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六自由度并聯(lián)機(jī)器人篇一

機(jī) 器 人

工業(yè)機(jī)器人是在生產(chǎn)環(huán)境中以提高生產(chǎn)效率的工具，它能做常規(guī)乏味的裝配線工作，或能做那些對(duì)于工人來說是危險(xiǎn)的工作，例如，第一代工業(yè)機(jī)器人是用來在 核電站中更換核燃料棒，如果人去做這項(xiàng)工作，將會(huì)遭受有害的放射線的輻射。工業(yè)機(jī)器人亦能工作在裝配線上將小元件裝配到一起，如將電子元件安放在電路印制板，這樣，工人就能從這項(xiàng)乏味的常規(guī)工作中解放出來。機(jī)器人也能按程序要求用來拆除炸彈，輔助殘疾人，在社會(huì)的很多應(yīng)用場(chǎng)合下履行職能。

機(jī)器人可以認(rèn)為是將手臂末端的工具、傳感器和（或）手爪移到程序指定位置的一種機(jī)器。當(dāng)機(jī)器人到達(dá)位置后，它將執(zhí)行某種任務(wù)。這些任務(wù)可以是焊接、密封、機(jī)器裝料、拆卸以及裝配工作。除了編程以及系統(tǒng)的開停之外，一般來說這些工作可以在無人干預(yù)下完成。如下敘述的是機(jī)器人系統(tǒng)基本術(shù)語(yǔ)：

1.機(jī)器人是一個(gè)可編程、多功能的機(jī)械手，通過給要完成的不同任務(wù)編制各種動(dòng)作，它可以移動(dòng)零件、材料、工具以及特殊裝置。這個(gè)基本定義引導(dǎo)出后續(xù)段落的其他定義，從而描繪出一個(gè)完整的機(jī)器人系統(tǒng)。

2.預(yù)編程位置點(diǎn)是機(jī)器人為完成工作而必須跟蹤的軌跡。在某些位

置點(diǎn)上機(jī)器人將停下來做某些操作，如裝配零件、噴涂油漆或焊接。這些預(yù)編程點(diǎn)貯存在機(jī)器人的貯存器中，并為后續(xù)的連續(xù)操作所調(diào)用，而且這些預(yù)編程點(diǎn)想其他程序數(shù)據(jù)一樣，可在日后隨工作需要而變化。因而，正是這種編程的特征，一個(gè)工業(yè)機(jī)器 人很像一臺(tái)計(jì)算機(jī)，數(shù)據(jù)可在這里儲(chǔ)存、后續(xù)調(diào)用與編譯。

3.機(jī)器手是機(jī)器人的手臂，它使機(jī)器人能彎曲、延伸和旋轉(zhuǎn)，提供這些運(yùn)動(dòng)的是機(jī)器手的軸，亦是所謂的機(jī)器人的自由度。一個(gè)機(jī)器人能有3~16軸，自由度一詞總是與機(jī)器人軸數(shù)相關(guān)。

4.工具和手爪不是機(jī)器人自身組成部分，但它們是安裝在機(jī)器人手臂末端的附件。這些連在機(jī)器人手臂末端的附件可使機(jī)器人抬起工件、點(diǎn)焊、刷漆、電弧焊、鉆孔、打毛刺以及根據(jù)機(jī)器人的要求去做各種各樣的工作。

5.機(jī)器人系統(tǒng)還可以控制機(jī)器人的工作單元，工作單元是機(jī)器人執(zhí)行任務(wù)所處的整體環(huán)境，該單元包括控制器、機(jī)械手、工作平臺(tái)、安全保護(hù)裝置或者傳輸裝置。所有這些為保證機(jī)器人完成自己任務(wù)而必須的裝置都包括在這一工作單元中。另外，來自外設(shè)的信號(hào)與機(jī)器人通訊，通知機(jī)器人何時(shí)裝配工件、取工件或放工件到傳輸裝置上。機(jī)器人系統(tǒng)有三個(gè)基本部件：機(jī)械手、控制器和動(dòng)力源。

a.機(jī)械手

機(jī)械手做機(jī)器人系統(tǒng)中粗重工作，它包括兩個(gè)部分：機(jī)構(gòu)與附件，機(jī)械手也用聯(lián)接附件基座，圖21-1表示了一機(jī)器人基座與附件之間的聯(lián)接情況。

機(jī)械手基座通常固定在工作區(qū)域的地基上，有時(shí)基座也可以移動(dòng)，在這種情況下基座安裝在導(dǎo)軌回軌道上，允許機(jī)械手從一個(gè)位置移到另外一個(gè)位置。

正如前面所提到的那樣，附件從機(jī)器人基座上延伸出來，附件就是機(jī)器人的手臂，它可以是直動(dòng)型，也可以是軸節(jié)型手臂，軸節(jié)型手臂也是大家所知的關(guān)節(jié)型手臂。

機(jī)械臂使機(jī)械手產(chǎn)生各軸的運(yùn)動(dòng)。這些軸連在一個(gè)安裝基座上，然后再連到拖架上，拖架確保機(jī)械手停留在某一位置。

在手臂的末端上，連接著手腕（圖21-1），手腕由輔助軸和手腕凸緣組成，手腕是讓機(jī)器人用戶在手腕凸緣上安裝不同的工具來做不同的工作。

機(jī)械手的軸使機(jī)械手在某一區(qū)域內(nèi)執(zhí)行任務(wù)，我們將這個(gè)區(qū)域?yàn)闄C(jī)器人的工作單元，該區(qū)域的大小與機(jī)械手的尺寸相對(duì)應(yīng)，圖21-2列舉了一個(gè)典型裝配機(jī)器人的工作單元。隨著機(jī)器人機(jī)械結(jié)構(gòu)尺寸的增加，工作單元的范圍也必須相應(yīng)的增加。

機(jī)械手的運(yùn)動(dòng)有執(zhí)行元件或驅(qū)動(dòng)系統(tǒng)來控制。執(zhí)行元件或驅(qū)動(dòng)系統(tǒng)

允許各軸力經(jīng)機(jī)構(gòu)轉(zhuǎn)變?yōu)闄C(jī)械能，驅(qū)動(dòng)系統(tǒng)與機(jī)械傳動(dòng)鏈相匹配。由鏈、齒輪和滾珠絲杠組成的機(jī)械傳動(dòng)鏈驅(qū)動(dòng)著機(jī)器人的各軸。

b.控制器

機(jī)器人控制器是工作單元的核心�？刂破鲀�(chǔ)存著預(yù)編程序供后續(xù)調(diào)用、控制外設(shè)，及與廠內(nèi)計(jì)算機(jī)進(jìn)行通訊以滿足產(chǎn)品更新的需要。

控制器用于控制機(jī)械手運(yùn)動(dòng)和在工作單元內(nèi)控制機(jī)器人外設(shè)。用戶可通過手持的示教盒將機(jī)械手運(yùn)動(dòng)的程序編入控制器。這些信息儲(chǔ)存在控制器的儲(chǔ)存器中以備后續(xù)調(diào)用，控制器儲(chǔ)存了機(jī)器人系統(tǒng)的所有編程數(shù)據(jù)，它能儲(chǔ)存幾個(gè)不同的程序，并且所有這些程序均能編輯。

控制器要求能夠在工作單元內(nèi)與外設(shè)進(jìn)行通信。例如控制器有一個(gè)輸入端，它能標(biāo)識(shí)某個(gè)機(jī)加工操作何時(shí)完成。當(dāng)該加工循環(huán)完成后，輸入端接通，告訴控制器定位機(jī)械手以便能抓取已加工工件，隨后，機(jī)械手抓取一未加工件，將其放置在機(jī)床上。接著，控制器給機(jī)床發(fā)出開始加工的信號(hào)。

控制器可以由根據(jù)事件順序而步進(jìn)的機(jī)械式輪鼓組成，這種類型的控制器可用在非常簡(jiǎn)單的機(jī)械系統(tǒng)中。用于大多數(shù)機(jī)器人系統(tǒng)中的控制器代表現(xiàn)代電子學(xué)的水平，是更復(fù)雜的裝置，即它們是由微處理器操縱的。這些微處理器可以是8位、16位或32位處理器。它們可以使得控制器在操作過程中顯得非常柔性。

控制器能通過通信線發(fā)送電信號(hào)，使它能與機(jī)械手各軸交流信息，在機(jī)器人的機(jī)械手和控制器之間的雙向交流信息可以保持系統(tǒng)操作和位置經(jīng)常更新，控制器亦能控制安裝在機(jī)器人手腕上的任何工具。

控制器也有與廠內(nèi)各計(jì)算機(jī)進(jìn)行通信的任務(wù)，這種通信聯(lián)系使機(jī)器人成為計(jì)算機(jī)輔助制造（cam）系統(tǒng)的一個(gè)組成部分。

存儲(chǔ)器。給予微處理器的系統(tǒng)運(yùn)行時(shí)要與固態(tài)的存儲(chǔ)裝置相連，這些存儲(chǔ)裝置可以是磁泡，隨機(jī)存儲(chǔ)器、軟盤、磁帶等。每種記憶存儲(chǔ)裝置均能貯存、編輯信息以備后續(xù)調(diào)用和編輯。

c.動(dòng)力源

動(dòng)力源是給機(jī)器人和機(jī)械手提供動(dòng)力的單元。傳給機(jī)器人系統(tǒng)的動(dòng)力源有兩種，一種是用于控制器的交流電，另一種是用于驅(qū)動(dòng)機(jī)械手各軸的動(dòng)力源，例如，如果機(jī)器人的機(jī)械手是有液壓和氣壓驅(qū)動(dòng)的，控制信號(hào)便傳送到這些裝置中，驅(qū)動(dòng)機(jī)器人運(yùn)動(dòng)。

液壓與氣壓系統(tǒng)

僅有以下三種基本方法傳遞動(dòng)力：電氣，機(jī)械和流體。大多數(shù)應(yīng)用系統(tǒng)實(shí)際上是將三種方法組合起來而得到最有效的最全面的系統(tǒng)。為了合理地確定采取哪種方法。重要的是了解各種方法的顯著特征。例如液壓系統(tǒng)在長(zhǎng)距離上比機(jī)械系統(tǒng)更能經(jīng)濟(jì)地傳遞動(dòng)力。然而液壓系統(tǒng)與電氣系統(tǒng)相比，傳遞動(dòng)力的距離較短。

液壓動(dòng)力傳遞系統(tǒng)涉及電動(dòng)機(jī)，調(diào)節(jié)裝置和壓力和流量控制，總的來說，該系統(tǒng)包括：

泵：將原動(dòng)機(jī)的能量轉(zhuǎn)換成作用在執(zhí)行部件上的液壓能。閥：控制泵產(chǎn)生流體的運(yùn)動(dòng)方向、產(chǎn)生的功率的大小，以及到達(dá)執(zhí)行部件流體的流量。功率大小取決于對(duì)流量和壓力大小的控制。

執(zhí)行部件：將液壓能轉(zhuǎn)成可用的機(jī)械能。

介質(zhì)即油液：可進(jìn)行無壓縮傳遞和控制，同時(shí)可以潤(rùn)滑部件，使閥體密封和系統(tǒng)冷卻。

聯(lián)接件：聯(lián)接各個(gè)系統(tǒng)部件，為壓力流體提供功率傳輸通路，將液體返回油箱（貯油器）。

油液貯存和調(diào)節(jié)裝置：用來確保提供足夠質(zhì)量和數(shù)量并冷卻的液體。

液壓系統(tǒng)在工業(yè)中應(yīng)用廣泛。例如沖壓`鋼類工件的磨削幾一般加工業(yè)、農(nóng)業(yè)、礦業(yè)、航天技術(shù)、深�？碧�、運(yùn)輸、海洋技術(shù)，近海天然氣和石油勘探等行業(yè)，簡(jiǎn)而言之，在日常生活中有人不從液壓技術(shù)中得到某種益處。

