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并聯(lián)機(jī)床實(shí)驗(yàn)臺(tái)總體結(jié)構(gòu)設(shè)計(jì)并聯(lián)機(jī)床實(shí)驗(yàn)臺(tái)的優(yōu)越之處n剛度重量比大：因采用并聯(lián)閉環(huán)桿系結(jié)構(gòu)，傳動(dòng)構(gòu)件理論上為僅受拉壓載荷的二力桿，故傳動(dòng)機(jī)構(gòu)的單位重量具有很高的承載能力。n響應(yīng)速度快：允許動(dòng)平臺(tái)獲得很高的進(jìn)給速度和加速度，因而特別適于各種高速數(shù)控作業(yè)。n環(huán)境適應(yīng)性強(qiáng)：便于可重組和模塊化設(shè)計(jì)，且可構(gòu)成形式多樣的布局和自由度組合。在動(dòng)平臺(tái)上可進(jìn)行多樣性改裝。n技術(shù)附加值高：并聯(lián)機(jī)床具有“硬件”簡(jiǎn)單，“軟件”復(fù)雜的特點(diǎn)，是一種技術(shù)附加值很高的機(jī)電一體化產(chǎn)品。重要零部件選型 n依照主軸功率確定電主軸型號(hào) n選擇主軸下部刀具夾頭 n工件裝卡夾具選用 電主軸型號(hào)n按課題要求主軸切削功率為1kw，以課題的三桿并聯(lián)機(jī)床結(jié)構(gòu)來看，周邊立柱呈現(xiàn)120度圓周矩陣形式，主軸必然要在正中心，固定于三連桿下端的動(dòng)平臺(tái)上。所選電主軸參數(shù)n主軸功率1w，可知主軸所產(chǎn)生的外力偶矩m=9550P/n，主軸電機(jī)選型轉(zhuǎn)速n=24000r/min，由此可推算出外力偶矩m=95501/24000=0.398Nmn經(jīng)過多方查詢，最終確定了電主軸型號(hào)：為XCSD100Z24 銑夾頭軸端連接n銑夾頭與電主軸的連接軸端采用關(guān)節(jié)軸承。n已知關(guān)節(jié)軸承型號(hào)，查手冊(cè)其裝卡直徑為10mm。彈簧銑夾頭參數(shù)n關(guān)鍵參數(shù)均為已知量，接下來就可以選擇所需的刀具夾頭刀柄了。n并聯(lián)實(shí)驗(yàn)臺(tái)的結(jié)構(gòu)確定了它扮演著一臺(tái)數(shù)控立銑的角色，所以刀柄的選用范圍也就確定下來，應(yīng)為裝卡直徑10mm的數(shù)控銑夾頭，查詢后得出：JT(BT)40-QH1-75工件裝卡夾具選用 n裝卡范圍：R=175的半球，徑向長(zhǎng)度是350，也就是說卡具夾持的最大值至少為350mm。翻閱了卡具設(shè)計(jì)手冊(cè)，對(duì)各種機(jī)床的卡具樣式進(jìn)行了對(duì)比，可用于此并聯(lián)實(shí)驗(yàn)臺(tái)的有：車床的三抓卡盤（需作改動(dòng)）、銑床的平口虎鉗。n因?yàn)樗杓庸すぜ螤畹牟淮_定性，所以以車床的三爪卡盤比較適合，它能夠解決工件夾裝時(shí)的自定心問題。只要在車床卡盤的基礎(chǔ)上，取消卡盤隨主軸的轉(zhuǎn)動(dòng)即可?？ūP尺寸確定n按照要求所需夾持直徑350mm。n由右側(cè)表格可知，規(guī)格D500反爪加緊范圍150500，滿足徑向350mm，可定下卡盤規(guī)格為D500。三爪卡盤參數(shù)n依照所要求的裝卡尺寸，選擇外徑500的卡盤。n型號(hào)：K11500A/A115 卡盤特殊要求n用于并聯(lián)機(jī)床實(shí)驗(yàn)臺(tái)的三爪卡盤需作改動(dòng)，免去了車床卡盤中盤體隨主軸轉(zhuǎn)動(dòng)這一動(dòng)作，所以，卡盤中軸部分予以取消?？ūP與機(jī)架連接部分只需加工六個(gè)圓周陣列的M20的沉頭通孔，用于與機(jī)架相連的螺釘貫穿卡盤，其固定作用。