safety factor Fig 6 The 2 DOF distributed actuation robot manipulator 1226 S H Kim et al Mechatronics 24 2014 1223 1230 S H Kim et al Mechatronics Subjected to the load of a 13 kg mass the maximum deflections at the joint of JM and DM are 1273lrad and 444lrad respectively This clearly shows that DM has higher positional accuracy at the end tip under loads Also the high joint stiffness results in then high natural frequency which avoids the undesirable structural vibration which may be caused during the manipulation of pay loads Using that from 34 35 f n 1 2p M J K JM DM MJ q where M K JM DM and J are the inertia of link and load the joint stiffness of JM and DM and the rotor inertia reflected to the link side of gear reduction respectively the natural frequencies of DM and JM are 2 1 kHz and 1 2 kHz respectively It is known that the low natural frequency of the manipulator may cause the residual vibration and degrades the position control performance 35 37 3 Design and experiments 3 1 Design of the 2 DOF robot manipulator The overall design procedure is described in Fig 5 Step 1 Define the target tasks e g payload workspace and etc Step 2 Given the target tasks the link length and motor are specified with workspace payload and the speed of end tip Also the required torque is calculated Step 3 The stroke of the slider should be constrained to the region of x 2 min x 2 max depending on the workspace and the link Fig 7 Experimental setup of mass lifting task joint position control scheme top the bottom Table 3 Via points of the desired trajectory in Cartesian space t sec 0 0 3 0 13 0 23 0 26 0 y d mm 0 0 0 0 100 0 0 0 0 0 x d mm 602 8 602 8 602 8 602 8 602 8 control system of 2 DOF single slider distributed actuation robot manipulator 24 2014 1223 1230 1227 lengths Also the thrust force F 2 is calculated by the selected motor considering the payload Step 4 x 1 fixed and h 2 should be determined by considering the weight and the tolerable deflection of the parts A large x 1 fixed increases the generated torque However there is a trade off between increases in the weight and the bending deflection Simi larly a large h 2 also increases the generated torque but it exacer bates the structural bending and interferes the workspace Thus the samples of design parameters x 1 fixed i h 2 j are determined by considering limitations x 1 fixed min 6 x 1 fixed i 6 x 1 fixed max i 1 n 1 h 2 min 6 h 2 j 6 h 2 max j 1 n 2 2 Step 5 For every combination of x 1 fixed i and h 2 j the samples of connecting rod L rod ij k are calculated by using the working range of joint and the range of stroke of slider of the manipulator L rod min h min x 2 max 6 L rod ij k 6 L rod max h max x 2 min k 1 n 3 3 Step 6 The samples of angle offset h offset m m 1 n 4 are defined by considering the workspace Then the set of design parameters R is defined as follows R x 1 i h 2 j L rod ij k h offset m C8C9 4 and each of samples is equally spaced Step 7 For every set of parameters the generated torque s r is simulated and the difference between the generated torque and the required torque s req is also calculated If the generated torque is smaller than required torque the corresponding set of parame ters is neglected Step 8 The optimal set of design parameters r opt is determined by maximizing the minimum difference between the generated 1228 S H Kim et al Mechatronics torque and required torque In addition the design procedure is repeated until the robot with r opt satisfy the target tasks r opt arg max r2R min h2 h min hmax C138 s r h C0s req h C8C9 C20C21 subjected to s r h Ps req h 5 Through the proposed procedure a 2 DOF robot was designed and the parameters of it are summarized in Table 2 Also the pro totype was developed as shown in Fig 6 A 2 DOF robot was devel oped to verify the feasibility and performance of the manipulator in the Cartesian task space as shown in Fig 6 Aluminum alloy Fig 8 The experimental results a position response of joint 1 b position response of f control input of joint 2 24 2014 1223 1230 AL7075 is selected to ensure the rigid but light structure Flat type BLDC motors EC 60 maxon motor AG and ball screws with the 2 mm lead pitch MDK 1002 THK Co Ltd are adopted for lin ear actuation 3 2 Mass lifting experiment on the 2 DOF Arm In this experiment a DSP TMS320F28335 Texas Instruments Inc is used to control the position of each slider and a PD control with a 1 kHz sampling rate is applied The experimental setup is shown in Fig 7 The lifting task for a 13 kgf payload is conducted joint 2 c tracking error of h 1 d tracking error of h 2 e control input of joint 1 and at an extreme bound of the workspace To this end the trajectory was chosen to handle the payload at the maximum extension of the manipulator A 5 th order polynomial was used for shaping the trajectory in the x y plane The via points are shown in Table 3 Ini tially the manipulator stops with no load t 0 3 0 s Then a 13 0 kgf is applied to the manipulator as the end tip moves upward t 3 0 13 0 s Finally the end tip moves downward t 13 0 23 0 s and the manipulator returns to the initial point The dynamic model of the distributed actuation manipulator can be expressed as an elastic joint 34 M q K q C0 h 0 link equation J h K h C0 q s motor equation 6 where M is the inertia of links K is the equivalent joint stiffness of manipulator including the speed reducer ball screw J is the iner tia of the motor q is the angle of link and h is the angle of motor Also PD controller is implemented for the position control of the end tip as follows s 1 s 2 C18C19 K P h 1d C0 h 1 h 2d C0 h 2 C18C19 K D h 1d C0 h 1 h 2d C0 h 2 7 Then the closed loop transfer function of each joints is derived by T c h h d K D Ms 3 K P Ms 2 K D Ks K P K MJs 4 K D Ms 3 M J K K P M s 2 K D Ks K P K 8 where h d is the desired angle of motor If K P and K D are positive the characteristics equation is Hurwitz and the closed loop system is stable Routh Hurwitz criteria Furthermore the experimental gains K P diag 109 8 109 8C138 and K D diag 14 6 14 6C138 are deter mined by the Ziegler Nichols method The experimental results are shown in Fig 8 When lifting a 1