液壓系統(tǒng)成功而又廣泛使用的秘密在于它的通用性和易操作性。液壓動(dòng)力傳遞不會(huì)象機(jī)械系統(tǒng)那樣受到機(jī)器幾何形狀的制約，另外，液壓系統(tǒng)不會(huì)像電氣系統(tǒng)那樣受到材料物理性能的制約，它對(duì)傳遞功率幾乎沒有量的限制。例如，一個(gè)電磁體的性能受到鋼的磁飽和極限的限制，相反，液壓系統(tǒng)的功率僅僅受材料強(qiáng)度的限制。

企業(yè)為了提高生產(chǎn)率將越來越依靠自動(dòng)化，這包括遠(yuǎn)程和直接控制生產(chǎn)操作、加工過程和材料處理等。液壓動(dòng)力之所以成為自動(dòng)化的組成部分，是因?yàn)樗�有如下主要的特點(diǎn)：

1.控制方便精確

通過一個(gè)簡(jiǎn)單的操作桿和按扭，液壓系統(tǒng)的操作者便能立即起動(dòng)，停止、加減速和能提供任意功率、位置精度為萬分之一英寸的位置控制力。圖13-1是一個(gè)使飛機(jī)駕駛員升起和落下起落架的液壓系統(tǒng)，當(dāng)飛行向某方向移動(dòng)控制閥，壓力油流入液壓缸的某一腔從而降下起落架。飛行員向反方向移動(dòng)控制閥，允許油液進(jìn)入液壓缸的另一腔，便收回起落架。

2.增力 一個(gè)液壓系統(tǒng)（沒有使用笨重的齒輪、滑輪和杠桿）能簡(jiǎn)單

有效地將不到一盎司的力放大產(chǎn)生幾百噸的輸出。

3.恒力或恒扭矩

只有液壓系統(tǒng)能提供不隨速度變化而變化的恒力或恒扭矩，他可以驅(qū)動(dòng)對(duì)象從每小時(shí)移動(dòng)幾英寸到每分鐘幾百英寸，從每小時(shí)幾轉(zhuǎn)到每分鐘幾千轉(zhuǎn)。

4.簡(jiǎn)便、安全、經(jīng)濟(jì)

總的來說，液壓系統(tǒng)比機(jī)械或電氣系統(tǒng)使用更少的運(yùn)動(dòng)部件，因此，它們運(yùn)行與維護(hù)簡(jiǎn)便。這使得系統(tǒng)結(jié)構(gòu)緊湊，安全可靠。例如 一種用于車輛上的新型動(dòng)力轉(zhuǎn)向控制裝置一淘汰其他類型的轉(zhuǎn)向動(dòng)力裝置，該轉(zhuǎn)向部件中包含有人力操縱方向控制閥和分配器。因?yàn)檗D(zhuǎn)向部件是全液壓的，沒有方向節(jié)、軸承、減速齒輪等機(jī)械連接，使得系統(tǒng)簡(jiǎn)單緊湊。

另外，只需要輸入很小的扭矩就能產(chǎn)生滿足極其惡劣的工作條件所需的控制力，這對(duì)于因操作空間限制而需要小方向盤的場(chǎng)合很重要，這也是減輕司機(jī)疲勞度所必須的。

液壓系統(tǒng)的其他優(yōu)點(diǎn)包括雙向運(yùn)動(dòng)、過載保護(hù)和無級(jí)變速控制，在已有的任何動(dòng)力、系統(tǒng)中液壓系統(tǒng)也具有最大的單位質(zhì)量功率比。

盡管液壓系統(tǒng)具有如此的高性能，但它不是可以解決所有動(dòng)力傳遞問題的靈丹妙藥。液壓系統(tǒng)也有缺點(diǎn)，液壓油有污染，并且泄露不可能完全避免，另外如果油液滲漏發(fā)生在灼熱設(shè)備附近，大多數(shù)液壓油能引起火災(zāi)。

氣壓系統(tǒng)

氣壓系統(tǒng)是用壓力氣體傳遞和控制動(dòng)力，正如名稱所表明的那樣，氣壓系統(tǒng)通常用空氣（不用其他氣體）作為流體介質(zhì)，因?yàn)榭諝馐前踩�、成本低而又隨處可得的流體，在系統(tǒng)部件中產(chǎn)生電弧有可能點(diǎn)燃泄露物的場(chǎng)合下（使用空氣作為介質(zhì)）尤其安全。

在氣壓系統(tǒng)中，壓縮機(jī)用來壓縮并提供所需的空氣。壓縮機(jī)一般有活塞式、葉片式和螺旋式等類型。壓縮機(jī)基本上是根據(jù)理想氣體法則，通過減小氣體體積來增加氣體壓力的。氣壓系統(tǒng)通常考慮采用大的中央空氣壓縮機(jī)作為一個(gè)無限量的氣源，這類似于電力系統(tǒng)中只要將插頭插入插座邊可獲得電能。用這種方法，壓力氣體可以總氣體源輸送到整個(gè)工廠的各個(gè)角落，壓力氣體可通過空氣濾清器除去污物，這些污染可能會(huì)損壞氣動(dòng)組件的精密配合部件如閥和汽缸等，隨后輸送到各個(gè)回路中，接著空氣流經(jīng)減壓閥以減小氣壓值適合某一回路使用。因?yàn)榭諝獠皇呛玫臐?rùn)滑油，氣壓系統(tǒng)需要一個(gè)油霧器將細(xì)小的油霧注射到經(jīng)過減壓閥減壓空氣中，這有幫助于減少氣動(dòng)組件精密配合運(yùn)動(dòng)件的磨損。

由于來自大氣中的空氣含不同數(shù)量的水分，這些水分是有害的，它可以帶走潤(rùn)滑劑引起的過分磨損和腐蝕，因此，在一些使用場(chǎng)合中，要用空氣干燥器來除去這些有還的水分。由于氣壓系統(tǒng)直接向大氣排

氣，會(huì)產(chǎn)生過大的噪聲，因此可在氣閥和執(zhí)行組件排氣口安裝銷聲器來降低噪聲，以防止操作人員因接觸噪聲及高速空氣粒子有可能引發(fā)的傷害。

用氣動(dòng)系統(tǒng)代替液壓系統(tǒng)有以下幾條理由：液體的慣性遠(yuǎn)比氣體大，因此，在液壓系統(tǒng)中，當(dāng)執(zhí)行組件加速減速和閥突然開啟關(guān)閉時(shí)，油液的質(zhì)量更是一個(gè)潛在的問題，根據(jù)牛頓運(yùn)動(dòng)定律，產(chǎn)生加速度運(yùn)動(dòng)油液所需的力要比加速同等體積空氣所需的力高出許多倍。液體比氣體具有更大的粘性，這會(huì)因?yàn)閮?nèi)摩擦而引起更大的壓力和功率損失；另外，由于液壓系統(tǒng)使用的液體要與大氣隔絕，故它們需要特殊的油箱和無泄露系統(tǒng)設(shè)計(jì)。氣壓系統(tǒng)使用可以直接排到周圍環(huán)境中的空氣，一般來說氣壓系統(tǒng)沒有液體系統(tǒng)昂貴。

然而，由于空氣的可壓縮性，使得氣壓系統(tǒng)執(zhí)行組件不可能得到精確的速度控制和位置控制。氣壓系統(tǒng)由于壓縮機(jī)局限，其系統(tǒng)壓力相當(dāng)?shù)停ǖ陀?50psi），而液壓力可達(dá)1000psi之高，因此液壓系統(tǒng)可以是大功率系統(tǒng)，而氣動(dòng)系統(tǒng)僅用于小功率系統(tǒng)，典型例子有沖壓、鉆孔、夾緊、組裝、鉚接、材料處理和邏輯控制操作等。

六自由度并聯(lián)機(jī)器人篇二

六自由度并聯(lián)機(jī)器人基于grassmann-cayley代數(shù)的奇異性條件

patricia ben-horin和moshe shoham，會(huì)員，ieee

摘要

本文研究了奇異性條件大多數(shù)的六自由度并聯(lián)機(jī)器人在每一個(gè)腿上都有一個(gè)球形接頭。首先,確定致動(dòng)器螺絲在腿鏈中心。然后用凱萊代數(shù)和相關(guān)的分解方法用于確定哪些條件的導(dǎo)數(shù)(或剛度矩陣)包含這些螺絲是等級(jí)不足。這些工具是有利的,因?yàn)樗麄兎奖悴倏v坐標(biāo)-簡(jiǎn)單的表達(dá)式表示的幾何實(shí)體,從而使幾何解釋的奇異性條件是更容易獲得。使用這些工具,奇異性條件(至少)144種這類的組合被劃定在四個(gè)平面所相交的一個(gè)點(diǎn)上。這四個(gè)平面定義為這個(gè)零距螺絲球形關(guān)節(jié)的位置和方向。指數(shù)terms-grassmann-cayley代數(shù)，奇點(diǎn)，三條腿的機(jī)器。

一、介紹

在過去的二十年里,許多研究人員廣泛研究并聯(lián)機(jī)器人的奇異性。不像串聯(lián)機(jī)器人,失去在奇異配置中的自由度,盡管并聯(lián)機(jī)器人的執(zhí)行器都是鎖著但是他們的的自由度還是可以獲得的。因此,這些不穩(wěn)定姿勢(shì)的全面知識(shí)為提高機(jī)器人的設(shè)計(jì)和確定機(jī)器人的路徑規(guī)劃是至關(guān)重要的。

主要的方法之一,用于尋找奇異性并行機(jī)器人是基于計(jì)算雅可比行列式進(jìn)行的。gosselin和安杰利斯[1]分類奇異性的閉環(huán)機(jī)制通過考慮兩個(gè)雅克比定義輸入速度和輸出速度之間的關(guān)系。當(dāng)圣魯克和gosselin[2]減少了算術(shù)操作要求定義的雅可比行列式高夫·斯圖爾特平臺(tái)(gsp),從而使數(shù)值計(jì)算得到多項(xiàng)式。

另一個(gè)重要的工具,為分析螺旋理論中的奇異性,首先闡述了1900的論文[6]和開發(fā)機(jī)器人應(yīng)用程序。幾項(xiàng)研究已經(jīng)應(yīng)用這個(gè)理論找到并聯(lián)機(jī)器人的奇異性,例如,[11]-[14]。特別注意到情況,執(zhí)行機(jī)構(gòu)是線性和代表螺絲是零投的。在這些情況下,奇異的配置是解決通過使用幾何,尋找可能的致動(dòng)器線依賴[15]-[17]。其他分類方法閉環(huán)機(jī)制可以被發(fā)現(xiàn)在[18]-[22]。

在本文中,我們分析了奇異點(diǎn)的一大類三條腿的機(jī)器人,在每個(gè)腿鏈有一個(gè)球形接頭上的任何點(diǎn)。我們只關(guān)注了正運(yùn)動(dòng)學(xué)奇異性。首先,我們發(fā)現(xiàn)螺絲相關(guān)執(zhí)行機(jī)構(gòu)的每個(gè)鏈。因?yàn)槊恳粋�(gè)鏈包含一個(gè)球形接頭,自致動(dòng)器螺絲是相互聯(lián)合的,他們是通過球形關(guān)節(jié)的零螺距螺桿螺絲。然后我們使用grassmann-cayley代數(shù)和相關(guān)的發(fā)展獲得一個(gè)代數(shù)方程,它源于管理行機(jī)器人包含的剛度矩陣。直接和高效檢索的幾何意義的奇異配置是最主要的一個(gè)優(yōu)點(diǎn),在這里將介紹其方法。