實(shí)驗(yàn)臺(tái)支承部分及其連接的方案 n機(jī)架的設(shè)計(jì)方案n鑄造機(jī)架的材料及熱處理n機(jī)架的截面形狀、壁厚及周邊筋的布置 n立柱與底座的連接方式 n底座的造型 機(jī)架的設(shè)計(jì)n機(jī)架作為實(shí)驗(yàn)臺(tái)的支承部分，是本次設(shè)計(jì)的一個(gè)重點(diǎn)。n機(jī)架設(shè)計(jì)的基本準(zhǔn)則應(yīng)保證：剛度、強(qiáng)度、穩(wěn)定性。n在滿足強(qiáng)度和剛度的前提下，機(jī)架的重量應(yīng)要求輕、成本低；抗震性好，把受迫震動(dòng)振幅限制在允許范圍內(nèi)；噪聲小；溫度場(chǎng)分布合理，熱變形對(duì)精度的影響??；結(jié)構(gòu)設(shè)計(jì)合理，工藝性良好，便于鑄造、焊接和機(jī)械加工；結(jié)構(gòu)力求便于安裝與調(diào)整，方便修理和更換零部件；有道軌的機(jī)架要求導(dǎo)軌受力合理、耐磨性良好；造型好，使之既適用經(jīng)濟(jì)，又美觀大方。n按照以上機(jī)架設(shè)計(jì)的要求準(zhǔn)則，首先確定機(jī)架的制造形式，為鑄造機(jī)架?？傮w結(jié)構(gòu)造型n(1)工作空間呈柱形，具有較大的編程空間與機(jī)床體積比，且平行于工作臺(tái)任意截面的運(yùn)動(dòng)學(xué)性能等同。n(2)位置及速度正、逆解均有顯式解析解答，可實(shí)施快速PVT插補(bǔ)和在線運(yùn)動(dòng)學(xué)標(biāo)定。n(3)支鏈采用帶消極約束的三桿平行四邊形剛架結(jié)構(gòu)，不但可有效地消除鉸鏈間隙，且可大幅度提高動(dòng)平臺(tái)抵抗切削顛覆力矩的能力。n(4)除底座和動(dòng)平臺(tái)外，主要結(jié)構(gòu)件均為三對(duì)稱，可大幅度減少零部件設(shè)計(jì)工作和制造成本。鑄造機(jī)架的材料及熱處理n材料選擇查閱鑄造機(jī)架常用材料后得出，鑄鐵機(jī)架用于并聯(lián)實(shí)驗(yàn)臺(tái)比其他金屬性價(jià)比高，是機(jī)架使用最多的一種材料，它的流動(dòng)性好，體收縮和線收縮小，容易獲得形狀復(fù)雜的鑄件。n鑄鐵機(jī)架的時(shí)效處理時(shí)效處理的目的是在不降低鑄鐵力學(xué)性能的前提下，是鑄鐵的內(nèi)應(yīng)力和機(jī)加工切削應(yīng)力得到消除或隱定，以減少長(zhǎng)期使用中的變形，保證幾何精度。n人工時(shí)效普遍應(yīng)用熱處理方法，將鑄件緩慢加熱到共析點(diǎn)以下（一般為500600），保溫一段時(shí)間，然后緩慢冷卻，消除內(nèi)應(yīng)力。機(jī)架的截面形狀 n此種空心矩形的抗彎、抗扭慣性矩比值分別為：抗彎慣性矩相對(duì)值：3.45 抗扭慣性矩相對(duì)值：1.27 n鑄件壁厚的選擇取決于其強(qiáng)度、剛度、材料、鑄件尺寸、質(zhì)量和工藝等因素。n就鑄鐵機(jī)架而言，按目前工藝水平，砂模鑄造鑄鐵件的壁厚，可利用當(dāng)量尺寸N,來確定。nN=（2L+B+H）/3 L、B、H分別為主見的長(zhǎng)、寬、高n利用上述公式，結(jié)合查表鑄鐵機(jī)架的壁厚，確定出實(shí)驗(yàn)臺(tái)立柱的壁厚為20mm。壁厚及加強(qiáng)筋n對(duì)于保證立柱剛度的加強(qiáng)筋和肋，由于次實(shí)驗(yàn)臺(tái)設(shè)有頂端端蓋，用于安裝并聯(lián)機(jī)構(gòu)。為了能夠更好的保障立柱剛度，立柱內(nèi)部設(shè)有交叉十字肋；另外柱體外側(cè)周邊添置筋板有效地提高了剛度、穩(wěn)定性和抗振能力。n筋的尺寸查表可知：厚度=0.8s 高度1.5s s為立柱的壁厚n得出筋高為100，厚16。肋厚度查表 為立柱壁厚的0.6倍 厚度為12mm。n加入肋后，尤其是45度對(duì)角肋，對(duì)扭轉(zhuǎn)剛度的提高有明顯的效果，抗彎剛度可提高60%，扭轉(zhuǎn)剛度可提高4.58.5倍。