外文翻譯--輕量級絲杠作動器設計在便攜的機器人的應用

1、<p>　　輕量級絲杠作動器設計在便攜的機器人的應用</p><p><b>　　機械設計報</b></p><p>　　凱文·W.霍蘭德·托馬斯G.唐</p><p>　　一個便攜機器人是直接與它的用戶聯(lián)系的一個受控和開動的設備。同樣，也要求這個設備必須也是便攜的，輕量級的，最重要的是安全的。為了達到這些目標。標

2、準絲杠的設計通常不能很好的按要求執(zhí)行這些。典型的絲杠有很低投球角度和大的半徑，從而產生很低的機械效率和很大的重量?？墒?，使用文本中的設計程序，效率和重量是被改進的; 因而可以產生一種與人的肌肉相似的絲杠系統(tǒng)。例子中的問題說明一個可行性的絲杠設計應該是277 的功率質量比，接近驅動它的馬達，即312W/kg，并且機械效率為0.74和最大動能到11.3 kN/kg的絲杠設計。 </p><p><b>　　

3、1引言</b></p><p>　　在美國，有五分之一的人有不同形式的殘疾，這些人當中，61％的人患有感覺或身體殘疾。在老年人中，8％到19 ％是步態(tài)失調。許多殘疾人可以獨立的受益于某種形式機器人的協(xié)助。一個便攜機器人是一個被計算機控制和驅動的裝置，是直接接觸用戶的。這種裝置的目的是增強用戶的行為能力。在病人治療期間，它可以用于訓練，或是僅僅當作一種協(xié)助病人完成日常生活的裝置。"便攜&quo

4、t;的含義是指機器人必須攜帶方便，重量輕，而且安全是最重要的。相比之下，工廠車間的機器人是沒有這些功能的，因此，要簡單修改現(xiàn)有的技術是不可能實現(xiàn)的。設計便攜機器人的標準方法有三大局限性;</p><p><b>　　1低電池功率密度；</b></p><p>　　2電機的低強度質量比；</p><p>　　3重量和安全性的機械傳動系統(tǒng)。<

5、/p><p>　　這些工作的目的是審查絲杠驅動器的設計過程;結果顯示在局限性第三項方面有了重大改進，即，重量和安全性的機械傳動系統(tǒng)。</p><p><b>　　2 背景</b></p><p>　　有趣的是，在便攜機器人學領域的研究已經超過了過去十年的增長。最近，浪涌的利益可以歸因于電子小型化、微處理器能力和無線技術擴散的推進。提高便攜計算機控制

6、設備的能力的可行性是可以實現(xiàn)的。</p><p>　　然而，除便攜式的計算平臺的可及性之外，必須談及物理機制的問題。在便攜機器人發(fā)展中，主要的問題是強度質量比、重量和安全。有多少可利用的動力可完成機械功？機器人設備有多少額外的力給人？還有，如何轉移這些動力和怎么一直維護安全等？用戶和開動的機器人之間的安全互作用在便攜機器人設計中是一個首要問題。</p><p>　　一個便攜的機器人系統(tǒng)的目

7、的是將操作員通過存貯設備獲得的努力和能量抵消，即，電池、燃料電池和空氣坦克。作動器的效率和整個系統(tǒng)的重量沉重影響分享在操作員和機器人之間的工作負擔。在很多情況下，機器人加給用戶的額外力量，能多完成一項測量任務。這意味著機器人不僅必須增添操作員的能力，也必須補嘗它自己另外的重量。</p><p>　　2.1 作動器的比較。</p><p>　　很多機器人作動器被比作成人的骨骼肌的標準。設計師