雖然之前的研究[53]分析7架構(gòu)普惠制,各有至少三條并發(fā)關(guān)節(jié),本文擴(kuò)展了奇點(diǎn)分析程度更廣泛的一類機(jī)器人有三條腿和一個(gè)球形關(guān)節(jié)。使用降低行列式和grassmann-cayley運(yùn)營(yíng)商我們獲得一個(gè)通用的條件,這些機(jī)器人的奇異性提供在一個(gè)簡(jiǎn)單的幾何意義方式計(jì)算中。

本文的結(jié)構(gòu)如下。第二節(jié)詳細(xì)描述了運(yùn)動(dòng)學(xué)結(jié)構(gòu)的并聯(lián)機(jī)器人。第三節(jié)包含一個(gè)簡(jiǎn)短的在螺絲和大綱性質(zhì)的背景下驅(qū)動(dòng)器螺絲,零距螺絲作用于中心的球形關(guān)節(jié)。第四部分包含一個(gè)介紹grassmann-cayley代數(shù)的基本工具用于尋找奇異性條件。這部分還包括剛度矩陣(或?qū)��?shù))分解成坐標(biāo)自由表達(dá)。第五節(jié)中一個(gè)常見的例子給出了這種方法。最后,第六章比較了使用本方法結(jié)果與結(jié)果的其他技術(shù)。

二、運(yùn)動(dòng)構(gòu)架

本文闡述了6自由度并聯(lián)機(jī)器人有六間連通性基礎(chǔ)和移動(dòng)平臺(tái)。肖海姆和羅斯[54]提供了調(diào)查可能的結(jié)構(gòu),產(chǎn)生基于流動(dòng)公式6自由度的grubler和kutzbach。他們尋找了所有的可能性,滿足這個(gè)公式對(duì)關(guān)節(jié)的數(shù)目和任何鏈接。gsp和三條腿的機(jī)器人結(jié)構(gòu)的一個(gè)子集所列出的6自由度shoham和羅斯。一個(gè)類似的例子也證實(shí)了了podhorodeski和pittens[55],他發(fā)現(xiàn)了一個(gè)類的三條腿的對(duì)稱并聯(lián)機(jī)器人,球形關(guān)節(jié)、轉(zhuǎn)動(dòng)關(guān)節(jié)的平臺(tái)在每個(gè)腿比其他結(jié)構(gòu)潛在有利。正如上面所討論的,大多數(shù)的報(bào)告文獻(xiàn)限制他們的分析結(jié)構(gòu)和球形關(guān)節(jié)位于移動(dòng)平臺(tái)和棱柱關(guān)節(jié)作為驅(qū)動(dòng)的關(guān)節(jié)。在這個(gè)分類,我們包括五種類型的關(guān)節(jié)和更多的可選職位的球形關(guān)節(jié)。

我們處理機(jī)器人有三個(gè)鏈連接到移動(dòng)平臺(tái),每個(gè)驅(qū)動(dòng)有兩個(gè)1自由度關(guān)節(jié)或一個(gè)二自由度關(guān)節(jié)。這些鏈不一定是平等的,但都有移動(dòng)和連接六個(gè)基地和之間的平臺(tái)。除了球形接頭(s),關(guān)節(jié)考慮是棱鏡(p),轉(zhuǎn)動(dòng)(r)、螺旋(h)、圓柱(c)和通用(u),前三個(gè)是1自由度關(guān)節(jié)和最后兩個(gè)二自由度的關(guān)節(jié)。所有的可能性都顯示在表i和ii。該列表只包含機(jī)器人,有平等的連鎖,總計(jì)144種不同的結(jié)構(gòu),但是機(jī)器人與任何可能的組合鏈也可以被認(rèn)為是membersof這類方法。組合的總數(shù),大于500 000,計(jì)算方式如下:

三、管理方法

本節(jié)涉及螺絲和平臺(tái)運(yùn)動(dòng)的確定。因?yàn)榭紤]機(jī)器人有三個(gè)串行鏈,每個(gè)驅(qū)動(dòng)器螺絲的方向可以由其互惠到其他關(guān)節(jié)螺釘固定在鏈條。被動(dòng)球形接頭在每個(gè)鏈部隊(duì)驅(qū)動(dòng)器螺絲為零距(行)并且通過它的中心。因此,三個(gè)平面是創(chuàng)建中心位于自己的球形關(guān)節(jié)。

以下簡(jiǎn)要介紹了螺旋理論,廣泛的解決[7],[73],[75];我們解決在第二節(jié)中列出相互的所有關(guān)節(jié)螺釘系統(tǒng)。

上述類的機(jī)器人的幾何結(jié)果奇點(diǎn)現(xiàn)在相比其他方法獲得的結(jié)果要準(zhǔn)確。首先,我們比較奇異條件在上述3 gsp平臺(tái)與結(jié)果報(bào)告線幾何方法。

根據(jù)相對(duì)幾何條件的他行方法區(qū)分不同的幾種類型沿著棱鏡致動(dòng)器[81]的奇異性。我們表明,所有這些奇異點(diǎn)是特定情況下的條件通過(17 c)提供,這是有效的三條腿以及6:3 gsp平臺(tái)的機(jī)器人的考慮。這種結(jié)構(gòu)的奇異的配置根據(jù)線幾何分析包括五種類型:3 c、4 b、4 d,5 a和5 b[17],[36]。

四、奇異性分析

本節(jié)確定奇異性條件定義在第二節(jié)的機(jī)器人。第一部分包括尋找方向的執(zhí)行機(jī)構(gòu)的行動(dòng)路線,基于解釋第三節(jié)中介紹。他行通過球形接頭中心,而他們的方向取決于關(guān)節(jié)的分布和位置。第二部分包括應(yīng)用程序的方法使用了grassmann-cayley代數(shù)在第四節(jié)定義奇點(diǎn)。因?yàn)槊繉?duì)線滿足在一個(gè)點(diǎn)(球形接頭),所有例子的解決方案是象征性地平等,無論點(diǎn)位置的腿或腿的對(duì)稱性。我們從文獻(xiàn)中舉例說明使用三個(gè)機(jī)器人的解決方案。

1.方向的致動(dòng)器螺絲

第一個(gè)例子是3-prps機(jī)器人提出behi[61][見圖3(a)]。對(duì)于每個(gè)腿驅(qū)動(dòng)螺絲躺在這家由球形接頭中心和轉(zhuǎn)動(dòng)關(guān)節(jié)軸。特別是,致動(dòng)器螺桿是垂直于軸的,和致動(dòng)器螺桿是垂直于軸的,這些方向被描繪在圖3(b)。第二個(gè)例子是the3-usr機(jī)器人提出simaan et al。[66][見圖4(a)]。每條腿有驅(qū)動(dòng)器螺絲躺在通過球形接頭中心和包含轉(zhuǎn)動(dòng)關(guān)節(jié)軸中。驅(qū)動(dòng)器螺絲穿過球形接頭中心并與轉(zhuǎn)動(dòng)關(guān)節(jié)軸相連。這些方向被描繪在圖4(b)。

第三個(gè)例子是3-ppsp byun建造的機(jī)器人和[65][見圖5(一個(gè))]。每條腿,驅(qū)動(dòng)螺絲躺在飛機(jī)通過球形接頭中心和正常的棱鏡接頭軸。驅(qū)動(dòng)器螺絲垂直于軸的,和致動(dòng)器螺桿是垂直于軸的,這些方向被描繪在圖5(b)。

圖3(a)3-prps機(jī)器人提出behi[61]

(b)飛機(jī)和致動(dòng)器螺絲

圖4(a)3自由度機(jī)器人提出simaan和shoham[66]

(b)飛機(jī)和致動(dòng)器螺絲的3自由度機(jī)器人

圖5(a)3-ppsp機(jī)器人提出byun[65]

(b)飛機(jī)和致動(dòng)器螺絲

2、.奇異性條件

雅克(或superbracket)的機(jī)器人是分解成普通支架monomials使用麥克米蘭的分解,即(16)。解釋部分3—b機(jī)器人，本文認(rèn)為每個(gè)鏈有兩個(gè)零距驅(qū)動(dòng)器螺絲通過球形接頭。拓?fù)?這個(gè)描述等于行6:3 gsp(或在[53]),這三條線,每經(jīng)過一個(gè)雙球面上的接頭平臺(tái)(見圖6)。這意味著每對(duì)線共享一個(gè)公共點(diǎn)(這些點(diǎn)在圖6中)。因此類的機(jī)器人被認(rèn)為是在本文中,我們可以使用相同的標(biāo)記點(diǎn)的至于6:3 gsp。六線與相關(guān)各機(jī)器人通過雙點(diǎn),并且,用同樣的方式在圖6。

圖6 6-3 gsp

五、結(jié)果

本文提出一個(gè)廣義奇異性分析并聯(lián)機(jī)器人組成元素。這些是有一個(gè)球形接頭在每個(gè)腿鏈的三條腿的6自由度機(jī)器人。因?yàn)榍蛐侮P(guān)節(jié)需要驅(qū)動(dòng)器，螺絲是純粹的力量作用于他們的中心,他們的位置沿鏈?zhǔn)遣恢匾�的。組成元素包括144機(jī)制不同類型的關(guān)節(jié),每個(gè)都有不同的聯(lián)合裝置沿鏈。提出并建立描述幾個(gè)機(jī)器人出現(xiàn)在列表中。大量的機(jī)器人相關(guān)的分析組合不同被認(rèn)為是。奇點(diǎn)的分析是由第一個(gè)找到的執(zhí)行機(jī)構(gòu)使用互惠的螺絲。然后,借助組合方法和grassmann-cayley方法,得到剛度矩陣行列式在一個(gè)可以操作的協(xié)調(diào)自由形式,可以翻譯成一個(gè)簡(jiǎn)單的幾何條件之后。其定義是幾何條件由執(zhí)行機(jī)構(gòu)位置的線條和球形接頭,至少有一個(gè)相交點(diǎn)。這個(gè)有效的奇異點(diǎn)條件考慮所有組成元素中的機(jī)器人。一個(gè)比較的結(jié)果與結(jié)果的奇點(diǎn)證明了其他技術(shù)所有先前描述奇異條件實(shí)際上是特殊情況下的幾何條件的四架飛機(jī)交叉在一個(gè)點(diǎn),一個(gè)條件獲取的方法直接在這里提出。

singularity condition of six-degree-of-freedom three-legged parallel robots based on grassmann–cayley algebra patricia ben-horin and moshe shoham, associate member, ieee

