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南京理工大學(xué)泰州科技學(xué)院 畢業(yè)設(shè)計(jì) 論文 開題報告 學(xué) 生 姓 名 張廣濟(jì) 學(xué) 號 1201010160 專 業(yè) 機(jī)械工程及自動化 設(shè) 計(jì) 論 文 題 目 蘋果裝箱機(jī)械手設(shè)計(jì) 指 導(dǎo) 教 師 胡小秋 2016 年 1 月 11 日 畢 業(yè) 設(shè) 計(jì) 論 文 開 題 報 告 1 結(jié)合畢業(yè)設(shè)計(jì) 論文 課題情況 根據(jù)所查閱的文獻(xiàn)資料 每人撰寫 2000 字左右的文獻(xiàn)綜述 文 獻(xiàn) 綜 述 摘要 裝箱機(jī)械手控制系統(tǒng)的研究是近代自動控制領(lǐng)域中出現(xiàn)的一項(xiàng)新技術(shù) 并巳成為 現(xiàn)代機(jī)械制造生產(chǎn)系統(tǒng)中的一個重要組成部分 本文從工作原理和工作結(jié)構(gòu)方面介紹了 裝箱機(jī)械手 對控制系統(tǒng)做了簡要說明 并從歷史發(fā)展角度談了裝箱機(jī)械手對現(xiàn)代工業(yè) 應(yīng)用的積極意義與優(yōu)勢 關(guān)鍵詞 裝箱機(jī)械手 工作原理 基本結(jié)構(gòu) 1 機(jī)械手的作用和意義 在機(jī)械工業(yè)中 應(yīng)用機(jī)械手的意義可以概括如下 一 以提高生產(chǎn)過程中的自動化程度 應(yīng)用機(jī)械手有利于實(shí)現(xiàn)材料的傳送 工件的 裝卸 刀具的更換以及機(jī)器的裝配等的自動化的程度 從而可以提高勞動生產(chǎn)率和降低 生產(chǎn)成本 1 二 以改善勞動條件 避免人身事故 在高溫 高壓 低溫 低壓 有 灰塵 噪聲 臭味 有放射性或有其他毒性污染以及工作空間狹窄的場合中 用人手直 接操作是有危險或根本不可能的 而應(yīng)用機(jī)械手即可部分或全部代替人安全的完成作業(yè) 使勞動條件得以改善 三 可以減輕人力 并便于有節(jié)奏的生產(chǎn) 應(yīng)用機(jī)械手代替人進(jìn) 行工作 這是直接減少人力的一個側(cè)面 同時由于應(yīng)用機(jī)械手可以連續(xù)的工作 這是減 少人力的另一個側(cè)面 綜上所述 有效的應(yīng)用機(jī)械手 是發(fā)展機(jī)械工業(yè)的必然趨勢 2 裝箱機(jī)械手及其發(fā)展 2 1 裝箱機(jī)械手的工作原理 灌裝生產(chǎn)線上的機(jī)械手運(yùn)行在一個半環(huán)型的軌道上 如圖 1 所示 機(jī)械手有四種運(yùn) 行模式 尋參考點(diǎn) 示教 手動 自動 2 自動運(yùn)行模式中 機(jī)械手根據(jù)瓶子是否 OK 箱子是否 OK 信號自動往復(fù)運(yùn)行于抓瓶子 放瓶子位置 抓瓶子過程中 如果瓶子 OK 機(jī) 械手就直接走向抓瓶位置 否則機(jī)械手將先走向平衡位置然后等待 直到瓶子 OK 放瓶 子過程和抓瓶過程相似 但是由于此時機(jī)械手負(fù)重 運(yùn)行分成三段速度 分別是 speed1 區(qū) 低速 脫離該區(qū)起動瓶子傳送帶 Speed2 高速 Speed3 再低速 進(jìn)人該區(qū)停止箱子傳 送帶 3 5 圖1 裝箱機(jī)械手工作原理示意圖 2 2 