8、了解他們好的功率強度比和優(yōu)秀的強制生產能力就是為了動作器與骨骼肌相比擬。為了匹配骨骼肌的性能，重要的是知道其中一些措施。不幸地是，生物文學中的普遍性是:被測量的肌肉參數(shù)是變化繁多的。雖然報告參數(shù)有一個寬的變化，這些參數(shù)一直能給生物材料行為標度的感覺。制成表的數(shù)據(jù)和幾個原始估計數(shù)據(jù)被用于描述人的肌肉表現(xiàn)屬性和結果如表1所示。</p><p>　　表1：作動器比較：通過機械效率，勢能，和校正動能對各種各樣的作動器類型

9、進行比較：</p><p>　　允許與有效能的運用直接進行比較。然而，在便攜機器人作動器的發(fā)展中這兩個參量需要得到審查。考慮到所有作動器在100%效率中運行，然后整個小組能直接地由他們各自的功率強度比進行比較?？墒牵绻麆菽苤械膭恿Ρ惶峁┙o每臺作動器，由于他們各自的效率僅僅是輸出一小部分動力。所以，適當?shù)乇容^上面被描述的作動器，他們校正的勢能必須計算,即：</p><p><b>

10、;　　(1)</b></p><p>　　機械效率和Pwt是原始的功率質量比。對各種動作器演算的結果如表1所示</p><p>　　表1的內容是從文獻或基于那些文獻的估計中獲得的。dc馬達的參數(shù)是:Maxon RE40馬達。 傳動箱組合的參數(shù)在Maxon 2004編目中能夠找到。一臺電系列有彈性作動器的參數(shù)用于估計這些參數(shù)。然而，一個一般大小的絲杠系統(tǒng)可能有更好的強度質量比，因

11、為它有很高的負載能力，并且有很低的重量。對于McKibben樣式的空氣肌肉，從各種各樣文獻中發(fā)現(xiàn)了描述它的相關方法。</p><p>　　比較中顯然顯示的是校正功率質量比，cP，dc馬達的參數(shù)，空氣肌肉和人的骨骼肌是都是簡單匹配的。然而，馬達上一旦加上額外的硬件，它的執(zhí)行力會極大減小。基于動作器的重量，如果能修改一個不是很大的dc馬達重量的機械傳動系統(tǒng)，則它接近于人的骨骼肌的功能可能會實現(xiàn)。</p>

12、<p><b>　　3絲杠設計</b></p><p>　　如上所見，當一個典型絲杠系統(tǒng)與其他便攜機器人作動器在概念上進行比較時，它的性能是有限的。產生這種低性能的主要原因是它的機械效率很低。如果在一個標準絲杠系統(tǒng)中使用大約是=0.36的摩擦系數(shù)，會有更好的潤滑效果。</p><p>　　相反，典型的球螺絲系統(tǒng)有非常好機械效率。 滾珠軸承的滾動接觸對這個系

13、統(tǒng)的摩擦作用會保持很低。然而，效率雖然有了改進，球螺絲作動器的cPt參數(shù)仍然低于那骨骼肌，這是因為球螺絲系統(tǒng)的重量很大。如果改進球螺絲的cP性能，那么重量的減少就可以實現(xiàn)了。</p><p><b>　　機械設計學報</b></p><p>　　圖1 絲杠外形; 主角l…在一個單一螺旋螺絲中是等效的</p><p>　　用于設計圍攏絲杠的基本數(shù)

14、學也適用于球螺絲系統(tǒng)。這兩個機械傳輸之間的主要差別是他們的摩擦系數(shù)。在以下部分會考慮影響絲杠重量和機械效率的設計參數(shù)，并且對它的cP進行改進。</p><p><b>　　3.1絲杠外形</b></p><p>　　在圖1顯示的是普通絲杠的基本外形。絲杠的關鍵參量是主角l，螺絲半徑r和前置角。主角l是螺絲每次改進達到的位移數(shù)量，一個高精度螺絲有非常小或非常好的主角。在

