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本科生畢業(yè)設(shè)計(jì) (論文) 外 文 翻 譯 原 文 標(biāo) 題 A Novel Linear Folding Mechanism: Configuration and Position Precision Analysis 譯 文 標(biāo) 題 一種新型線性折疊機(jī)構(gòu)：配置和定位機(jī)構(gòu)分析 作者所在系別 機(jī)電工程學(xué)院 作者所在專(zhuān)業(yè) 機(jī)械設(shè)計(jì)制造及其自動(dòng)化 作者所在班級(jí) B13113 作 者 姓 名 張琳怡 作 者 學(xué) 號(hào) 20134011302 指導(dǎo)教師姓名 劉衛(wèi) 指導(dǎo)教師職稱(chēng) 副教授 完 成 時(shí) 間 2017 年 3 月 13 北華航天工業(yè)學(xué)院教務(wù)處制 譯文標(biāo)題 一種新型線性折疊機(jī)構(gòu)：配置和定位機(jī)構(gòu)分析 原文標(biāo)題 A Novel Linear Folding Mechanism: Con?guration and Position Precision Analysis 作 者 LeiyuZhang YangYang 譯 名 張磊宇 楊陽(yáng) 國(guó) 籍 中國(guó) 原文出處 Advances in Reconfigurable Mechanisms and RobotsⅡ 一種新型線性折疊機(jī)構(gòu)：配置和定位機(jī)構(gòu)分析 摘要：線性折疊機(jī)構(gòu)用于將末端執(zhí)行器移動(dòng)到所需位置，可以提高安全性，減少多關(guān)節(jié)機(jī)器人占用的空間。設(shè)計(jì)了一種矩形塊作為折疊機(jī)構(gòu)的通用元件。以剛性方式連接一系列塊以形成折疊臂。四個(gè)相鄰塊之間的連接方法?；谶B接方法,幾個(gè)配置的遠(yuǎn)距觀測(cè)儀的機(jī)制提出了。此外,折疊臂的定位精度進(jìn)行了分析,由折疊距離和其他因素的影響。分析結(jié)果表明,提出的折疊臂配置具有高定位精度和長(zhǎng)折疊距離。這種類(lèi)型的線性折疊機(jī)制可以應(yīng)用到服務(wù)機(jī)器人與人類(lèi)合作。 關(guān)鍵詞 折疊機(jī)制 矩形塊 同步帶 精密分析配置 1 介紹 折疊機(jī)制通常連接基礎(chǔ)部分和末端執(zhí)行器,以確保遠(yuǎn)程終端執(zhí)行器的運(yùn)動(dòng)。有幾種類(lèi)型的機(jī)制用于移動(dòng)遠(yuǎn)程處理設(shè)備。剪刀高空作業(yè)平臺(tái)是典型的類(lèi)型的望遠(yuǎn)鏡設(shè)備,廣泛用于高海拔的運(yùn)轉(zhuǎn)和維護(hù)。Enders等人開(kāi)發(fā)的折疊機(jī)制延伸通過(guò)引進(jìn)流體和縮進(jìn)排氣液體. Lee等人公開(kāi)了一種用于橋梁運(yùn)輸系統(tǒng)的折疊管組，其包括多個(gè)圓筒形管和延伸/收縮線。Lee等人。 設(shè)計(jì)了一種由鋼絲和鋼絲組成的鋼絲驅(qū)動(dòng)雙向折疊機(jī)構(gòu)。然而,在這些類(lèi)型的折疊機(jī)制之上,基礎(chǔ)部分的體積相當(dāng)大為了達(dá)到足夠的剛度。此外，終端執(zhí)行器需要一個(gè)相當(dāng)大的擴(kuò)展長(zhǎng)度的差異,以確保一個(gè)適當(dāng)?shù)囊苿?dòng)空間。此外，終端執(zhí)行器需要一個(gè)相當(dāng)大的擴(kuò)展長(zhǎng)度的差異,以確保一個(gè)適當(dāng)?shù)囊苿?dòng)空間。因此，折疊機(jī)制上面提到的體積收縮狀態(tài)將會(huì)十分笨重。 孔等人已經(jīng)開(kāi)發(fā)了一個(gè)可折疊的樣品罐捕獲機(jī)制（TSCCM）為翻滾的樣品容器在軌道上檢索。另一個(gè)直線折疊機(jī)構(gòu)由川淵等人發(fā)明的。包括多個(gè)塊。折疊臂以剛性連接的方式實(shí)現(xiàn)。黎平和葉濃描述一個(gè)往復(fù)推送鏈可擴(kuò)展在它自身的重力下以直線水平方向。推動(dòng)鏈通常用于將對(duì)象從一個(gè)位置到另一個(gè)地方。一些作者提出使用折疊機(jī)制以緊湊的體積為機(jī)械臂的發(fā)展方向。然而,上述研究缺乏足夠的配置和相對(duì)精度分析. 線性折疊機(jī)制提出了一種新型折疊機(jī)制。這種類(lèi)型的折疊機(jī)制可以提高安全通過(guò)消除這種風(fēng)險(xiǎn),不可避免的對(duì)于一個(gè)典型的機(jī)器人手臂肘關(guān)節(jié),物體在機(jī)器人手臂肘關(guān)節(jié)時(shí)手臂部分之間被關(guān)閉。此外,折疊臂組成的塊可以存儲(chǔ)在一個(gè)緊湊的情況下。因此,這種機(jī)制可以減少空間來(lái)容納傳統(tǒng)的關(guān)節(jié)。本文幾個(gè)配置這種機(jī)制的支持。相對(duì)位置精度分析的數(shù)值模擬是通過(guò)折疊臂的數(shù)學(xué)模型。 2 折疊機(jī)構(gòu)的結(jié)構(gòu) 有各種各樣新型折疊機(jī)構(gòu)的配置。一般來(lái)說(shuō)，這種折疊機(jī)構(gòu)包括多個(gè)塊、存儲(chǔ)箱、驅(qū)動(dòng)單元和終端執(zhí)行器。自由連接的塊被存儲(chǔ)在存儲(chǔ)盒中。驅(qū)動(dòng)單元驅(qū)動(dòng)的塊可以在任意方向上伸出，并以剛性方式對(duì)齊以形成剛性對(duì)準(zhǔn)。因此,折疊臂可以由剛性的塊對(duì)齊，如圖1所示。端部執(zhí)行器安裝在折疊臂前端。這種折疊機(jī)構(gòu)與傳統(tǒng)的多關(guān)節(jié)機(jī)器人相比，收縮狀態(tài)占用更少的空間。 (a) (b) 圖1折疊機(jī)構(gòu)的兩種狀態(tài) a收縮狀態(tài)b擴(kuò)張狀態(tài) 2.1 折疊機(jī)構(gòu)的配置 為了保持?jǐn)U展塊以剛性的方式,本節(jié)提出了幾種連接方法。