立柱與底座的連接方式 n由于立柱與底座需要進(jìn)行連接，考慮到立柱下端受應(yīng)力較大，而且用螺紋連接打孔不便，綜合各種因素，選怎了焊接的形式。n焊接時(shí)，會(huì)產(chǎn)生局部應(yīng)力，為了保證定位精度，立柱下端設(shè)計(jì)了定位銷孔，孔徑為d8。分別布置在力主四個(gè)底角的中心位置。n在焊接前，現(xiàn)將定位銷插入銷孔，兩者過渡連接，使其立柱在焊接過程中不會(huì)由于焊接應(yīng)力的原因，與底座產(chǎn)生相對(duì)偏移。焊坡參數(shù)n焊縫尺寸的確定方法一般為：按焊縫的工作應(yīng)力；安等強(qiáng)原則；按剛度條件。由于焊接機(jī)床的床身，立柱，橫梁和箱體等一般按剛度設(shè)計(jì)，所以焊縫尺寸宜采用依照剛度原則確定。n按剛度條件選擇角焊縫尺寸的經(jīng)驗(yàn)做法是：根據(jù)被焊鋼板中較薄的鋼板強(qiáng)度的33%、50%n、100%作為焊縫強(qiáng)度來確定焊縫尺寸。n為了保證實(shí)驗(yàn)臺(tái)的良好剛度，經(jīng)過查詢，立柱與機(jī)床機(jī)架的角焊縫尺寸有鋼板剛度的100%確定得出：板厚h 按照100%強(qiáng)度設(shè)計(jì) 則焊縫寬度=3/4hn前邊已經(jīng)確定板厚h=20mm 所以得出焊縫寬度K=3/4x20=15mmn接下來考慮焊縫應(yīng)力問題，在焊接接頭處，由于機(jī)床實(shí)驗(yàn)臺(tái)加工時(shí)的并聯(lián)機(jī)構(gòu)擺動(dòng)，會(huì)使立柱底端受剪切力，為了減小這種損害性力，焊坡需要呈現(xiàn)45度角，從而解決應(yīng)力過度集中的問題。底座的造型 n首先確定出了立柱的結(jié)構(gòu)，底座的造型就要基于立柱而確定。呈現(xiàn)三根立柱120度圓周陣列的連接體，高度200mm。與立柱材料一致，采用灰鑄鐵HT150，鑄造后同樣需要人工時(shí)效處理。前邊已經(jīng)確定了立柱、卡盤的構(gòu)造，在底座上要預(yù)留出配合時(shí)的安裝孔。有安裝卡盤的螺紋孔，還有定位立柱的銷孔，兩種孔的加工都已標(biāo)準(zhǔn)件螺釘和定位銷為基準(zhǔn)，采用輕微過盈量。在鑄造完畢時(shí)效處理后，按照表逐漸配合尺寸打孔、攻絲。n考慮到并聯(lián)實(shí)驗(yàn)臺(tái)的自身重量，底座邊緣分別留出了三個(gè)32mm的地腳螺栓安裝孔，以便實(shí)驗(yàn)臺(tái)安裝時(shí)的水泥澆筑地腳螺栓。實(shí)驗(yàn)臺(tái)電路設(shè)計(jì) n電路布線方案 n電路控制要求 n電路控制連線原理圖 電路布線方案 n實(shí)驗(yàn)臺(tái)電源配置380V三相交流電，在裝配圖中，按照電主軸及并聯(lián)機(jī)構(gòu)驅(qū)動(dòng)電機(jī)電源入口，在機(jī)架立柱上預(yù)留了一個(gè)50mm的電源孔，四周有安裝配電箱螺釘?shù)目住Ｖ麟娫淳€由地面，上連到配電箱，電源線外側(cè)套有絕緣蛇皮管。n電主軸和并聯(lián)機(jī)構(gòu)的配電，經(jīng)過配電箱的電源線，經(jīng)立柱內(nèi)側(cè)分配到各個(gè)電源接口。n電主軸已經(jīng)選出，實(shí)驗(yàn)臺(tái)裝配時(shí)，將電主軸用螺栓固定于動(dòng)平臺(tái)上。則主軸位于動(dòng)平臺(tái)中央，連接電源線須從立柱上端引出線，從實(shí)驗(yàn)臺(tái)頂蓋向下連入電主軸。n并聯(lián)機(jī)構(gòu)驅(qū)動(dòng)電機(jī)的電源入口，就在絲杠套筒的端口，所以和電主軸一樣，電源從立柱上端引出。電路控制要求 n并聯(lián)機(jī)構(gòu)在此不予考慮，那么電主軸的控制相對(duì)于并聯(lián)部分就簡(jiǎn)單的多，只需用繼電器控制電主軸的正反轉(zhuǎn)、加減速的簡(jiǎn)單動(dòng)作。電路控制連線原理圖 n左半部分是主軸正反轉(zhuǎn)連線；右邊部分是主軸正反轉(zhuǎn)、加減速、制動(dòng)控制部分。答辯陳述完結(jié)篇感謝各位老師機(jī)0405 11號(hào) 馬吟川 指導(dǎo)老師：許寶杰