15、圖1的正三角形顯示的螺絲的唯一一次改進被剝開的構造。前置角代表螺紋的斜面或傾斜度。 三角的基礎是螺絲軸的圓周，三角形的右腿是它的主角，螺線螺紋的弦代表路徑長度。</p><p>　　并且在正三角形中看出使螺母舉起負載的強大的力。負載的力量顯示為F，螺絲的扭矩強度是F,在螺絲螺紋上的正常反作用力是N，并且摩擦力是N。從這張圖中，舉起的扭矩的等式就可以是：</p><p><b>　

16、　(2)</b></p><p><b>　　3.2 對R。</b></p><p>　　還考慮，絲杠的外形在圖1可以顯示主角 l是由螺絲半徑r和前置角描述的。這些可改變量之間的關系是：</p><p><b>　　(3)</b></p><p><b>　　(4)</b

17、></p><p>　　公式4的意思是r、螺絲半徑和，前置角，都是需要螺絲主角l的。這意味著在r和之間存在一個連續(xù)的關系。雖然存在這個連續(xù)的關系，多數(shù)螺絲系統(tǒng)還是被設計成非常小的前置角。從首選螺絲大小的經驗來看，雖然各自的直徑都在變化，但前置角都小于3°。</p><p>　　在公式4種顯示對所有螺絲主角的需求，各種各樣的半徑都可以使用。這個意義在于螺絲半徑 r的變小，螺絲

18、的重量是通過r2減小的。因此，要補嘗小螺絲半徑，必須考慮前置角這個參數(shù)。 </p><p><b>　　前角，</b></p><p>　　圖2絲杠系統(tǒng)機械效率：遮蔽一部分的圖表多數(shù)是絲杠的典型設計區(qū)域。是小的，半徑大，重量大，并且效率是較低的。在圖表的未遮住的區(qū)域設計，是大的，暗示更小的半徑、更低的重量和更高的效率。</p><p>　　3

19、.3效率對阿爾法。</p><p>　　對于一個便攜機器人的設計，不僅絲杠作動器的重量是一個重要問題，而且作動器的效率也是非常關鍵的。如上所述，螺絲半徑的減小可以使動作器的重量大大減小。然而，要減小螺絲半徑，必須增加前置角 ，以保持恒定的主角。當看公式2時，可以看出要求承受負載的力矩Fw，取決于兩前置角和摩擦系數(shù).</p><p>　　影響螺絲效率的是前置角和摩擦系數(shù)，圖2顯示對摩擦系數(shù)_

20、和前置角_的沖擊在于絲杠系統(tǒng)的效率</p><p><b>　　(5)</b></p><p>　　在圖2的每條線是基于摩擦系數(shù)不同的參數(shù)。幾份普通的工程材料作為例子給讀者一個在絲杠系統(tǒng)中能有不同物質或涂層的作用的感覺。這個圖表示，當前置角增加，機械效率就增加; 或者至少到達一個峰值。</p><p>　　理論上，選擇最大效率采摘角度是有利的。

21、一個絲杠系統(tǒng)在高效率運行時需要使負載力矩達到最小Fw。在高峰值效率發(fā)生的角度可以取決于與角度效率有關的參數(shù)，結果是可以看到的。</p><p><b>　　(6)</b></p><p>　　雖然一個高前置角可能提高效率，但它也可能導致反驅動系統(tǒng)。一個反驅動系統(tǒng)是一種負載力矩，沒有力矩協(xié)助的情況下，螺絲可能自轉，因而允許負載自我降低。反驅動絲杠不適合應用于汽車起重器，

22、但是可以應用于便攜機器人當中。因此反驅動的前置角是：</p><p><b>　　(7)</b></p><p>　　不管產生多么高的負載力量，多么低的摩擦系數(shù)系統(tǒng)，前置角和摩擦系數(shù)總是影響這些條件的，例如球螺絲，反驅動是一個必然結果。</p><p><b>　　4 實用考慮</b></p><p&g