第一次連接方法具有最高的鉸鏈連接的可靠性，為 在圖2a所示。在自由連接方式的塊可以在相對(duì)于下一塊鉸鏈銷(xiāo)轉(zhuǎn)動(dòng)。鋼絲繩是另一種連接方法，如圖2b所示，對(duì)鋼絲繩的兩端分別固定在頭塊和最后一個(gè)，所有的塊都使連接在一起。 第三種連接方式是兩個(gè)相鄰的塊由同步帶連接，如圖2所示。同步帶，齒形帶，與上表面網(wǎng)格波紋每一塊結(jié)構(gòu)使塊固定以一個(gè)剛性的方式。如圖3a所示，有一個(gè)鎖緊機(jī)構(gòu)和凹進(jìn)部分的上表面。當(dāng)鎖機(jī)構(gòu)與相鄰塊的相應(yīng)凹入部分接合時(shí)，相鄰塊連接。因此,可以連續(xù)擴(kuò)展塊固定的最后方法。 (a) (b) 圖2兩個(gè)折疊機(jī)制的配置 (a) (b) 圖3 另兩個(gè)配置折疊機(jī)制 基于結(jié)構(gòu)和連接方法,提出了若干折疊機(jī)制的配置。為了確保擴(kuò)展塊相互固定,所有的上表面和正下方相鄰塊的連接形成一個(gè)可折疊的手臂。因此,這個(gè)線性折疊手臂可以沿任意方向擴(kuò)展。有一個(gè)終端執(zhí)行器安裝在前端的手臂。折疊臂也能承受在任何方向上施加在末端執(zhí)行器上的力。因?yàn)橛兴膫€(gè)連接方法,創(chuàng)建16個(gè)組合。這意味著有十六個(gè)折疊臂理論上的配置。根據(jù)加載條件和連接的可靠性,四種典型的配置如圖2和3所示。折疊臂的安排并不局限于上述配置的描述。新組合可一滿足一些特定的目的,如最小空間需求和方便的存儲(chǔ)。此外，此外,自由結(jié)合方式可能存儲(chǔ)在一個(gè)螺旋面情況下或其他情況下合適的形狀。 在傳動(dòng)方式的選擇上，可采用鏈輪傳動(dòng)和蝸桿傳動(dòng)，將擋塊推離。鏈輪傳動(dòng)可實(shí)現(xiàn)快速延伸和回縮。每一塊在底槽。然后鏈輪與凹槽接合，如圖3所示。由于多邊形效應(yīng)和嚙合沖擊，末端執(zhí)行器可能產(chǎn)生劇烈振動(dòng)。鏈輪驅(qū)動(dòng)的折疊機(jī)構(gòu)適用于高速、低精度場(chǎng)合。 與蝸桿傳動(dòng)折疊臂可以穩(wěn)步擴(kuò)展，如圖4所示。此外，延伸和回縮的速度是連續(xù)的和光滑的。帶蝸桿傳動(dòng)的折疊機(jī)構(gòu)可代替穆蒂關(guān)節(jié)臂在維修機(jī)器人中使用。因此，這種折疊臂應(yīng)該具有很高的定位精度。在2.2章，對(duì)折疊機(jī)構(gòu)的位置精度進(jìn)行了詳細(xì)的建模和分析。 O M f ,i Oi?1 O G i G 圖4 直線折疊機(jī)構(gòu) 2.2 直線折疊機(jī)構(gòu)的設(shè)計(jì) 本節(jié)重點(diǎn)研究了帶蝸輪傳動(dòng)的折疊機(jī)構(gòu)。同步帶的結(jié)合和鉸鏈采用折疊臂的配置,如圖4所示。它的齒形帶前端與第一塊粘合。它的齒嚙合的上表面波紋結(jié)構(gòu)確保相鄰兩塊面之間的緊密聯(lián)系。與鋼絲繩相比,同步帶通常擁有足夠的強(qiáng)度和剛度。在該機(jī)制中,一個(gè)中國(guó)標(biāo)準(zhǔn)的帶,指標(biāo)選擇10噸。壓力輥用于壓縮帶緊。然后折疊臂由剛性塊的方式支持兩個(gè)支撐輪。折疊距離,延長(zhǎng)長(zhǎng)度,是擴(kuò)展塊的長(zhǎng)度的總和。折疊臂縮回時(shí)，同步帶通過(guò)刮刀與波紋結(jié)構(gòu)分離。塊是分開(kāi)的 從剛性排列到離散排列。然而，離散塊仍以鉸鏈連接，可在任何方向彎曲。因此,離散的可安置在一個(gè)合適的形狀。 這種線性折疊機(jī)制（圖4）是由蝸輪傳動(dòng)驅(qū)動(dòng)的。手臂的移動(dòng)方向相同的方向轉(zhuǎn)動(dòng)蝸桿的軸。此外，這種機(jī)制包括基架可以旋轉(zhuǎn)中心O改變仰角α的折疊臂相對(duì)于水平方向。 3 折疊臂位置精度分析 終端執(zhí)行器的位置精度對(duì)實(shí)現(xiàn)抓取任務(wù)非常重要。在塊的重力與物體，同步帶張緊。然后，將彎曲折疊臂。然后終端執(zhí)行器將偏離目標(biāo)的位置。為了確定偏差,定位精度的數(shù)學(xué)模型。為簡(jiǎn)化復(fù)雜性,符合降低假設(shè)在力學(xué)模型的推導(dǎo)過(guò)程。 (1)鉸鏈中的間隙被忽略。 (2)每個(gè)塊的變形被忽略。 4 模擬結(jié)果和討論 對(duì)上述數(shù)學(xué)模型的計(jì)算方法與MATLAB編程。對(duì)于這種線性折疊機(jī)構(gòu)，最大折疊距離為1500 mm，折疊臂由O形折疊臂組成30塊。計(jì)算程序中使用的主要參數(shù)見(jiàn)表1。 通過(guò)數(shù)值模擬，得到了折疊臂末端α= 30°的偏差，如圖5所示。橫向偏差dh上漲增加的擴(kuò)展長(zhǎng)度。與此同時(shí),整個(gè)偏差在一定長(zhǎng)度的增加上升。dh和dv的分布是相似的。折疊臂無(wú)負(fù)荷的最大偏差是0.104毫米和0.06毫米在水平和垂直方向i= 30,分別。 那么這兩個(gè)偏差達(dá)到最大值 i = 30,mt= 2.5公斤。 表1直線折疊機(jī)構(gòu)主要參數(shù) 圖5 在α= 30°的偏差 水平偏差dh 垂直偏差dv 圖6顯示了仰角α對(duì)偏差的影響某些質(zhì)量（mt = 2.5 kg）。但是，仰角α由于折疊臂的限制和基礎(chǔ)框架只能改變?70°到70°。在一定長(zhǎng)度的偏差度達(dá)到最大時(shí)，仰角α等于零，如圖6a所示的。 兩側(cè)，整個(gè)偏差dh為折疊臂繞中心旋轉(zhuǎn)向上或向下逐漸降低從水平位置的。dh幾乎為零的偏差時(shí) 角α等于 70° 或 ?70°。然而，垂直偏差dv幾乎是零角度時(shí)α等于 70° ，0，?70°如圖6B所示。dv 出現(xiàn)偏差的最大值 在上部和下部的旋轉(zhuǎn)范圍內(nèi)?？梢园l(fā)現(xiàn)偏差dh和dv 有相對(duì)的角α雙邊對(duì)稱(chēng)。這是因?yàn)閮蓚€(gè)偏差是 主要受Mi 這是對(duì)稱(chēng)的角度α。 