abstract this paper addresses the singularity condition of a broad class of six-degree-of-freedom three-legged parallel robots that have one spherical joint somewhere along each , the actuator screws for each leg-chain are grassmann–cayley algebra and the associated superbracket decomposition are used to find the condition for which the jacobian(or rigidity matrix)containing these screws is tools are advantageous since they facilitate manipulation of coordinate-free expressions representing geometric entities, thus enabling the geometrical interpretation of the singularity condition to be obtained more these tools, the singularity condition of(at least)144 combinations of this class is delineated to be the intersection of four planes at one four planes are defined by the locations of the spherical joints and the directions of the zero-pitch terms—grassmann–cayley algebra, singularity, three-legged uction during the last two decades, many researchers have extensively investigated singularities of parallel serial robots that lose degrees of freedom(dofs)in singular configurations, parallel robots might also gain dofs even though their actuators are ore, thorough knowledge of these unstable poses is essential for improving robot design and determining robot path of the principal methods used for finding the singularities of parallel robots is based on calculation of the jacobian determinant in and angeles [1] classified the singularities of closed-loop mechanisms by considering two jacobians that define the relationship between input and output -onge and gosselin [2] reduced the arithmetical operations required to define the jacobian determinant for the gough–stewart platform(gsp), and thus enabled numerical calculation of the obtained polynomial in ov et al.[3]–[5] expanded the classification proposed by gosselin and angeles to define six types of singularity that are derived using equations containing not only the input and output velocities but also explicit passive joint r important tool that has served in the analysis of singularities is the screw theory, first expounded in ball’s 1900 treatise [6] and developed for robotic applications by hunt [7]–[9] and sugimoto et al.[10].several studies have applied this theory to find singularities of parallel robots, for example, [11]–[14].special attention was paid to cases in which the actuators are linear and the representing screws are these cases, the singular configurations were solved by using line geometry, looking for possible actuator-line dependencies [15]–[17].other approaches taken to classify singularities of closed-loop mechanisms can be found in [18]–[22].in this paper, we analyze the singularities of a broad class of three-legged robots, having a spherical joint at any point in each individual focus only on forward kinematics , we find the screws associated with the actuators of each every chain contains a spherical joint, and since the actuator screws are reciprocal to the joint screws, they are zero-pitch screws passing through the spherical we use grassmann–cayley algebra and related developments to get an algebraic equation which originates from the rigidity matrix containing the governing lines of the direct and efficient retrieval of the geometric meaning of the singular configurations is one of the main advantages of the method presented the previous study [53] analyzed only seven architectures of gsp, each having at least three pairs of concurrent joints, this paper expands the singularity analysis to a considerably broader class of robots that have three legs with a spherical joints somewhere along the the reduced determinant and grassmann–cayley operators we obtain one single generic condition for which these robots are singular and provide in a simple manner the geometric meaning of this structure of this paper is as n ii describes in detail the kinematic architecture of the class of parallel robots under n iii contains a brief background on screws and outlines the nature of the actuator screws, which are zero-pitch screws acting on the centers of the spherical n iv contains an introduction to grassmann–cayley algebra which is the basic tool used for finding the singularity section also includes the rigidity matrix(or jacobian)decomposition into coordinate-free section v a general example of this approach is y, section vi compares the results obtained using the present method with results obtained by other tic architecture this paper deals with 6-dof parallel robots that have connectivity six between the base and the moving and roth [54] provided a survey of the possible structures that yield 6-dof based on the mobility formula of grübler and searched for all the possibilities that satisfy this formula with respect to the number of joints connected to any of the gsp and three-legged robots are a subset of the structures with 6-dof listed by shoham and roth.a similar enumeration was provided also by podhorodeski and pittens [55], who found a class of three-legged symmetric parallel robots that have spherical joints at the platform and revolute joints in each leg to be potentially advantageous over other discussed above, most of the reports in the literature limit their analysis to structures with spherical joints located on the moving platform and revolute or prismatic joints as actuated or passive additional ions are the family of 14 robots proposed by simaan and shoham [28] which contain spherical-revolute dyads connected to the platform, and some structures mentioned below which have revolute or prismatic joints on the this classification, we include five types of joints and more optional positions for the spherical deal with robots that have three chains connected to the moving platform, each actuated by two 1-dof joints or one 2-dof chains are not necessarily equal, but all have mobility and connectivity six between the base and the s the spherical joint(s), the joints taken into consideration are prismatic(p), revolute(r), helical(h), cylindrical(c), and universal(u), the first three being 1-dof joints and the last two being 2-dof the possibilities are shown in tables i and list contains only the robots that have equal chains, totaling 144 different structures, but robots with any possible combination of chains can also be considered as membersof this total number of combinations, , is larger than 500 000, calculated as follows:

ing lines this section deals with the screws that determine the platform the robots under consideration have three serial chains, the direction of each actuator screw can be determined by its reciprocity to the other joint screws in the passive spherical joint in each chain forces the actuator screws to have zero-pitch(lines)and to pass through its ore, three flat pencils are created having their centers located at the spherical ing a brief introduction to the screw theory that is extensively treated in [7], [73]–[75];we address the reciprocal screw systems of all the joints listed in section geometric result for the singularity of the aforementioned class of robots is now compared with the results obtained by other approaches in the , we compare the singularity condition described above for the 6-3 gsp platform with the results reported for the line geometry line geometry method distinguishes among several types of singularities, according to the relative geometric condition of he lines along the prismatic actuators [81].we show that all these singularities are particular cases of the condition provided by(17c), which is valid for the three-legged robots under consideration as well as for the 6-3 gsp singular configurations of this structure according to line geometry analysis include five types: 3c, 4b, 4d, 5a, and 5b [17], [36].arity analysis this section determines the singularity condition for the class of robots defined in section first part consists of finding the direction of the actuator lines of action, based on the explanation introduced in section lines pass through the spherical joint center while their directions depend on the distribution and position of the second part includes application of the approach using grassmann–cayley algebra presented in section iv for defining singularity when considering six lines attaching two every pair of lines meet at one point(the spherical joint), the solution for all the cases is symbolically equal, regardless of the points’ location in the leg or the symmetry of the exemplify the solution using three robots from the ion of the actuator screws the first example is the 3-prps robot as proposed by behi [61] [see fig.3(a)].for each leg the actuated screws lie on theplane defined by the spherical joint center and the revolute joint particular,the actuator screw is perpendicular to the axis of , and the actuator screw is perpendicular to the axis of , these directions being depicted in fig.3(b).the second example is the3-usr robot as proposed by simaan et al.[66][see fig.4(a)].every leg has the actuator screws lying on the plane passing through the spherical joint center and containing the revolute joint actuator screw passes through the spherical joint center and intersects the revolute joint axis rly, the actuator screw passes through the spherical joint center and intersects the revolute joint axis and , these directions being depicted in fig.4(b).the third example is the 3-ppsp robot built by byun and cho [65] [see fig.5(a)].for every leg the actuated screws lie on the plane passing through the spherical joint center and being normal to the prismatic joint actuator screw is perpendicular to the axis of , and the actuator screw is perpendicular to the axis of , these directions being depicted in fig.5(b).fig.3.(a)the 3-prps robot as proposed by behi [61].(b)planes and actuator .4.(a)the 3-usr robot as proposed by simaan and shoham [66].(b)planes and actuator

screws of the 3-usr .5.(a)3-ppsp robot as proposed by byun and cho [65].(b)planes and actuator arity condition

the jacobian(or superbracket)of a robot is decomposed into ordinary bracket monomials using mcmillan’s decomposition, namely(16).as explained in section iii-b, all the robots of the class considered in this paper have two zero-pitch actuator screws passing through the spherical joint of each gically, this description is equivalent to the lines of the 6-3 gsp(or in [53]), which has three pairs of lines, each passing through a double spherical joint on the platform(see fig.6).this means that each pair of lines share one common point(in fig.6 these points are , , and).therefore for the class of robots considered in this paper, we can use the same notation of points as for the 6-3 six lines associated with each robot pass through the pairs of points,and , in the same way as in to the common points of the pairs of lines ,and ,denoted , and respectively, many of the monomials of(16)vanish due to(4).fig.6.6-3 sion

this paper presents singularity analysis for a broad family of parallel are 6-dof three-legged robots which have one spherical joint in each the spherical joints entail the actuator screws to be pure forces acting on their centers, their location along the chain is not family includes 144 mechanisms incorporating diverse types of joints that each has a different joint arrangement along the l proposed and built robots described in the literature appear in this list.a larger number of robots are relevant to this analysis if combinations of different legs are singularity analysis was performed by first finding the lines of action of the actuators using the reciprocity of , with the aid of combinatorial methods and grassmann–cayley operators, the rigidity matrix determinant was obtained in a manipulable coordinate-free form that could be translated later into a simple geometric geometric condition consists of four planes, defined by the actuator lines and the position of the spherical joints, which intersect at least one singularity condition is valid for all the robots in the family under consideration.a comparison of this singularity result with results obtained by other techniques demonstrated that all the previously described singularity conditions are actually special cases of the geometrical condition of four planes intersecting at a point, a condition that was obtained straightforwardly by the method suggested here

六自由度并聯(lián)機(jī)器人篇三

動(dòng)態(tài)優(yōu)化的一種新型高速，高精度的三自由度機(jī)械手

①

彭蘭（蘭朋）②，魯南立，孫立寧，丁傾永

(機(jī)械電子工程學(xué)院，哈爾濱理工學(xué)院，哈爾濱 150001，中國(guó))(robotics institute。harbin institute of technology，harbin 150001，p。r。china)

摘要

介紹了一種動(dòng)態(tài)優(yōu)化三自由度高速、高精度相結(jié)合，直接驅(qū)動(dòng)臂平面并聯(lián)機(jī)構(gòu)和線性驅(qū)動(dòng)器，它可以提高其剛度進(jìn)行了動(dòng)力學(xué)分析軟件adams仿真模擬環(huán)境中，進(jìn)行仿真模擬實(shí)驗(yàn).設(shè)計(jì)調(diào)查是由參數(shù)分析工具完成處理的，分析了設(shè)計(jì)變量的近似的敏感性，包括影響參數(shù)的每道光束截面和相對(duì)位置的線性驅(qū)動(dòng)器上的性能.在適當(dāng)?shù)姆绞较�，模型可以獲得一個(gè)輕量級(jí)動(dòng)態(tài)優(yōu)化和小變形的參數(shù)。一個(gè)平面并聯(lián)機(jī)構(gòu)不同截面是用來改進(jìn)機(jī)械手的.結(jié)果發(fā)生明顯的改進(jìn)后的系統(tǒng)動(dòng)力學(xué)仿真分析和另一個(gè)未精制一個(gè)幾乎是幾乎相等.但剛度的改進(jìn)的質(zhì)量大大降低，說明這種方法更為有效的。

關(guān)鍵詞: 機(jī)械手、adams、優(yōu)化、動(dòng)力學(xué)仿真

0 簡(jiǎn)介

并聯(lián)結(jié)構(gòu)機(jī)械手（pkm）是一個(gè)很有前途的機(jī)器操作和裝配的電子裝置，因?yàn)樗麄冇幸恍┟黠@的優(yōu)勢(shì)，例如：串行機(jī)械手的高負(fù)荷承載能力，良好的動(dòng)態(tài)性能和精確定位的優(yōu)點(diǎn)等.一種新型復(fù)合3一dof臂的優(yōu)點(diǎn)和串行機(jī)械手，也是并聯(lián)機(jī)構(gòu)為研究對(duì)象，三自由度并聯(lián)機(jī)器人是少自由度并聯(lián)機(jī)器人的重要類型。三自由度并聯(lián)機(jī)器人由于結(jié)構(gòu)簡(jiǎn)單，控制相對(duì)容易，價(jià)格便宜等優(yōu)點(diǎn)，具有很好的應(yīng)用前景。但由于它們比六自由度并聯(lián)機(jī)器人更復(fù)雜的運(yùn)動(dòng)特性，增加了這類機(jī)構(gòu)型綜合的難度，因此對(duì)三自由度并聯(lián)機(jī)器人進(jìn)行型綜合具有理論意義和實(shí)際價(jià)值。本文利用螺旋理論對(duì)三自由度并聯(lián)機(jī)器人進(jìn)行型綜合，以總結(jié)某些規(guī)律，進(jìn)一步豐富型綜合理論，并為新機(jī)型的選型提供理論依據(jù)，以下對(duì)其進(jìn)行闡述。