23、t;　　理論上，如先前的文獻所顯示，是希望螺絲半徑 r減小的，甚至到一個幾乎微觀尺度。然而，從設計和制造業(yè)方面來講，這不是一種實用的解決方案。雖然從重量和效率的角度來講小螺絲的直徑和高前置角是極其重要的，但他們可能不允許設計師適應物理系統(tǒng)的力量需要。例如軸向產生，壓縮折和機制困境都需要被考慮?？紤]到單一的超薄的螺絲也許是輕量級的，它可能沒有一個系統(tǒng)所需要足夠的負載能力。但可以使用單一的，或幾個螺絲，就會有足夠大的負載能力。用幾個小螺絲承

24、受大載荷是沒有重量優(yōu)勢的，作為因計算一個螺絲斷面產生的重量和壓強。然而，使用幾個小螺絲承受載荷可能允許對高前置角的持續(xù)使用和在高效率中運行，甚至在很高負載。通過推擠絲杠原材料物產極限，可以達到軸向很高的負載。這種工作方法的好處在于一個緊張系統(tǒng)比它壓縮軸承更好運作的系統(tǒng)。當考慮到減小一個既長又細的螺絲的負載時，類似于McKibben作動器甚至人的肌肉，（絲杠作動器能被設計負擔僅緊張裝載），因而消除共折的考慮。在一個便攜機器人中創(chuàng)建緊張驅動

25、系統(tǒng)不一定意味著需要一個對抗性。實際上，與一個協(xié)助機器人相比，殘疾人在做單一的直接動作時，肌肉存在弱點，因此，這些人是非常需要動</p><p>　　對于那些推擠螺絲半徑和因此導致前置角的極限超過最大效率的設計師，摩擦極限角度多少是可以傾斜的。所有這些的物理解釋是系統(tǒng)捆綁或鎖，由導出的公式2可以看見。一個由公式（2）導出，可以產生以下關系</p><p><b>　　(8)<

26、;/b></p><p>　　除被列出的實用考慮之外，還可能存在著許多其他問題。包括扭轉力僵硬或屈服力甚至熱擴散等。這些因素中的每一個都是重要的并且都需要我們考慮?？墒?，這個練習的目的是展示選擇一個設計或選擇螺絲系統(tǒng)的典型方法。這個選擇方法的好處是可直接適用于一個便攜機器人系統(tǒng)的設計。</p><p><b>　　5 例子中的問題</b></p>

27、<p>　　展示一份粗糙設計報告，考慮高峰距小腿關節(jié)扭矩在到一個有能力裝載80 kg的個體并且是0.8 Hz的跨步頻率期間的連接扭矩。在步態(tài)期間的腳腕扭矩峰值大約是100毫微米。這個峰值大致發(fā)生在45%的步態(tài)周期。步態(tài)周期是指一只腳跟的停止到這支腳跟下一次停止的時間。腳趾是承受另一只腿重力和開始搖擺的點。 搖擺階段的判斷是步態(tài)再次安置腳回到腳跟停止位置時，然后下一個步態(tài)周期開始。</p><p>　　例

28、如，讓我們考慮修造一個腳腕步態(tài)協(xié)助絲杠作動器。我們假設協(xié)助水平在30%左右和到小腿關節(jié)是12厘米的力矩臂。</p><p>　　表2作動器問題比較：絲杠設計I和II與人的肌肉的效率比較，對勢能的比較，校正勢能和動能的措施的比較。</p><p>　　這些參數(shù)都可以根據(jù)自己的個人經驗并且在合理的范圍內進行修改和變化。參數(shù)和可用的參量接近于Maxon馬達，即RE40，這個例子中，主角長度的范圍

29、已經確定了;它的范圍可以是</p><p>　　解決設計兩個絲杠的問題:第一個設計問題是解決最大效率。假設是2 mm和=0.05，螺絲在=43.5°、半徑是0.34mm 的地方產生的效率是90%。這樣小的一條半徑，需要多個螺絲承受負載。即使如此，估計作動器的勢能是280 W/kg 。通過馬達重量和預測的傳輸系統(tǒng)，劃分需要的功率峰值就可以得出勢能的大小。我們從以前的工作知道了，輔助組分的重量成比例可以減小