由于調(diào)頻的限制力F，我總是要滿足式（4）。然后最大值FN，最大的力FN，我可以計(jì)算其中Fn，max = 432.38，根據(jù)T的影響 他α和mt參數(shù)以上，力FN，我通過(guò)在α= 0和MT = 2.5公斤的數(shù)值模擬獲得的，如圖7所示?？梢钥闯?，折疊機(jī)構(gòu)的安全負(fù)荷 從2.5公斤的有效折疊長(zhǎng)度為1500 mm。 圖6 在mt = 2.5 kg.的偏差 水平偏差dh 垂直偏差dv 圖7 力FN,i 5 結(jié)論 （1）該塊采用的折疊機(jī)構(gòu)的主要組成部分。四相鄰兩塊之間的連接方法。根據(jù)各連接方式的優(yōu)點(diǎn)提出了機(jī)構(gòu)，提供了四個(gè)切實(shí)可行的折疊配置。 （2）建立了位置精度的數(shù)學(xué)模型，得到了擴(kuò)展長(zhǎng)度、質(zhì)量mt和仰角α。 （3）一個(gè)精確的模型進(jìn)行數(shù)值模擬，利用MATLAB。隨著延伸長(zhǎng)度或質(zhì)量太增加DH和DV興起的偏差。 因此，這種體積小巧的折疊機(jī)構(gòu)具有優(yōu)良的定位精度和較長(zhǎng)的折疊長(zhǎng)度。 A Novel Linear Folding Mechanism: Con?guration and Position Precision Analysis Abstract: The linear folding mechanism, which is used to move the end effector to a desired position, can enhance the safety and reduce the space to be occupied by the multi-joint robot. A rectangle shaped block is designed as the general element of the folding mechanism. A series of blocks are connected in a rigid manner to form a folding arm. Four connection methods between the adjacent blocks are presented. Based on the connection methods, several con?gurations of the tele- scopic mechanism are proposed. Besides, the position precision of the folding arm is analyzed which is influenced by the folding distance and other factors. The analysis results show that the folding arm with the proposed con?guration possesses high position precision and a long folding distance. This type of linear folding mechanism can be applied to service robots which cooperate with humans. Keywords folding mechanism Rectangle shaped block Con?guration Precision analysis Synchronous belt 1 Introduction The folding mechanism usually connects the base portion and the end effector to ensure the long-distance movement of the end effector. There are several types of this mechanisms used to move a remote handling equipment. The scissors aerial work platform is a typical type of folding equipment that is widely used for high altitude operation and maintenance . A folding mechanism developed by Enders et al. extends by rapidly introducing a fluid and retracts by venting the fluid . Lee et al. disclosed a folding tube set for a bridge transport system, which includes several cylindrical tubes and extension/retraction lines. Lee et al. designed a wire-driven bidirectional folding mechanism consisting of stages and steel wires. However, in these types of folding mechanisms above, the volume of the base portion is quite large in order to achieve suf?cient stiffness. In addition, the end effector needs a considerable difference in extension lengths so as to ensure an adequate moving space. As a result, the volume of folding mechanisms men- tioned above in the contraction state will be quite bulky. Kong et al. have developed a telescoping sample