如圖-1所示 機(jī)械手組成的平面并聯(lián)機(jī)構(gòu)(ppm)包括平行四邊形結(jié)構(gòu)和線性驅(qū)動(dòng)器安裝在ppm.兩直接驅(qū)動(dòng)電機(jī)c整合交流電高分辨率編碼器的一部分作為驅(qū)動(dòng)平面并聯(lián)機(jī)械裝置.線型致動(dòng)器驅(qū)動(dòng)的聲音線圈發(fā)動(dòng)機(jī).這被認(rèn)為是理想的驅(qū)動(dòng)短行程的一部分.作為一個(gè)非換直接驅(qū)動(dòng)類，音圈電機(jī)可以提供高位置敏感和完美的力量與中風(fēng)的角色，高精密線性編碼作為回饋部分保證在垂直方向可重復(fù)性。

另一方面，該產(chǎn)品具有較高的剛度比串行機(jī)械手，因?yàn)樗�的特點(diǎn)和低封閉環(huán)慣性轉(zhuǎn)矩。同時(shí)，該系統(tǒng)可以克服了柔性耦合力學(xué)彈性、齒輪、軸承、被撕咬支持，連接軸和其他零件，包括古典驅(qū)動(dòng)設(shè)備，因此該機(jī)械手是更容易得到動(dòng)力學(xué)性能好、精度高。

圖-1 3自由度的混合結(jié)構(gòu)的機(jī)械手

當(dāng)長(zhǎng)度的各個(gè)環(huán)節(jié)的平面并聯(lián)機(jī)時(shí)，構(gòu)決定于運(yùn)動(dòng)學(xué)分析和綜合[4-7]，機(jī)械優(yōu)化設(shè)計(jì)的首要任務(wù)，應(yīng)加大僵硬、降低質(zhì)量.關(guān)于幾個(gè)參數(shù)模型.這是它重要和必要的影響，研究了各參數(shù)對(duì)模型表現(xiàn)以進(jìn)一步優(yōu)化。本文就開展設(shè)計(jì)研究工具，通過參數(shù)分析亞當(dāng)斯，又要適當(dāng)?shù)姆绞絹慝@得一個(gè)輕量級(jí)的優(yōu)化和小變形系統(tǒng)。仿真模型

adams(automatic dynamic analysis 0f mechanical system)自動(dòng)機(jī)械系統(tǒng)動(dòng)力學(xué)分析是一個(gè)完美的軟件，對(duì)機(jī)械系統(tǒng)動(dòng)力學(xué)模擬可處理機(jī)制包括有剛性和靈活的部分，仿真模型可以創(chuàng)造出機(jī)械手的亞當(dāng)斯環(huán)境 如圖-2。oxyz是全球性的參考幀，并oxyz局部坐標(biāo)系，兩個(gè)直流驅(qū)動(dòng)電機(jī)、交流和02m o1a表示，與線性驅(qū)動(dòng)器ch被視為剛性轉(zhuǎn)子轉(zhuǎn)動(dòng)慣量電機(jī)傳動(dòng)的120kg/cm2。大眾的線性驅(qū)動(dòng)器是1.5kg，連接ab、德、03f和lj被視為柔性體立柱、橫梁gk，通用公司和公里，形成一個(gè)三角形，也被當(dāng)作柔性傳動(dòng)長(zhǎng)度的鏈接是決定提前運(yùn)動(dòng)學(xué)設(shè)計(jì)為ab =o3f = 7cm，de=ij=7cm，gk= 7cm，gm =11.66cm，= 8.338cm。其它維度，這個(gè)數(shù)字是01a = 02m =7cm，cb=cd=hj 2.5cm。ef=eg=jk= 3cm。

雖然總平面并聯(lián)機(jī)構(gòu)的運(yùn)動(dòng)都是在水平、垂直和水平剛度必須在豎向剛度特征通常低于水平僵硬，因?yàn)樗�的角色在垂直懸臂梁的截面尺寸�?jì)算每一束平面并聯(lián)機(jī)構(gòu)和相對(duì)位置的線性驅(qū)動(dòng)器是兩個(gè)非常僵硬的影響因素的系統(tǒng)。

運(yùn)動(dòng)支鏈可分為三類：“主動(dòng)鏈（由驅(qū)動(dòng)器賦予確定獨(dú)立運(yùn)動(dòng)的支鏈。一般是單驅(qū)動(dòng)器控制一個(gè)自由度的運(yùn)動(dòng)），從動(dòng)鏈（不帶驅(qū)動(dòng)器、被迫作確定運(yùn)動(dòng)的支鏈。又分為以下兩種：約束鏈：獨(dú)立限制機(jī)構(gòu)自由度的從動(dòng)鏈。冗余鏈：重復(fù)限制機(jī)構(gòu)自由度的從動(dòng)鏈）復(fù)合鏈（有單驅(qū)動(dòng)器、但限制一個(gè)以上的機(jī)構(gòu)自由度的支鏈，實(shí)際是主動(dòng)鏈與約束鏈的組合）-并聯(lián)機(jī)構(gòu)是由這幾種支鏈用不同形式組合起來的。動(dòng)鏈中的約束鏈除了可以提高機(jī)構(gòu)剛度和作為測(cè)量鏈外，其更主要的作用是用來約束動(dòng)平臺(tái)的某一個(gè)或幾個(gè)自由度，以使其實(shí)現(xiàn)預(yù)期的運(yùn)動(dòng)。

圖-2 仿真模型 仿真模擬結(jié)果

在本節(jié)中，平均位移的末端是用來描述動(dòng)態(tài)剛度，這是在不同的配置在不同的線性驅(qū)動(dòng)器向前，從最初的位置的目的地，一般的豎向位移的機(jī)械手是作為目標(biāo)來研究豎向剛度，平均差別的橫坐標(biāo)、縱坐標(biāo)點(diǎn)之間有一個(gè)剛性數(shù)學(xué)模型，模型，作為目標(biāo)來研究水平剛度。

并聯(lián)機(jī)器人的構(gòu)型設(shè)計(jì)即型綜合是并聯(lián)機(jī)器人設(shè)計(jì)的首要環(huán)節(jié)，其目的是在給定所需自由度和運(yùn)動(dòng)要求條件下，尋求并聯(lián)機(jī)構(gòu)桿副配置、驅(qū)動(dòng)方式和總體布局等的各種可能組合。國(guó)內(nèi)的許多學(xué)者正致力于這方面的研究，其中比較有代表性的有如下幾種方法：”黃真為代表的約束綜合法；楊廷力等人的結(jié)構(gòu)綜合法；代表的李代數(shù)綜合法。以上各種方法自成體系，各有特點(diǎn)，都缺乏理論的完備性。本文提出添加約束法，是從限制自由度的角度出發(fā)，增加約束，去除不需要的自由度，因每條主動(dòng)鏈只有一個(gè)驅(qū)動(dòng)裝置，讓其控制一個(gè)自由度，其余自由度通過純約束鏈去除，這樣可以使主、從動(dòng)運(yùn)動(dòng)鏈的作用分離，運(yùn)動(dòng)解耦，有利于控制。具有三自由度的并聯(lián)機(jī)床，當(dāng)采用條主動(dòng)支鏈作為驅(qū)動(dòng)時(shí)，機(jī)構(gòu)就需要約束另三個(gè)自由度，通過選擇無驅(qū)動(dòng)裝置的從動(dòng)鏈來完成，則整個(gè)機(jī)構(gòu)成為有確定運(yùn)動(dòng)的三自由度的并聯(lián)機(jī)構(gòu)。黃真等提出的約束綜合法對(duì)完全對(duì)稱的少自由度并聯(lián)機(jī)器人機(jī)構(gòu)進(jìn)行了型綜合，完全對(duì)稱的支鏈結(jié)構(gòu)相同，都屬于復(fù)合鏈，每條支鏈除都有一個(gè)單驅(qū)動(dòng)器，控制一個(gè)自由度外，還應(yīng)約束一個(gè)以上自由度才能使機(jī)構(gòu)的六個(gè)自由度全部受控，使機(jī)構(gòu)有確定的運(yùn)動(dòng)。

2.1 截面效應(yīng)

扭轉(zhuǎn)變形位移的連結(jié)將會(huì)引起的，所以，扭轉(zhuǎn)常數(shù)的橫截面，重力是研究裝系統(tǒng)來研究，采取扭轉(zhuǎn)剛度的垂直切片lxx不變的各個(gè)環(huán)節(jié)和梁作為設(shè)計(jì)變量的變化，從 0.1 x 105mm4 與 3.5 x 105 mm4。

圖-3 不斷的效果在垂直變形扭轉(zhuǎn)

圖-3顯示了平均位移與截面扭轉(zhuǎn)常數(shù)末端的各個(gè)環(huán)節(jié)和梁，根據(jù)它的變化速率的環(huán)節(jié)，是最大的，ab是鏈接，lj依次分別gk梁和km有在豎向剛度性能。其他的仿真結(jié)果表明，水平位移之間的差異進(jìn)行比較，結(jié)果表明該模型體育智力h和剛性模型變化小就改變了恒定不變的時(shí)候扭加載慣性力的線性驅(qū)動(dòng)器，但是水平位移的變化，這意味著在這種模擬豎向變形的生產(chǎn)水平位移系統(tǒng)機(jī)械手。注意端面線性驅(qū)動(dòng)器的主要原因是水平變形、線性驅(qū)動(dòng)器機(jī)器人是由兩個(gè)節(jié)點(diǎn)c和h.所以，我們計(jì)算了不同的z-coordinate攝氏度之間，如圖所示，在圖4-扭轉(zhuǎn)常數(shù)的影響差別的鏈接德。其次是最有效的通用和連接梁，連接o3f，梁gk有效果。

因此，應(yīng)采取ab和連接區(qū)段大扭常數(shù)的免疫力，豎向剛度較大并行扭轉(zhuǎn)不變的鏈接德也使較少的均勻性，降低線性驅(qū)動(dòng)器不可以降低水平變形。

圖-4 在不影響扭不變

如圖-

5、6所展示的影響是區(qū)域慣性轉(zhuǎn)矩的設(shè)計(jì)變量是區(qū)域剛度和慣性轉(zhuǎn)矩的各個(gè)環(huán)節(jié)和梁lz，圖顯示增加lw卡爾減少的速度高于垂直位移的不斷增加ixx扭轉(zhuǎn)。這個(gè)yxx ab、梁的鏈接，鏈接o3f是iyy三個(gè)主要因素決定了豎向剛度。

圖-6 所示 鏈接的ab、梁公里，連接03f也是其中的三個(gè)主要因素決定的均勻性線性傳動(dòng)裝置、不同的分析結(jié)果表明，izz效果好，具有至少兩個(gè)垂直和水平剛度，這意味著這種結(jié)構(gòu)，具有足夠的水平，降低izz剛度的鏈接和增加iyy ab、梁的鏈接，鏈接o3f公里的好方法，優(yōu)化系統(tǒng)。