30、螺絲和螺釘?shù)闹亓俊?lt;/p><p>　　第二個設計，絲杠II，從商業(yè)供營商得到可利用的維度。 螺絲的=13.6°和0.82的效率。 更大一些的維度也可行，動作器的勢能最好是277 W/kg。為了達到比較的目的，這個例子出現(xiàn)的問題結果制成了表格。表2顯示兩個絲杠設計方案的數(shù)字結果。這些參數(shù)與先前的dc馬達參數(shù)和人的骨骼肌的估計值進行比較。通過例子，動能大小是基于力的峰值進行計算的。</p>

31、<p><b>　　6 討論</b></p><p>　　在分析解決最大效率的方案上，絲杠設計I顯示了一個單一小半徑螺絲永遠不會處理所要求的負載。可是，多個螺絲同時平行執(zhí)行那項任務會有同樣高的效率。雖然使用典型的技術不容易制造出一個0.34 mm半徑的螺絲，但用這種方法是可以實現(xiàn)的（即，使用多個螺絲產生高效率）。要設計一個特殊的絲杠，效率是沒有極限的。絲杠設計II顯示，有一種可行的

32、解決方案可以解決腳腕的問題，校正功率質量比參數(shù)使其非常接近于人的肌肉。使用一種相似的方法，球形螺絲機制能有益于它的表現(xiàn)，一般方法是創(chuàng)建一個驅動的背面，低重量和高效率的螺絲系統(tǒng)可以使基于dc馬達的動作器的便攜機器人應用有一種有力解答。</p><p>　　圖3 原型作動器，高效率絲杠</p><p>　　前面提到，一臺便攜機器人作動器不僅要有好的執(zhí)行能力，而且還要對它的用戶有一定的安全性。在

33、考慮安全方面時，（駕駛）是便攜絲杠作動器所需要的。（ 駕駛）允許操作者任意安裝沒有動力的螺釘，因而使它的阻礙減到最小。另一方面，在螺絲的末端設計一塊閑置的部分以防止馬達和用戶受到損壞。對人的損傷可以通過安置螺絲的末端范圍在用戶的生理安全極限內來避免，即一旦遇到危險強度，可以得到短期的脫離。所有這些方法都需要得到重點考慮，并且應該在設計過程中早期解決。安置機械部件必須包括特別的防備措施。 防備措施必須超出軟件或控制器范圍; 因此，在機械設

34、計中應該包括他們。保證用戶的安全是在設計所有協(xié)助機器人時應該是最優(yōu)先考慮的事，我們的實驗室也調查了便攜作動器的其他類型?？磮D3。這些技術幫助我們保持設備的整體大小和重量打到最低。</p><p><b>　　7 結論</b></p><p>　　一臺便攜機器人作動器必須有好的功率勢能比，好的機械效率，好的強度質量比，并且一定是安全的。對于一個具有好的功率的dc馬達，改

35、進它力量的唯一方法是增加傳動系統(tǒng)。傳統(tǒng)上，這種方法導致了dc馬達作動器功率質量比的增加以至于它的執(zhí)行力筆直下降?？墒?，我們的方法可以用于設計絲杠和球形絲杠的力，例如一個便攜的協(xié)助機器人。</p><p>　　Design of Lightweight Lead Screw Actuators for Wearable Robotic Applications</p><p>　　Journ

36、al of Mechanical Design</p><p>　　Kevin W. Hollander Thomas G. Sugar</p><p>　　A wearable robot is a controlled and actuated device that is in direct contact with its user. As such, the implied re

37、quirements of this device are that it must be portable, lightweight, and most importantly safe. To achieve these goals, The design of the standard lead screw does not normally perform well in any of these categories. The

38、 typical lead screw has low pitch angles and large radii, thereby yielding low mechanical efficiencies and heavy weight. However, using the design procedure outlin</p><p>　　1 Introduction</p><p>