canister capture mechanism (TSCCM) for retrieval of tumbling sample containers on orbit. Another linear-motion folding mechanism invented by Kawabuchi et al. includes a plurality of blocks. A folding arm is achieved in a manner that blocks are rigidly connected with each other. Liping and Yenong escribe a reciprocating pushing chain which can be extended horizontally in a straight line under its own gravity. The pushing chain is usually used to push objects from one position to another. Several authors have proposed the use of folding mechanisms with the compact volume as the development direction of the robot arm. However, the researches above lack of enough con?gurations and the relative precision analysis. The linear folding mechanism presented in this paper is a novel folding mechanism. This type of folding mechanism can enhance safety by eliminating such a risk, inevitable for a typical robot arm having an elbow joint, that an object around the robot arm gets caught between arm sections when the elbow joint is closed. Besides, the folding arm consisting of blocks can be stored in a compact case. Hence this mechanism can reduce the space to be occupied by the traditional multi-joint robot. In this paper several con?gurations of this mechanism are pro- posed. The relative position precision analysis is achieved through the numerical simulation of the mathematical model of the folding arm. 2 Structure of the Folding Mechanism There are a variety of con?gurations of this novel folding mechanism. Generally, this folding mechanism includes a plurality of blocks, a storage case, drive units and an end effector. The freely-jointed blocks are stored in the storage case. The blocks driven by drive units are possible to be extended out in an arbitrary direction and aligned in a rigid manner to form a rigid alignment. Hence, a folding arm can be composed of the blocks in the rigid alignment, as shown in Fig. 1. The end effector is installed at the front end of the folding arm. This type of folding mechanism in a retraction state occupies less space compared with the traditional multi-joint robot. (a) (b) Fig. 1 Two states of the folding mechanism. a Retraction state, b Extension state 2.1 Con?gurations of the Folding Mechanism In order to keep the extended block in a rigid manner, several connection methods are proposed in this section. The ?rst connection method is the hinge which has the highest connection reliability, as shown in Fig. 2a. The block in the freely jointed manner can rotate around a hinge pin relative to the next block. The wirerope is another connection method, as shown in Fig. 2b. Both ends of the wirerope are ?xed on the head block and the end one, respectively. All the blocks are stringed together. The third connection method is that two adjacent