圖-5 瞬間的慣性效應(yīng)對(duì)垂直位移

圖-6 轉(zhuǎn)動(dòng)慣量不平衡的影響

2.2影響的線性驅(qū)動(dòng)器的相對(duì)位置

線性執(zhí)行器的慣性是主要載荷之一，在機(jī)械手的運(yùn)動(dòng)，不同的相對(duì)應(yīng)的垂直位置產(chǎn)生不同的變形，圖7顯示了絕對(duì)平均的最終效應(yīng)垂直位移時(shí)驅(qū)動(dòng)馬達(dá)以恒定的加速度旋轉(zhuǎn)，我們可以看到，過低或過高的相對(duì)位置會(huì)造成比格變形，最好的位置是一對(duì)z = 24毫米的地方大概是從中間環(huán)節(jié)連接o3f到 ab.圖-7

影響線性驅(qū)動(dòng)器的相對(duì)位置

分析改進(jìn)的機(jī)械手

根據(jù)上述模擬結(jié)果，所有改進(jìn)的機(jī)械手的設(shè)計(jì)，時(shí)間如下：鏈接截面ab，de，lj 與30mm的基礎(chǔ)和高度，10毫米的厚度;鏈接o3f和矩形空心梁與30mm的基礎(chǔ)和高度工型鋼，l0mm法蘭和6mm網(wǎng);梁競(jìng)，通用汽車與8mm的堅(jiān)實(shí)基礎(chǔ)和30mm高的矩形。

圖-8 梯形運(yùn)動(dòng)姿態(tài)

圖-9中回應(yīng)的是機(jī)械手，相比之下，圖-10中提高初始的反應(yīng)，在其中所有的鏈接和機(jī)械手的矩形截面梁的堅(jiān)實(shí)基礎(chǔ)，用30毫米，高度的差異是曲線，c和h的曲線積分，二是垂直位移的末端，改進(jìn)系統(tǒng)中最大位移0.7um最初的0.12um相比，爭(zhēng)論的振動(dòng)激勵(lì)后仍停留在o.06um±0.15% s±o.05um相比的初始變形改善系統(tǒng)的初始小于前者具有較少的慣性，因?yàn)樵谙嗤�的步伐不斷加快，保持振�?dòng)瓣膜差不多一樣，它對(duì)這整個(gè)系統(tǒng)中來說，仍然改善系統(tǒng)的剛度，幾乎相當(dāng)于初始制度，針對(duì)大規(guī)模的平面并聯(lián)機(jī)構(gòu)在該系統(tǒng)相比下降了30%，這樣的初始優(yōu)化是有效的。

圖-9、圖-10 動(dòng)態(tài)響應(yīng)

結(jié)論

本文設(shè)計(jì)了一種新型三自由度機(jī)械手變量的敏感性進(jìn)行了研究在adams環(huán)境中，可以得出以下結(jié)論：

1）機(jī)器人具有較大的水平剛度，最終水平位移，效應(yīng)主要是由機(jī)械手垂直變形造成的，因此，更重要的是增加的幅度比剛度豎向剛度。

2）參數(shù)ixx，iyy并鏈接'截面剛度izz有不同的效應(yīng)，iyy已經(jīng)對(duì)垂直剛度的影響最大，ixx在第二位的是，ixx具有在垂直剛度的影響最小，他們都較少對(duì)水平比垂直剛度剛度。3）橫截面的不同環(huán)節(jié)都有不同的影響，連線豎向剛度ab和德應(yīng)該使用區(qū)扭轉(zhuǎn)常數(shù)和慣性力矩大，如變形、長(zhǎng)方形、橫梁km，線 03f應(yīng)該使用區(qū)段形梁等重大時(shí)刻轉(zhuǎn)動(dòng)慣量、橫梁gk，和gm 可以使用盡可能的一小部分，從而降低了質(zhì)量。4）最佳的線性驅(qū)動(dòng)器的相對(duì)位置可以減少變形，最好的位置是垂直的平行結(jié)構(gòu)。5）改進(jìn)的機(jī)械手的動(dòng)態(tài)分析表明該優(yōu)化設(shè)計(jì)方法研究的基礎(chǔ)上的效率。

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六自由度并聯(lián)機(jī)器人篇四

robot robot is a type of mechantronics equipment which synthesizes the last research achievement of engine and precision engine, micro-electronics and computer, automation control and drive, sensor and message dispose and artificial intelligence and so the development of economic and the demand for automation control, robot technology is developed quickly and all types of the robots products are come into practicality use of robot products not only solves the problems which are difficult to operate for human being, but also advances the industrial automation present, the research and development of robot involves several kinds of technology and the robot system configuration is so complex that the cost at large is high which to a certain extent limit the robot abroad development economic practicality and high reliability robot system will be value to robot social application and economy the rapid progress with the control economy and expanding of the modern cities, the let of sewage is increasing quickly: with the development of modern technology and the enhancement of consciousness about environment reserve, more and more people realized the importance and urgent of sewage bacteria method is an effective technique for sewage disposal，the lacunaris plastic is an effective basement for active bacteria adhesion for sewage abundance requirement for lacunaris plastic makes it is a consequent for the plastic producing with automation and high ore, it is very necessary to design a manipulator that can automatically fulfill the plastic the analysis of the problems in the design of the plastic holding manipulator and synthesizing the robot research and development condition in recent years, a economic scheme is concluded on the basis of the analysis of mechanical configuration, transform system, drive device and control system and guided by the idea of the characteristic and complex of mechanical configuration, electronic, software and this article, the mechanical configuration combines the character of direction coordinate and the arthrosis coordinate which can improve the stability and operation flexibility of the main function of the transmission mechanism is to transmit power to implement department and complete the necessary this transmission structure, the screw transmission mechanism transmits the rotary motion into linear gear can give vary transmission of the transmission mechanisms have a characteristic of compact design of drive system often is limited by the environment condition and the factor of cost and technical lever.'the step motor can receive digital signal directly and has the ability to response outer environment immediately and has no accumulation error, which often is used in driving this driving system, open-loop control system is composed of stepping motor, which can satisfy the demand not only for control precision but also for the target of economic and this basis, the analysis of stepping motor in power calculating and style selecting is also analysis of kinematics and dynamics for object holding manipulator is given in completing the design of mechanical structure and drive tics analysis is the basis of path programming and track positive and reverse analysis of manipulator gives the relationship between manipulator space and drive space in position and relationship between manipulator’s tip position and arthrosis angles is concluded by coordinate transform geometry method is used in solving inverse kinematics problem and the result will provide theory evidence for control f0unction of dynamics is to get the relationship between the movement and force and the target is to satisfy the demand of real time this chamfer, newton-euripides method is used in analysis dynamic problem of the cleaning robot and the arthrosis force and torque are given which provide the foundation for step motor selecting and structure dynamic optimal l system is the key and core part of the object holding manipulator system design which will direct effect the reliability and practicality of the robot system in the division of configuration and control function and also will effect or limit the development cost and the demand of the pcl-839 card, the pc computer which has structure and is easy to be extended is used as the principal computer cell and takes the function of system initialization, data operation and dispose, step motor drive and error diagnose and so on.a t the same time, the configuration structure features, task principles and the position function with high precision of the control card pcl-839 are re is the matter foundation of the and the software is the spirit of the control target of the software is to combine all the parts in optimizing style and to improve the efficiency and reliability of the control software design of the object holding manipulator control system is divided into several blocks such as 2 system initialization block, data process block and error station detect and dispose model and so -839 card can solve the communication between the main computer and the control cells and take the measure of reducing the influence of the outer signal to the control start and stop frequency of the step motor is far lower than the maximum running order to improve the efficiency of the step motor, the increase and decrease of the speed is must considered when the step motor running in high speed and start or stop with great increase and decrease of the motor’s speed can be controlled by the pulse frequency sent to the step motor drive with a rational can be implemented either by hardware or by software.a step motor shift control method is proposed, which is simple to calculate, easy to realize and the theory means is motor' s acceleration can fit the torque-frequency curve properly with this the amount of calculation load is less than the linear acceleration shift control method and the method which is based on the exponential rule to change method is tested by last, the research content and the achievement are sum up and the problems and shortages in main the content are also development and application of robot in the future is expected.機(jī)器人

機(jī)器人是典型的機(jī)電一體化裝置，它綜合運(yùn)用了機(jī)械與精密機(jī)械、微電子與計(jì)算機(jī)、自動(dòng)控制與驅(qū)動(dòng)、傳感器與信息處理以及人工智能等多學(xué)科的最新研究成果，隨著經(jīng)濟(jì)的發(fā)展和各行各業(yè)對(duì)自動(dòng)化程度要求的提高，機(jī)器人技術(shù)得到了迅速發(fā)展，出現(xiàn)了各種各樣的機(jī)器人產(chǎn)品。機(jī)器人產(chǎn)品的實(shí)用化，既解決了許多單靠人力難以解決的實(shí)際問題，又促進(jìn)了工業(yè)自動(dòng)化的進(jìn)程。目前，由于機(jī)器人的研制和開發(fā)涉及多方面的技術(shù)，系統(tǒng)結(jié)構(gòu)復(fù)雜，開發(fā)和研制的成本普遍較高，在某種程度上限制了該項(xiàng)技術(shù)的廣泛應(yīng)用，因此，研制經(jīng)濟(jì)型、實(shí)用化、高可靠性機(jī)器人系統(tǒng)具有廣泛的社會(huì)現(xiàn)實(shí)意義和經(jīng)濟(jì)價(jià)值。

由于我國(guó)經(jīng)濟(jì)建設(shè)和城市化的快速發(fā)展，城市污水排放量增長(zhǎng)很快，污水處理己經(jīng)擺在了人們的議事日程上來。隨著科學(xué)技術(shù)的發(fā)展和人類知識(shí)水平的提高，人們?cè)絹碓秸J(rèn)識(shí)到污水處理的重要性和迫切性，科學(xué)家和研究人員發(fā)現(xiàn)塑料制品在水中是用于污水處理的很有效的污泥菌群的附著體。塑料制品的大量需求，使得塑料制品生產(chǎn)的自動(dòng)化和高效率要求成為經(jīng)濟(jì)發(fā)展的必然。

本文結(jié)合塑料一次擠出成型機(jī)和塑料抓取機(jī)械手的研制過程中出現(xiàn)的問題，綜述近幾年機(jī)器人技術(shù)研究和發(fā)展的狀況，在充分發(fā)揮機(jī)、電、軟、硬件各自特點(diǎn)和優(yōu)勢(shì)互補(bǔ)的基礎(chǔ)上，對(duì)物料抓取機(jī)械手整體機(jī)械結(jié)構(gòu)、傳動(dòng)系統(tǒng)、驅(qū)動(dòng)裝置和控制系統(tǒng)進(jìn)行了分析和設(shè)計(jì)，提出了一套經(jīng)濟(jì)型設(shè)計(jì)方案。采用直角坐標(biāo)和關(guān)節(jié)坐標(biāo)相結(jié)合的框架式機(jī)械結(jié)構(gòu)形式，這種方式能夠提高系統(tǒng)的穩(wěn)定性和操作靈活性。傳動(dòng)裝置的作用是將驅(qū)動(dòng)元件的動(dòng)力傳遞給機(jī)器人機(jī)械手相應(yīng)的執(zhí)行機(jī)構(gòu)，以實(shí)現(xiàn)各種必要的運(yùn)動(dòng)，傳動(dòng)方式上采用結(jié)構(gòu)緊湊、傳動(dòng)比大的蝸輪蝸桿傳動(dòng)和將旋轉(zhuǎn)運(yùn)動(dòng)轉(zhuǎn)換為直線運(yùn)動(dòng)的螺旋傳動(dòng)。機(jī)械手驅(qū)動(dòng)系統(tǒng)的設(shè)計(jì)往往受到作業(yè)環(huán)境條件的限制，同時(shí)也要考慮價(jià)格因素的影響以及能夠達(dá)到的技術(shù)水平。由于步進(jìn)電機(jī)能夠直接接收數(shù)字量，響應(yīng)速度快而且工作可靠并無累積誤差，常用作數(shù)字控制系統(tǒng)驅(qū)動(dòng)機(jī)構(gòu)的動(dòng)力元件，因此，在驅(qū)動(dòng)裝置中采用由步進(jìn)電機(jī)構(gòu)成的開環(huán)控制方式，這種方式既能滿足控制精度的要求，又能達(dá)到經(jīng)濟(jì)性、實(shí)用化目的，在此基礎(chǔ)上，對(duì)步進(jìn)電機(jī)的功率計(jì)一算及選型問題經(jīng)行了分析。