39、;　　One in five persons in the United States live with some form of disability, with 61% of those suffering from either a sensory or physical disability.As an example, within the elderly population,8% to 19% are affected

40、by gait disorders . Many disabled individuals could benefit from some form of robotic intervention. A wearable robot is a computer controlled and actuated device that is in direct contact with its user. The purpose of su

41、ch a device is the performance/strength enhancement of the wear</p><p>　　1 Low battery power density；</p><p>　　2 motors with low “strength to weight” ratios；</p><p>　　3 weight and s

42、afety of a mechanical transmission system.</p><p>　　The goal of this work is to review the design process of a lead screw actuator; the result of which will demonstrate significant improvements over the limi

43、tations described in item number 3, i.e., the weight and safety of the mechanical transmission system.</p><p>　　2 Background</p><p>　　Interest in the area of wearable robotics has grown over the

44、 last decade. The recent surge of interest can be attributed to advancements in electronic miniaturization, microprocessor capabilities, and wireless technology proliferation. The feasibility of a portable computer contr

45、olled strength enhancing device is closer to reality</p><p>　　However, aside from the availability of portable computation platforms, issues of the physical mechanism must still be addressed. The main issues

46、 in any wearable robot development are power, weight, and safety. How much power is available to do mechanical work? How much additional weight does the robotic device add to the person? And, how can this power be transf

47、erred and still maintain safety? The safe interaction between the wearer and theactuated robot has to be the primary concern in a weara</p><p>　　The purpose of a wearable robotic system is to offset the effo

48、rt or energy of the operator by some amount of energy from a storage device, i.e., battery, fuel cell, and air tank. The sharing of the work load between the operator and the robot is heavily influenced by actuator effic

49、iencies and the overall system weight. The additional weight that the robot adds to the user, in many cases, can increase the total amount of work required to accomplish a given task. This means that the robot not only&l

50、t;/p><p>　　2.1 Actuator Comparisons. </p><p>　　Human skeletal muscle is the “gold” standard by which many robotic actuators are compared. Known for their good “power to weight” ratios and excellent

51、 force production capabilities, skeletal muscle performance is what most actuator designers would like to match. In order to match the performance capabilities of skeletal muscle, it is important to know some of its meas

52、ures. Unfortunately, common throughout biological literature is a wide variation of measured muscle properties. Although reported </p><p>　　Table1：Actuator comparison: Compares various actuator types by mech

53、anical efficiency, power to weight ratio, “corrected”power to weight ratio, and strength to weight ratio Measures</p><p>　　allows the direct comparisons to be made based upon utilization of available energy.

54、 However, both of these parameters need to be examined in the development of a wearable robotic actuator. Consider that if all actuators were to operate at 100% efficiency, then the entire group could be compared directl

55、y by their respective power to weight ratios. However, if only the power stated in the power to weight ratio were supplied to each actuator, then because of their respective efficiency, only a fra</p><p><

56、;b>　　(1)</b></p><p>　　where is the mechanical efficiency and Pwt is the original power to weight ratio. The results of this calculation for various kinds of actuators can be seen in Table 1.</p&

57、gt;<p>　　Values in Table 1 were obtained either by referenced literature or estimations based upon that literature. The values for the dc motor are for the Maxon RE40 motor. The values for the + gearbox combinatio

58、n were also found in the Maxon 2004 catalog. values from an electric Series Elastic Actuator were used to estimate these parameters. However, a similiarly sized lead screw system will likely have a better strength to wei

59、ght ratio, due to its ability to carry higher loads and its nut is of lower </p><p>　　Immediately evident in this comparison is that the corrected power to weight, cP, values of the dc motor, the air muscle

60、and human skeletal muscle are all similarly matched. However, once additional hardware is added to the dc motor, its performance decreases significantly. If one could create a mechanical transmission system that did not

61、significantly alter the weight of the dc motor based actuator, then performances very near that of human skeletal muscle could be achieved.</p><p>　　3 Lead Screw Design。</p><p>　　Seen above, the