blocks are connected by the synchronous belt, as shown in Fig. 2. The synchronous belt, toothed belt, meshes with the upper-surface corrugated structures of each block to make the blocks ?xed to each other in a rigid manner. As shown in Fig. 3a, there is a latch mechanism and a recessed portion in the upper-surface. When the latch mechanism engages with the corresponding recessed portion of the adjacent block, the adjacent block is connected. Hence, the extended blocks can be serially ?xed by the last method. (a) (b) Fig. 2 Two con?guration of the folding mechanism (a) (b) Fig. 3 The other two con?guration of the folding mechanism Based on the structures and the connection methods, several con?gurations of the folding mechanism are presented. In order to ensure the extended blocks ?xed to each other ?rmly, all the upper-surface and the underface are connected to these of the adjacent block forming a folding arm. Hence, this linear folding arm can be extended along an arbitrary direction. There is a end effector installed at the front end of the arm. The folding arm also can bear the forces imposed on the end-effector in any direction. Since there are four connection methods, sixteen combinations are created. That means that there are sixteen con?gurations of the folding arm theoretically. According to loading conditions and the reliability of connections, four typical con?gurations are illustrated in Figs. 2 and 3. The arrangement of the folding arm is not limited to the description of con?gurations above yet. A new combination can be proposed for some certain purposes, such as minimum space requirements and the convenience of storage. Furthermore, the blocks in free-jointed manner may be stores in a helicoids case or other cases with suitable shape. On the selection of the drive modes, both the sprocket drive and the worm drive can be adopted to push the blocks out of the storage case. The sprocket drive can accomplish the rapid extension and retraction. Each block has a groove in the undersurface. Then the sprocket engages with the groove, as shown in Fig. 3. A drastic vibration of end effector may generate owing to the polygon effect and meshing impact. The folding mechanism driven by the sprocket is suitable for high speed and low precision occasions. The folding arm with the worm drive can be extended steadily, as shown in Fig. 4. Besides, the velocity of the extension and retraction is continuous and smooth. The folding mechanism with the worm drive can be used in the service robots instead of muti-jointed arms. Hence, this type of folding arm should have high position precision. In the Sect. 2.2, the position precision of the folding mechanism is modelled and analyzed in detail. O M f ,i Oi?1 O G i G Fig. 4 The linear folding mechanism 2.2Design