在完成機(jī)械結(jié)構(gòu)和驅(qū)動(dòng)系統(tǒng)設(shè)計(jì)的基礎(chǔ)上，對(duì)物料抓取機(jī)械手運(yùn)動(dòng)學(xué)和動(dòng)力學(xué)進(jìn)行了分析。運(yùn)動(dòng)學(xué)分析是路徑規(guī)劃和軌跡控制的基礎(chǔ)，對(duì)操作臂進(jìn)行了運(yùn)動(dòng)學(xué)正、逆問題的分析可以完成操作空間位置和速度向驅(qū)動(dòng)空間的映射，采用齊次坐標(biāo)變換法得到了操作臂末端位置和姿態(tài)隨關(guān)節(jié)夾角之間的變換關(guān)系，采用幾何法分析了操作臂的逆向運(yùn)動(dòng)學(xué)方程求解問題，對(duì)控制系統(tǒng)設(shè)計(jì)提供了理論依據(jù)。機(jī)器人動(dòng)力學(xué)是研究物體的運(yùn)動(dòng)和作用力之間的關(guān)系的科學(xué)，研究的目的是為了4 滿足是實(shí)時(shí)性控制的需要，本文采用牛頓-歐拉方法對(duì)物料抓取機(jī)械手動(dòng)力學(xué)進(jìn)行了分析，計(jì)算出了關(guān)節(jié)力和關(guān)節(jié)力矩，為步進(jìn)電機(jī)的選型和動(dòng)力學(xué)分析與結(jié)構(gòu)優(yōu)化提供理論依據(jù)。

控制部分是整個(gè)物料抓取機(jī)械手系統(tǒng)設(shè)計(jì)關(guān)鍵和核心，它在結(jié)構(gòu)和功能上的劃分和實(shí)現(xiàn)直接關(guān)系到機(jī)器人系統(tǒng)的可靠性、實(shí)用性，也影響和制約機(jī)械手系統(tǒng)的研制成本和開發(fā)周期。在控制主機(jī)的選用上，采用結(jié)構(gòu)緊湊、擴(kuò)展功能強(qiáng)和可靠性高的pc工業(yè)控制計(jì)算機(jī)作為主機(jī)，配以pcl-839卡主要承擔(dān)系統(tǒng)功能初始化、數(shù)據(jù)運(yùn)算與處理、步進(jìn)電機(jī)驅(qū)動(dòng)以及故障診斷等功能;同時(shí)對(duì)pcl-839卡的結(jié)構(gòu)特點(diǎn)、功能原理和其高定位功能等給與了分析。硬件是整個(gè)控制系統(tǒng)以及極限位置功能賴以存在的物質(zhì)基礎(chǔ)，軟件則是計(jì)算機(jī)控制系統(tǒng)的神經(jīng)中樞，軟件設(shè)計(jì)的目的是以最優(yōu)的方式將各部分功能有機(jī)的結(jié)合起來，使系統(tǒng)具有較高的運(yùn)行效率和較強(qiáng)的可靠性。在物料抓取機(jī)械手軟件的設(shè)計(jì)上，采用的是模塊化結(jié)構(gòu)，分為系統(tǒng)初始化模塊、數(shù)據(jù)處理模塊和故障狀態(tài)檢測(cè)與處理等幾部分。主控計(jì)算機(jī)和各控制單元之間全部由pcl-839卡聯(lián)系，并且由該卡實(shí)現(xiàn)抗干擾等問題，減少外部信號(hào)對(duì)系統(tǒng)的影響。

步進(jìn)電機(jī)的啟停頻率遠(yuǎn)遠(yuǎn)小于其最高運(yùn)行頻率，為了提高工作效率，需要步進(jìn)電機(jī)高速運(yùn)行并快速啟停時(shí)，必須考慮它的升，降速控制問題。電機(jī)的升降速控制可以歸結(jié)為以某種合理的力一式控制發(fā)送到步進(jìn)電機(jī)驅(qū)動(dòng)器的脈沖頻率，這可由硬件實(shí)現(xiàn)，也可由軟件方法來實(shí)現(xiàn)。本文提出了一種算法簡(jiǎn)單、易于實(shí)現(xiàn)、理論意義明確的步進(jìn)電機(jī)變速控制策略:定時(shí)器常量修改變速控制方案。該方法能使步進(jìn)電機(jī)加速度與其力矩——頻率曲線較好地?cái)M合，從而提高變速效率。而且它的計(jì)算量比線性加速度變速和基于指數(shù)規(guī)律加速度的變速控制小得多。通過實(shí)驗(yàn)證明了該方法的有效性。

最后，對(duì)論文主要研究?jī)?nèi)容和取得的技術(shù)成果進(jìn)行了總結(jié)，提出了存在的問題和不足，同時(shí)對(duì)機(jī)器人技術(shù)的發(fā)展和應(yīng)用進(jìn)行了展望。

六自由度并聯(lián)機(jī)器人篇五

improved genetic algorithm and its performance analysis

abstract: although genetic algorithm has become very famous with its global searching, parallel computing, better robustness, and not needing differential information during r, it also has some demerits, such as slow convergence this paper, based on several general theorems, an improved genetic algorithm using variant chromosome length and probability of crossover and mutation is proposed, and its main idea is as follows : at the beginning of evolution, our solution with shorter length chromosome and higher probability of crossover and mutation;and at the vicinity of global optimum, with longer length chromosome and lower probability of crossover and y, testing with some critical functions shows that our solution can improve the convergence speed of genetic algorithm significantly , its comprehensive performance is better than that of the genetic algorithm which only reserves the best c algorithm is an adaptive searching technique based on a selection and reproduction mechanism found in the natural evolution process, and it was pioneered by holland in the has become very famous with its global searching, parallel computing, better robustness, and not needing differential information during r, it also has some demerits, such as poor local searching, premature converging, as well as slow convergence recent years, these problems have been this paper, an improved genetic algorithm with variant chromosome length and variant probability is g with some critical functions shows that it can improve the convergence speed significantly, and its comprehensive performance is better than that of the genetic algorithm which only reserves the best section 1, our new approach is h optimization examples, in section 2, the efficiency of our algorithm is compared with the genetic algorithm which only reserves the best section 3 gives out the y, some proofs of relative theorems are collected and presented in ption of the algorithm 1.1 some theorems before proposing our approach, we give out some general theorems(see

appendix)as follows: let us assume there is just one variable(multivariable can be divided into many sections, one section for one variable)x ∈ [ a, b ] , x ∈ r, and chromosome length with binary encoding is m 1

minimal resolution of chromosome is s = b?a 2l?1theorem 2

weight value of the ith bit of chromosome is

wi = b?ai?1(i = 1,2,…l)2l?1theorem 3

mathematical expectation ec(x)of chromosome searching step with one-point crossover is ec(x)= b?apc 2lwhere pc is the probability of m 4

mathematical expectation em(x)of chromosome searching step with bit mutation is em(x)=(b-a)pm

1.2 mechanism of algorithm

during evolutionary process, we presume that value domains of variable are fixed, and the probability of crossover is a constant, so from theorem 1 and 3, we know that the longer chromosome length is, the smaller searching step of chromosome, and the higher resolution;and vice ile, crossover probability is in direct proportion to searching theorem 4, changing the length of chromosome does not affect searching step of mutation, while mutation probability is also in direct proportion to searching the beginning of evolution, shorter length chromosome(can be too shorter, otherwise it is harmful to population diversity)and higher probability of crossover and mutation increases searching step, which can carry out greater domain searching, and avoid falling into local at the vicinity of global optimum, longer length chromosome and lower probability of crossover and mutation will decrease searching step, and longer length chromosome also improves resolution of mutation, which avoid wandering near the global optimum, and speeds up algorithm

y, it should be pointed out that chromosome length changing keeps individual fitness unchanged, hence it does not affect select ion(with roulette wheel selection).1.3 description of the algorithm

owing to basic genetic algorithm not converging on the global optimum, while the genetic algorithm which reserves the best individual at current generation can, our approach adopts this evolutionary process, we track cumulative average of individual average fitness up to current is written as 1x(t)= gg?ft?1avg(t)where g is the current evolutionary generation, is individual average when the cumulative average fitness increases to k times(k> 1, k ∈ r)of initial individual average fitness, we change chromosome length to m times(m is a positive integer)of itself , and reduce probability of crossover and mutation, which can improve individual resolution and reduce searching step, and speed up algorithm procedure is as follows:

step 1 initialize population, and calculate individual average fitness and set change parameter equal to 0, step 2 based on reserving the best individual of current generation, carry out selection, regeneration, crossover and mutation, and calculate cumulative average of individual average fitness up to current generation

favg;

favgstep 3 if

favg0≥k and flag equals 1, increase chromosome length to m times of itself, and reduce probability of crossover and mutation, and set flag equal to 0;otherwise continue 4 if end condition is satisfied, stop;otherwise go to step 2.2 test and analysis

we adopt the following two critical functions to test our approach, and compare it with the genetic algorithm which only reserves the best individual: f1(x,y)?0.5?sin2x2?y2?0.5[1?0.01x?y?222?]

x,y∈ [?5,5]

[?1,1] f2(x,y)?4?(x2?2y2?0.3cos(3πx)?0.4cos(4πy))

x,y∈2.1 analysis of convergence during function testing, we carry out the following policies: roulette wheel select ion, one point crossover, bit mutation, and the size of population is 60, l is chromosome length, pc and pm are the probability of crossover and mutation we randomly select four genetic algorithms reserving best individual with various fixed chromosome length and probability of crossover and mutation to compare with our .1 gives the average converging generation in 100 our approach, we adopt initial parameter l0= 10, pc0= 0.3, pm0= 0.1 and k= 1.2, when changing parameter condition is satisfied, we adjust parameters to l= 30, pc= 0.1, pm= tab.1, we know that our approach improves convergence speed of genetic algorithm significantly and it accords with above analysis.2.2 analysis of online and offline performance

quantitative evaluation methods of genetic algorithm are proposed by dejong, including online and offline former tests dynamic performance;and the latter evaluates convergence better analyze online and offline performance of testing function, w e multiply fitness of each individual by 10, and we give a curve of 4 000 and 1 000 generations for f1 and f2, respectively.(a)online

(b)online

fig.1 online and offline performance of f1

(a)online

(b)online

fig.2 online and offline performance of f2

from fig.1 and fig.2, we know that online performance of our approach is just little worse than that of the fourth case, but it is much better than that of the second, third and fifth case, whose online performances are nearly the the same time, offline performance of our approach is better than that of other four sion in this paper, based on some general theorems, an improved genetic algorithm using variant chromosome length and probability of crossover and mutation is g with some critical functions shows that it can improve convergence speed of genetic algorithm significantly, and its comprehensive performance is better than that of the genetic algorithm which only reserves the best ix with the supposed conditions of section 1, we know that the validation of theorem 1 and theorem 2 are m 3 mathematical expectation ec(x)of chromosome searching step with one point crossover is b?apc2lec(x)=

where pc is the probability of

as shown in fig.a1, we assume that crossover happens on the kth locus, ’s locus from k to l do not change, and genes on the locus from 1 to k are exchanged.1during crossover, change probability of genes on the locus from 1 to k is 2