62、 performance of a typical lead screw system is limited when compared to other wearable robotic actuator concepts. The primary reason for its low performance is poor mechanical efficiency. The coefficient of friction in a

63、 standard lead screw system is approximately =0.36., metal on metal, better results are possible if lubrication is used.</p><p>　　In contrast, the typical ball screw system has very good mechanical efficien

64、cy. The rolling contact of the ball bearings keeps the frictional effects on this system to an absolute minimum. However, even with its improved efficiencies, the cP value for the ball screw actuator is still well below

65、that of skeletal muscle, due directly to the considerable weight of the ball screw system. To improve the cP performance of a ball screw, a significant</p><p>　　reduction of weight must be achieved.</p>

66、;<p>　　Journal of Mechanical Design</p><p>　　Fig. 1 Lead screw geometry; as drawn, pitch ?p… and lead ?l…</p><p>　　are equivalent in a single helix screw</p><p>　　The basic m

67、athematics surrounding the design of a lead screw can also apply to a ball screw system. The primary difference between these two mechanical transmissions is their coefficient of friction. In the following section, an ex

68、ploration of the design parameters that influence weight and mechanical efficiency of a lead screw will be considered and thus improvements to its ccan be made.</p><p>　　3.1 Lead Screw Geometry.</p>&

69、lt;p>　　Shown in Fig. 1 is the basic geometry of a common lead screw. The key parameter of a lead screw is the lead, l, which is dependent on screw radius, r, and lead angle. The lead, l, is the amount of displacement

70、achieved for each revolution of the screw. A high precision screw has a very short or fine lead. The right triangle in Fig. 1 shows the unwrapped geometry of a single revolution of a screw. The lead angle , represents th

71、e incline or slope of the screw thread. The base of the triangle is th</p><p>　　Also seen on the right triangle are the forces present on a screw that is lifting a load. The force of the load is shown as Fw,

72、 the force resulting from the torque on the screw is F, the normal reaction force on the thread of the screw isN, and the frictional force is N. From this diagram, the following equation for a lifting torque can be deriv

73、ed </p><p><b>　　(2) </b></p><p>　　3.2 Alpha Versus R.</p><p>　　Considering, again, the geometry of a lead screw in Fig. 1, it can be shown that leadl, is described both

74、by screw radiusr, and lead angle. The relationship between these variables is given in</p><p><b>　　(3)</b></p><p><b>　　（4）</b></p><p>　　The meaning of Eq（4）i

75、s that both r, screw radius, and, lead angle, are necessary to create a screw lead, l. This means that there exists a continuous relationship between r and . Although this continuous relationship exists, most screw syste

76、ms are designed with very small lead angles. A review of the preferred ACME screw sizes reveal that although the individual diameters vary, the lead angles are all less than 3°.</p><p>　　From Eq（4）.it

77、is shown that for any screw lead desired, a variety of radii could be used. The significance of this is that as screw radius, r, shrinks, the weight of the screw shrinks by a factor.r2 Thus, to compensate for small screw

78、 radii, a larger value of lead angle , must be considered.</p><p>　　Fig. 2 Mechanical efficiency of lead screw systems: Shaded part of the graph is the typical design region for the majority of lead screws.

79、 is small, radius is large, weight is large, and efficiencies are lower. Designs in the unshaded region of the graph, where is large, implies smaller radii, lower weight, and higher efficiencies. </p><p>　　

80、3.3 Efficiency Versus Alpha. </p><p>　　For a wearable robot design, not only is the weight of a lead screw actuator an important issue, but the efficiency of an actuator is also key. As mentioned before, a d

81、ecrease in screw radius can achieve significant reductions in actuator weight. However, while the screw radius is reduced, the lead angle, must be increased to maintain a constant lead. When looking at Eq(2). it is seen

82、that the torque required to lift a load, Fw, is dependent upon both lead angle, as well as the coefficient of fr</p><p>　　Relating the efficiency of a screw to both lead angle and coefficient of friction, Fi