裝箱機(jī)械手的基本結(jié)構(gòu) 手部 機(jī)械手的手部是最重要的執(zhí)行機(jī)構(gòu) 是用來握持的部件 如圖 2 所示 6 圖 2 機(jī)械手手部機(jī)構(gòu)圖 腕部 是連接手部和臀部的部件 并可用來調(diào)節(jié)被抓物體的方位 以擴(kuò)大機(jī)械手的 動作范圍 并使機(jī)械手變得更靈巧 適應(yīng)性更強(qiáng) 手腕有獨(dú)立的自由度 7 臀部 手臂部件是機(jī)械手的重要握持部件 它的作用是支撐腕部和手部 并帶動他 們做空間運(yùn)動 8 行走機(jī)構(gòu) 有的工業(yè)機(jī)械手帶有行走機(jī)構(gòu) 本課題的機(jī)械手不具有行走機(jī)構(gòu) 9 驅(qū)動機(jī)構(gòu) 驅(qū)動機(jī)構(gòu)是工業(yè)機(jī)械手的重要組成部分 10 按照動力源分為液壓 氣 壓 電動驅(qū)動三大類 根據(jù)需要 也可以將這三種基本類型合成復(fù)合式的驅(qū)動系統(tǒng) 11 2 3 機(jī)械手控制系統(tǒng) 裝箱機(jī)械手的重要指標(biāo)有快速性 定位精度和平穩(wěn)性等 12 以煤餅生產(chǎn)線的裝箱 工序?yàn)槔?機(jī)械手完成一次動作循環(huán)的時間僅 3 秒鐘左右 裝箱的定位精度需要控制在 2 m m 之內(nèi) 單片微型計(jì)算機(jī)在功能上與單板微型計(jì)算機(jī)相當(dāng) 且具有價格低廉 體 積小結(jié)構(gòu)簡單 可靠性高等優(yōu)點(diǎn) 13 機(jī)械手的信號定位是通過側(cè)位開關(guān)發(fā)出位置到達(dá)信 號 待 PLC 收到該信號之后立即停發(fā)輸往步進(jìn)驅(qū)動器的脈沖 從而使步進(jìn)電機(jī)預(yù)定位 置 14 控制系統(tǒng)的硬件主要由伺服電機(jī) 伺服放大器 人機(jī)界面 現(xiàn)場執(zhí)行設(shè)備等組 成 15 系統(tǒng)的通訊設(shè)計(jì)中 請求報文和響應(yīng)報文通過不斷循環(huán)地與伺服放大 器交換過 程數(shù)據(jù)來對伺服放大器進(jìn)行控制 系統(tǒng)的軟件設(shè)計(jì)主要包括兩部分 PLC 軟件和 SEW 伺 服軟件 16 2 4 國內(nèi)外研究進(jìn)展與發(fā)展趨勢 機(jī)械手是一種模擬人手操作的自動機(jī)械 它可按固定程序抓取 搬運(yùn)物件或操持工 具完成某些特定操作 17 應(yīng)用機(jī)械手可以代替人從事單調(diào) 重復(fù)或繁重的體力勞動 實(shí)現(xiàn)生產(chǎn)的機(jī)械化和自動化 代替人在有害環(huán)境下的手工操作 改善勞動條件 保證人 身安全 因而廣泛應(yīng)用于機(jī)械制造 冶金 電子 輕工和原子能等部門 20 世紀(jì) 40 年 代后期 美國在原子能實(shí)驗(yàn)中 首先采用機(jī)械手搬運(yùn)放射性材料 人在安全間操縱機(jī)械 手進(jìn)行各種操作和實(shí)驗(yàn) 18 50 年代以后 機(jī)械手逐步推廣到工業(yè)生產(chǎn)部門 用于在高 溫 污染嚴(yán)重的地方取放工件和裝卸材料 也作為機(jī)床的輔助裝置在自動機(jī)床 自動生 產(chǎn)線和加工中心中應(yīng)用 完成上下料或從刀庫中取放刀具并按固定程序更換刀具等操作 我國工業(yè)機(jī)械手的研究與開發(fā)起步較晚 