(“1” to “0” or “0” to “1”).so, after crossover, mathematical expectation of chromosome searching step on locus from 1 to k is

k11b?a1b?aeck(x)??wj???l?2j?1??l?(2k?1)

22?12?1j?12j?12furthermore, probability of taking place crossover on each locus of k1chromosome is equal, namely l ore, after crossover, mathematical expectation of chromosome searching step is 1ec(x)???pc?eck(x)

k?1lsubstituting eq.(a1)into eq.(a2), we obtain l?1pb?ap?(b?a)11b?a1?pc??l?(2k?1)?c?l?[(2i?1)?l]?c(1?l)22?12l2?12l2?1k?1llb?a?0, so ec(x)?pc where l is large, l2l2?1ec(x)??l?1

fig.a1 one point crossover

theorem 4 mathematical expectation em(x)of chromosome searching step with bit mutation em(x)?(b?a)?pm, where pm is the probability of mutation probability of genes on each locus of chromosome is equal, say pm, therefore, mathematical expectation of mutation searching step is em(x)=?pm·wi=?pm·i=1i=1llb-ai-1b-a·2=p··(2i-1)=(b-a)·pm mli2-12-1

一種新的改進(jìn)遺傳算法及其性能分析

摘要：雖然遺傳算法以其全局搜索、并行計(jì)算、更好的健壯性以及在進(jìn)化過程中不需要求導(dǎo)而著稱，但是它仍然有一定的缺陷，比如收斂速度慢。本文根據(jù)幾個(gè)基本定理，提出了一種使用變異染色體長(zhǎng)度和交叉變異概率的改進(jìn)遺傳算法，它的主要思想是：在進(jìn)化的開始階段，我們使用短一些的變異染色體長(zhǎng)度和高一些的交叉變異概率來解決，在全局最優(yōu)解附近，使用長(zhǎng)一些的變異染色體長(zhǎng)度和低一些的交叉變異概率。最后，一些關(guān)鍵功能的測(cè)試表明，我們的解決方案可以顯著提高遺傳算法的收斂速度，其綜合性能優(yōu)于只保留最佳個(gè)體的遺傳算法。

遺傳算法是一種以自然界進(jìn)化中的選擇和繁殖機(jī)制為基礎(chǔ)的自適應(yīng)的搜索技術(shù)，它是由holland 1975年首先提出的。它以其全局搜索、并行計(jì)算、更好的健壯性以及在進(jìn)化過程中不需要求導(dǎo)而著稱。然而它也有一些缺點(diǎn)，如本地搜索不佳，過早收斂，以及收斂速度慢。近些年，這個(gè)問題被廣泛地進(jìn)行了研究。

本文提出了一種使用變異染色體長(zhǎng)度和交叉變異概率的改進(jìn)遺傳算法。一些關(guān)鍵功能的測(cè)試表明，我們的解決方案可以顯著提高遺傳算法的收斂速度，其綜合性能優(yōu)于只保留最佳個(gè)體的遺傳算法。

在第一部分，提出了我們的新算法。第二部分，通過幾個(gè)優(yōu)化例子，將該算法和只保留最佳個(gè)體的遺傳算法進(jìn)行了效率的比較。第三部分，就是所得出的結(jié)論。最后，相關(guān)定理的證明過程可見附錄。

1算法的描述

1.1 一些定理

在提出我們的算法之前，先給出一個(gè)一般性的定理（見附件），如下：我們假設(shè)有一個(gè)變量（多變量可以拆分成多個(gè)部分，每一部分是一個(gè)變量）x ∈ [ a, b ] , x ∈ r，二進(jìn)制的染色體編碼是1.定理1 染色體的最小分辨率是

s =

b?a l2?1定理2 染色體的第i位的權(quán)重值是

b?ai?1(i = 1,2,…l)2l?1定理3 單點(diǎn)交叉的染色體搜索步驟的數(shù)學(xué)期望ec(x)是

wi =

ec(x)= b?apc 2l其中pc是交叉概率

定理4 位變異的染色體搜索步驟的數(shù)學(xué)期望em(x)是

em(x)=(b-a)pm

其中pm是變異概率 算法機(jī)制

在進(jìn)化過程中，我們假設(shè)變量的值域是固定的，交叉的概率是一個(gè)常數(shù)，所以從定理1 和定理3我們知道，較長(zhǎng)的染色體長(zhǎng)度有著較少的染色體搜索步驟和較高的分辨率；反之亦然。同時(shí)，交叉概率與搜索步驟成正比。由定理4，改變?nèi)旧�體的長(zhǎng)度不影響變異的搜索步驟，而變異概率與搜索步驟也是成正比的。

進(jìn)化的開始階段，較短染色體（可以是過短，否則它不利于種群多樣性）和較高的交叉和變異概率會(huì)增加搜索步驟，這樣可進(jìn)行更大的域名搜索，避免陷入局部最優(yōu)。而全局最優(yōu)的附近，較長(zhǎng)染色體和較低的交叉和變異概率會(huì)減少搜索的步驟，較長(zhǎng)的染色體也提高了變異分辨率，避免在全局最優(yōu)解附近徘徊，提高了算法收斂速度。

最后，應(yīng)當(dāng)指出，染色體長(zhǎng)度的改變不會(huì)使個(gè)體適應(yīng)性改變，因此它不影響選擇（輪盤賭選擇）。

算法描述

由于基本遺傳算法沒有在全局優(yōu)化時(shí)收斂，而遺傳算法保留了當(dāng)前一代的最佳個(gè)體，我

們的方法采用這項(xiàng)策略。在進(jìn)化過程中，我們跟蹤到當(dāng)代個(gè)體平均適應(yīng)度的累計(jì)值。它被寫成：

1gx(t)= favg(t)?gt?1其中g(shù)是當(dāng)前進(jìn)化的一代，favg是個(gè)體的平均適應(yīng)度。

當(dāng)累計(jì)平均適用性增加到最初個(gè)體平均適應(yīng)度的k(k> 1, k ∈ r)倍，我們將染色體長(zhǎng)度變?yōu)槠渥陨淼膍(m 是一個(gè)正整數(shù))倍，然后減小交叉和變異的概率，可以提高個(gè)體分辨率、減少搜索步驟以及提高算法收斂速度。算法的執(zhí)行步驟如下：

第一步：初始化群體，并計(jì)算個(gè)體平均適應(yīng)度favg0，然后設(shè)置改變參數(shù)的標(biāo)志flag。flag設(shè)為1.第二步：在所保留的當(dāng)代的最佳個(gè)體，進(jìn)行選擇、再生、交叉和變異，并計(jì)算當(dāng)代個(gè)體的累積平均適應(yīng)度favg

favg0第三步：如果

favg?k 且flag = 1，把染色體的長(zhǎng)度增加至自身的m倍，減少交叉和變異概率，并設(shè)置flag等于0;否則繼續(xù)進(jìn)化。

第四步：如果滿足結(jié)束條件，停止；否則轉(zhuǎn)自第二步。

測(cè)試和分析

我們采用以下兩種方法來測(cè)試我們的方法，和只保留最佳個(gè)體的遺傳算法進(jìn)行比較：

f1(x,y)?0.5?sin2x2?y2?0.5[1?0.01x?y?222?] [?5,5]

x,y∈ [?1,1] f2(x,y)?4?(x2?2y2?0.3cos(3πx)?0.4cos(4πy))

x,y∈收斂的分析

在功能測(cè)試中，我們進(jìn)行了以下政策：輪盤賭選擇，單點(diǎn)交叉，位變異。種群的規(guī)

模是60。l是染色體長(zhǎng)度，pc和pm分別是交叉概率和變異概率。我們隨機(jī)選擇4個(gè)遺傳算法所保留的最佳個(gè)體來與我們的方法進(jìn)行比較，它們具有不同的固定染色體長(zhǎng)度和交叉和變異的概率。表1給出了在100次測(cè)試的平均收斂代。

在我們的方法中，我們采取的初始參數(shù)是l0 = 10，pc0 = 0.3，pm0 = 0.1和k = 1.2，當(dāng)滿足改變參數(shù)的條件時(shí)，我們調(diào)整參數(shù)l = 30，pc = 0.1，pm = 0.01。

1.1 在線和離線性能的分析

dejong提出了遺傳算法的定量評(píng)價(jià)方法，包括在線和離線性能評(píng)價(jià)。前者測(cè)試動(dòng)態(tài)性能，而后者評(píng)估收斂性能。為了更好地分析測(cè)試功能的在線和離線性能，我們把個(gè)體的適應(yīng)性乘以10，并f1和f2分別給出了4 000和1 000代的曲線：

(a)在線

(b)離線

圖1 f1的在線與離線性能

(a)在線

(b)離線

從圖1和圖2可以看出，我們方法的在線性能只比第四種情況差一點(diǎn)點(diǎn)，但比第二種、第三種、第五種好很多，這幾種情況下的在線性能幾乎完全相同。同時(shí)，我們方法的離線性能也比其他四種好很多

結(jié)論

本文提出了一種使用變異染色體長(zhǎng)度和交叉變異概率的改進(jìn)遺傳算法。一些關(guān)鍵功能的測(cè)試表明，我們的解決方案可以顯著提高遺傳算法的收斂速度，其綜合性能優(yōu)于只保留最佳個(gè)體的遺傳算法。

附件

有了第一部分中假定的條件，定理1和定理2的驗(yàn)證是顯而易見的。下面給出定理3和定理4的證明過程：

定理3 單點(diǎn)交叉的染色體搜索步驟的數(shù)學(xué)期望ec(x)是

ec(x)= 其中pc是交叉概率

b?apc 2l證明：

如圖a1所示，我們假設(shè)交叉發(fā)生在第k個(gè)基因位點(diǎn)，從k到l的父基因位點(diǎn)沒有變化，基因位點(diǎn)1到k上的基因改變了。

在交叉過程中，1到k基因位點(diǎn)上的基因改變的概率為0.5(“1”變化”0”或者”0”變?yōu)椤?”)，因此，交叉之后，基因位點(diǎn)上的染色體搜索步驟從1到k的數(shù)學(xué)期望是

k11b?a1b?aeck(x)??wj???l?2j?1??l?(2k?1)

22?12?1j?12j?121此外，每個(gè)位點(diǎn)的染色體發(fā)生交叉的概率是相等的，即lpc。交叉后，染色

k體搜索步驟的數(shù)學(xué)期望是

1ec(x)???pc?eck(x)k?1l

把eq.(a1)替換為eq.(a2)，我們得到 l?1pb?ap?(b?a)11b?a1?pc??l?(2k?1)?c?l?[(2i?1)?l]?c(1?l)l22l2l2?12?12?1k?1lb?a?0，所以ec(x)?pc 其中l(wèi)是非常大的，l2l2?1ec(x)??l?1圖1 單點(diǎn)交叉

定理4 位變異的染色體搜索步驟的數(shù)學(xué)期望是

em(x)?(b?a)?pm

其中pm是變異概率。證明：

每個(gè)基因位點(diǎn)上的基因的變異概率是相等的，比如pm，因此變異搜索步驟的數(shù)學(xué)期望是：

em(x)=?pm·wi=?pm·i=1i=1ll

b-ai-1b-a·2=p··(2i-1)=(b-a)·pmmli2-12-1