83、gure 2 shows the impact on both coefficient of friction, and lead angle, on the efficiency of a lead screw system</p><p><b>　?。?）</b></p><p>　　Each line in Fig. 2 is based upon a dif

84、ferent value of the coefficient of friction. Several common engineering materials are given as examples to give the reader a sense of what effect different materials or coatings could have on the efficiency of a lead scr

85、ew system. This figure shows that as the lead angle increases, so does the mechanical efficiency; or at least until a peak value is reached.</p><p>　　Ideally, it would be advantageous to pick the angle, base

86、d upon maximum efficiency. A lead screw system operating at peak efficiency minimizes the input torque requirements to lift the load Fw. The angle at which peak efficiency occurs can be determined by taking the derivativ

87、e of efficiency with respect to angle, the result of which can be seen in</p><p><b>　　(6)</b></p><p>　　Although a high lead angle can lead to a high efficiency, it can also lead to a

88、 system that is “back-drivable”. A back-driveable system is one in which the load, Fw, can cause a rotation of the screw without the assistance of applied torque, thus allowing the load, Fw, to self-lower. A back-driveab

89、le lead screw is a bad idea for a car jack, but is desirable in a wearable robot. For the lead angles in which back-drive will occur</p><p><b>　　(7)</b></p><p>　　Lead angle and coeff

90、icient of friction are all that influence this condition, regardless of how high the load force becomes. Fora very low coefficient of friction system, such as a ball screw,back-drive is an inevitable consequence.</p&g

91、t;<p>　　4 Practical Considerations</p><p>　　Ideally, as shown in the previous text, it would be desirable to reduce our screw radius, r, to an almost microscopic scale. However, this is not a practica

92、l solution, neither from a design nor manufacturing perspective. Although small screw diameters and high lead angles are desired from the perspective of weight and efficiency, they may not allow the designer to meet the

93、strength demands of the physical system. Issues, such as axial yielding,compression buckling, and mechanism bind, need to be</p><p>　　For those designers who would push the limits of the screw radius and thu

94、s lead angle to beyond that of maximum efficiency, the presence of friction limits just how far the angle can be inclined. The physical interpretation of this is that the system willbind or lock. This can be seen by eval

95、uating Eq.（2）. An evaluation of the denominator in Eq.（2）. yields the following relation。</p><p><b>　　(8)</b></p><p>　　In addition to the practical considerations listed here, there

96、exists many other issues that could be detailed. Examples of which may include torsional stiffness/yielding or even heat dissipation. Each of these factors are important and worthy of consideration, however, the purpose

97、of this exercise is to demonstrate an alternative</p><p>　　to the typical approaches of designing or selecting screw systems. The benefits of this alternative approach are directly applicable to the design i

98、ssues of a wearable robotic system.</p><p>　　5 Example Problem</p><p>　　To demonstrate a crude design exercise, consider the peak ankle joint torque during gait of an able-bodied or normal indiv

99、idual that weighs 80 kg and walks at 0.8 Hz stepping frequency. The peak ankle torque during gait is approximately 100 Nm. This peak occurs at roughly 45% of the gait cycle, A gait cycle is defined by the heel strike of

100、a foot to the next heel strike of the same foot. Toe off is the point in which the weight of the individual has transferred to the opposite leg and the initia</p><p>　　As an example, let us consider building

101、 a lead screw actuator for ankle gait assistance. For our problem, let us assume the level</p><p>　　Table 2： Example problem actuator comparison: Compares lead screw designs I and II to human muscle in terms

102、 of mechanical efficiency, power to weight ratio, corrected power to weight ratio and strength to weight ratio, measures</p><p>　　of assistance to be at 30% and that the actuator acts with a 12 cm moment arm

103、 to the ankle joint. These values can be changed but, based upon personal experience, are reasonable in their scale. Using these values and parameters available for a chosen Maxon motor, the RE40, a range of lead lengths