比歐美要晚 30 年左右 起步于上世紀(jì) 70 年 代 1972 年我國第一臺機(jī)械手 在上海開發(fā)成功 隨之全國各省都開始研制和應(yīng)用機(jī)械 手 從第七個五年計(jì)劃 1986 1990 年 開始 我國政府大大加 大了對工業(yè)機(jī)器人的 重視程度 并且為此項(xiàng)目投入大量的資 金 在眾多學(xué)者及研究人員的參與下 研究開 發(fā)并且制造了一系列的工業(yè)機(jī)器人 與此同時 一系列的機(jī)器人關(guān)鍵部件也被開發(fā)出來 如機(jī)器人專用軸承 減震齒輪 直流伺服電機(jī) 編碼器等等 19 國外機(jī)械手的發(fā)展趨勢是大力研制具有某種智能的機(jī)械手 使它具有一定的傳感能 力 能反饋外界條件的變化 作相應(yīng)的變更 重點(diǎn)是研究視覺功能和觸覺功能 隨著傳 感技術(shù)的發(fā)展機(jī)械手裝配作業(yè)的能力也將進(jìn)一步提高 更重要的是將機(jī)械手 柔性制造 系統(tǒng)和柔性制造單元相結(jié)合 從而根本改變目前機(jī)械制造系統(tǒng)的人工操作狀態(tài) 20 3 結(jié)論 經(jīng)實(shí)踐證明 裝箱機(jī)械手把工人從簡單重復(fù)勞動中解脫出來 大大提高了裝箱的效 率 并且安全可靠 對于改進(jìn)生產(chǎn)線 提高生產(chǎn)率有很大幫助 同時有效解決了該工位 工人的高強(qiáng) 度重復(fù)性勞動 降低了企業(yè)的用工成本 具有較好的推廣應(yīng)用價值 參 考 文 獻(xiàn) 1 張憲民 工業(yè)機(jī)器人應(yīng)用基礎(chǔ) M 北京 機(jī)械工業(yè)出版社 2015 2 滕洪春 工業(yè)機(jī)器人與機(jī)械手 M 北京 電子工業(yè)出版社 2015 3 龔振邦 機(jī)器人機(jī)械設(shè)計(jì) M 北京 電子工業(yè)出版社 1995 4 吳瑞祥 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本課題研究的問題 課題為軍工企業(yè)設(shè)計(jì)搬運(yùn)及裝箱機(jī)械手 替代人工 實(shí)現(xiàn)圓柱形火工品裝箱的機(jī) 械化 充分利用箱內(nèi)空間 需要選擇一種最佳的擺放方式 并且設(shè)計(jì)出機(jī)械手夾持結(jié) 構(gòu) 并且要穩(wěn)定不得有震動 以便可以將其放入包裝箱內(nèi) 2 本課題的研究方法擬采用的研究手段 1 運(yùn)用 CAD PROE 等 建立相關(guān)模型 2 通過比較堆疊擺放和上下對齊的兩種蘋果擺放方式選擇出一種合適的裝箱方 法 3 了解被夾持對象數(shù)據(jù)并設(shè)計(jì)出能最大夾持的結(jié)構(gòu) 4 根據(jù)要求制定機(jī)械手運(yùn)行軌跡 確定工作行程 5 確定已制定方案的可行性 設(shè)計(jì) 計(jì)算 校核等等 畢 業(yè) 設(shè) 計(jì) 論 文 開 題 報 告 指導(dǎo)教師意見 1 對 文獻(xiàn)綜述 的評語 2 對本課題的深度 廣度及工作量的意見和對設(shè)計(jì) 論文 結(jié)果的預(yù)測 指導(dǎo)教師 年 月 日 所在專業(yè)審查意見 負(fù)責(zé)人 年 月 日 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