THE DESIGN OF PARALLEL KINEMATIC MACHINE
TOOLS USING KINETOSTATIC PERFORMANCE
CRITERIA
http://arxiv.org/ftp/arxiv/papers/0705/0705.1038.pdf
1. INTRODUCTION
Most industrial machine tools have a serial kinematic architecture, which means that
each axis has to carry the following one, including its actuators and joints. High Speed
Machining highlights some drawbacks of such architectures: heavy moving parts require
from the machine structure high stiffness to limit bending problems that lower the
machine accuracy, and limit the dynamic performances of the feed axes.
That is why PKMs attract more and more researchers and companies, because they
are claimed to offer several advantages over their serial counterparts, like high structural
rigidity and high dynamic capacities. Indeed, the parallel kinematic arrangement of the
links provides higher stiffness and lower moving masses that reduce inertia effects. Thus,
PKMs have better dynamic performances. However, the design of a parallel kinematic
machine tool (PKMT) is a hard task that requires further research studies before wide
industrial use can be expected.
Many criteria need to be taken into account in the design of a PKMT. We pay special
attention to the description of kinetostatic criteria that rely on the conditioning of the
Jacobian matrix of the mechanism. The organisation of this paper is as follows: next
section introduces general remarks about PKMs, then is explained why PKMs can be
interesting alternative machine tool designs. Then are presented existing PKMTs. An
application to the design of a small-scale machine tool prototype developed at IRCCyN
is presented at the end of this paper.