of the Linear Folding Mechanism The research focused on the folding mechanism with the worm gear drive is presented in this section. The combination of the synchronous belt and the hinge is adopted as the con?guration of the folding arm, as shown in Fig. 4. The front end of the toothed belt and the ?rst block are bonded. The teeth mesh with the upper-surface corrugated structures to ensure the close contact between the upsides of two adjacent blocks. Compared with wireropes, the synchronous belt generally owns suf?cient strength and rigidity. In this mechanism, a Chinese standard belt, Metric T Pd: T10, is chosen. The pinch rollers are used to compress the belt tightly on the block. Then the folding arm composed of the blocks in rigid manner is supported by two return roller. The folding distance, extended length, is the sum of the lengths of the extended blocks. When the folding arm is retracted, the synchronous belt is separated from the corrugated structures by a scraper. The blocks are separated from the rigid arrangement to the discrete arrangement. However, the discrete blocks are still connected by hinges and can be flexed in any direction. Therefore, the discrete ones can be housed inside a case with suitable shape. This linear folding mechanism (Fig. 4) is driven by the worm gear drive. The moving direction of the arm is the same as the direction of a rotational axis of the worm. Besides, this mechanism including the base frame can rotate around the center O to change the elevation angle α of the folding arm relative to the horizontal direction. 3 Position Precision Analysis of the Folding Arm The position precision of the end effector is very important to achieve the task of grasping. Under the gravity of the blocks and the objects, the synchronous belt is tensioned. Then, the folding arm will be bent. The end effector will deviate from the target location. In order to determine the deviations, the mathematical model of the position precision should be established. For simplifying complexity, the fol- lowing assumptions are made in the derivation of the mechanical model . . (1)The clearances in the hinges are neglected. (2)The deformation of each block is neglected. 4 Simulations and Discussions The calculation algorithm for the mathematical model above is programmed with MATLAB. For this linear folding mechanism, the maximum folding distance is 1500 mm and the folding arm consists of 30 blocks. The main parameters used in the calculation program are listed in Table 1. Through the numerical simulation, the deviations of the end of the folding arm at α = 30° are obtained, as shown in Fig.5. The horizontal deviation dh rises with the increasing of the extended length. Meanwhile, the whole deviations at the certain length rise along with the increasing of mt. The distribution of dh and dv are similar. The maximal deviations of the folding arm with no loads are 0.104 mm. Main parameters Value Main parameters Value Ks/(N/mm) 1 × 106 μ 0.3 h/mm 40 G/N 1.08 l/mm 50 mt/kg 2 N 30 Fm/N 26 rp/mm 5 β/(°) 40 Table 1 Main parameters of the linear folding mechanism Fig. 5 The deviations at α = 30°. a The horizontal deviation dh, b The vertical deviation dv and 0.06 mm in the horizontal and vertical directions at i = 30, respectively. Then the two deviations reach a maximum at i = 30 and mt = 2.5 kg. Figure 6 shows the influences of the elevation angle α on the deviations at the certain mass (mt = 2.5 kg). However, the elevation angle α can only change form ?70° to 70° due to the restrictions of the folding arm and the base frame. The deviations dh at a certain length reach a maximum when the elevation angle α is equal to zero, as shown in Fig. 6a. Besides, the whole deviations dh are reduced gradually as the folding arm is rotated around the center O upwards or down- wards from the horizontal position. The deviations dh are nearly zero when the angle α is equal to 70° or ?70°. However, the vertical deviations dv are nearly to zero when the angle α is equal to —70○, 0 or 70○, as shown in Fig. 6b. The maximum values of the deviations dv appear in the upper area and the lower area of the rotation range. It can be found that the deviations dh and dv have the bilateral symmetry relative to the angle α. That is because the two deviations are mainly affected by the moment Mi which is symmetrical to the angle α. Fig. 6 The deviations at mt = 2.5 kg. a The horizontal deviation dh, b The vertical deviation dv Fig. 7 The forces FN,i 5 Conclusions (1)The blocks are adopted as the major components of the folding mechanism. Four connecting methods between two adjacent blocks are presented. Meanwhile, four feasible con?gurations of the folding mechanism are proposed according to the advantages of each connecting method. (2)The mathematical model of the position precision is established to acquire the influences of the extended length, the mass mt and the elevation angle α. (3)A numerical simulation of the precision model is conducted using MATLAB. The deviations dh and dv rise with the increasing of the extended length or the mass mt. Hence, this type of folding mechanism with the compact volume possesses thethe excellent position precision and the long folding length. 第 45 頁(yè) 指 導(dǎo) 教 師 評(píng) 語(yǔ) 外文翻譯成績(jī)： 指導(dǎo)教師簽字： 年 月 日 注：1. 指導(dǎo)教師對(duì)譯文進(jìn)行評(píng)閱時(shí)應(yīng)注意以下幾個(gè)方面：①翻譯的外文文獻(xiàn)與畢業(yè)設(shè)計(jì)（論文）的主題是否高度相關(guān)，并作為外文參考文獻(xiàn)列入畢業(yè)設(shè)計(jì)（論文）的參考文獻(xiàn)；②翻譯的外文文獻(xiàn)字?jǐn)?shù)是否達(dá)到規(guī)定數(shù)量（3 000字以上）；③譯文語(yǔ)言是否準(zhǔn)確、通順、具有參考價(jià)值。 2. 外文原文應(yīng)以附件的方式置于譯文之后。 第15頁(yè)