2. ABOUT PARALLEL KINEMATIC MACHINES
2.1. General Remarks
The first industrial application of PKMs was the Gough platform (Figure 1),
designed in 1957 to test tyres1. PKMs have then been used for many years in flight
simulators and robotic applications2 because of their low moving mass and high dynamic
performances. Since the development of high speed machining, PKMTs have become
interesting alternative machine tool designs3, 4.
Figure 1. The Gough platform
In a PKM, the tool is connected to the base through several kinematic chains or legs
that are mounted in parallel. The legs are generally made of either telescopic struts with
fixed node points (Figure 2a), or fixed length struts with gliding node points (Figure 2b).
Along with high-speed cutting's unceasing development, the traditional tandem type organization constructs the platform the structure rigidity and the traveling carriage high speed becomes the technological development gradually the bottleneck, but the parallel platform then becomes the best candidate object, but was opposite in the tandem engine bed, the parallel working platform had the following characteristic and the merit:
(1) structure is simple, the price is low The engine bed mechanical spare part number is series connected constructs the platform to reduce largely, mainly by the ball bearing guide screw, the Hooke articulation, the ball articulation, the servo electrical machinery and so on common module is composed, these common modules may by the special factory production, thus this engine bed's manufacture and the inventory cost are much lower than the same function's traditional engine bed, easy to assemble and the transporting.
(2) structure rigidity is high Because used closeness structure (closed-loop structure) to enable it to have high rigid and the high speed merit, its structural load streamline was short, but shouldered decomposes pulls, the pressure also to withstand by six connecting rods, by materials mechanics' viewpoint, when the external force was certain, the bracket quantity's stress and the distortion were biggest, the both sides inserted the (build-in) next best, came is again both sides Jan supports (simply-supported), next was the bearing two strength structure, what the stress and the distortion were smallest was the tensity two strength structure, therefore it had the high rigidity. Its rigidity load ratio is higher than traditional the numerically-controlled machine tool.
(3) processing speed is high, the inertia is low If the structure withstands the strength will change the direction, (will be situated between tensity and pressure), two strength components will be most save the material the structure, but it will move to the moving parts weight to reduce to lowly and simultaneously will actuate by six actuating units, therefore machine very easy high speed, and will have the low inertia.
(4) working accuracy is high Because it for the multiple spindle parallel organization composition, six expandable pole poles long alone has an effect to cutting tool's position and the posture, thus does not have the traditional engine bed (i.e. connects engine bed) the geometrical error accumulation and the enlargement phenomenon, even also has the being uniform effect (averaging effect); It has the hot symmetrical structural design, therefore the thermal deformation is small; Therefore it has the high accuracy merit.
(5) multi-purpose flexible Is convenient as a result of this engine bed organization simple control, easily according to processing object, but designs it the special purpose machine, simultaneously may also develop the general engine bed, with realizes the milling, boring, processings and so on grinding, but may also provide the essential measuring tool to compose it the measuring engine, realizes engine bed's multi-purpose. This will bring the very big application and the market prospect, has the very broad application prospect in the national defense and the civil aspect.
(6) service life is long Because the stress structure is reasonable, the moving part attrition is small, and does not have the guide rail, does not have the iron filings either the refrigerant enters the guide rail interior to cause it to scratch, the attrition or the corrosion phenomenon.
(7) Stewart platform suits in the modular production Regarding the different machine scope, only need change the connecting rod length and the contact position, maintains also easily, does not need to carry on part's remaking and to adjust, only need the new organization parameter input.
(8) transformation coordinate system is convenient Because does not have the entity coordinate system, the engine bed coordinate system and the work piece coordinate system transform depend on the software to complete completely, is convenient.
When the Stewart platform applies in the engine bed and the robot, may reduce the static error (, because high rigidity), as well as dynamic error (because low inertia). But Stewart the platform inferiority lies in its working space to be small, and it has the singular point limit in the working space, but the serial operation platform, the controller meets time the singular point, accountant will figure out the actuation order which the drive is unable to achieve to create the ning error, but the Stewart platform will lose the support partial directions in the strange position the strength or moment of force ability, will be unable to complete the constant load object.
Figure 2a. A bipod PKM
Figure 2b. A biglide PKM
2.2. Singularities
The singular configurations (also called singularities) of a PKM may appear inside
the workspace or at its boundaries. There are two types of singularities5. A configuration
where a finite tool velocity requires infinite joint rates is called a serial singularity. A
configuration where the tool cannot resist any effort and in turn, becomes uncontrollable,
is called a parallel singularity. Parallel singularities are particularly undesirable because
they induce the following problems:
- a high increase in forces in joints and links, that may damage the structure,
- a decrease of the mechanism stiffness that can lead to uncontrolled motions of the
tool though actuated joints are locked.
Figures 3a and 3b show the singularities for the biglide mechanism of Fig. 2b. In
Fig. 3a, we have a serial singularity. The velocity amplification factor along the vertical
direction is null and the force amplification factor is infinite.
Figure 3b shows a parallel singularity. The velocity amplification factor is infinite
along the vertical direction and the force amplification factor is close to zero. Note that a
high velocity amplification factor is not necessarily desirable because the actuator
encoder resolution is amplified and thus the accuracy is lower.
Figure 3a. A serial singularity
Figure 3b. A parallel singularity
2.3. Working and Assembly Modes
A serial (resp. parallel) singularity is associated with a change of working mode6
(resp. of assembly mode). For example, the biglide has four possible working modes for
a given tool position (each leg node point can be to the left or to the right of the
intermediate position corresponding to the serial singularity, Fig. 4a) and two assembly
modes for a given actuator joint input (the tool is above or below the horizontal line
corresponding to the parallel singularity, Fig. 4b). The choice of the assembly mode and
of the working mode may influence significantly the behaviour of the mechanism5.
Figure 4a. The four working modes
Figure 4b. The two assembly modes
3. PKMs AS ALTERNATIVE MACHINE TOOL DESIGNS
3.1. Limitations of Serial Machine Tools
Today, newly designed machine tools benefit from technological improvements of
components such as spindles, linear actuators, bearings. Most machine tools are based on
a serial architecture (Figure 5), whose advantage is that input/output relations are simple.
Nevertheless, heavy masses to be carried and moved by each axis limit the dynamic
performances, like feed rates or accelerations. That is why machine tools manufacturers
have started being interested into PKMs since 1990.
3.2. PKMs Potentialities for Machine Tool Design
The low moving mass of PKMs and their good stiffness allow high feed rates (up to
100 m/min) and accelerations (from 1 to 5g), which are the performances required by
High Speed Machining.
PKMs are said to be very accurate, which is not true in every case4, but another
advantage is that the struts only work in traction or compression. However, there are
many structural differences between serial and parallel machine tools, which makes it
hard to strictly compare their performances.
3.3. Problems with PKMs
a) The workspace of a PKM has not a simple geometric shape, and its functional
volume is reduced, compared to the space occupied by the machine7, as we can see on
Fig. 5
Figure 5. Workspace sections of Tricept 805
b) For a serial mechanism, the velocity and force transmission ratios are constant in
the workspace. For a parallel mechanism, in contrast, these ratios may vary significantly
in the workspace because the displacement of the tool is not linearly related to the
displacement of the actuators. In some parts of the workspace, the maximal velocities
and forces measured at the tool may differ significantly from the maximal velocities and
forces that the actuators can produce. This is particularly true in the vicinity of THE DESIGN OF PKMT USING KINETOSTATIC PERFORMANCE CRITERIA 5
singularities. At a singularity, the velocity, accuracy and force ratios reach extreme
values.
c) Calibration of PKMs is quite complicated because of kinematic models
complexity8.
4. EXISTING PKMT DESIGNS
In this section will be presented some existing PKMTs.
4.1. Fully Parallel Machine Tools
What we call fully parallel machine tools are PKMs that have as many degrees of
freedom as struts. On Fig. 7, we can see a 3-RPR fully parallel mechanism with three
struts. Each strut is made of a revolute joint, a prismatic actuated joint and a revolute
joint.
Figure 6. 3-RPR fully parallel mechanism
Fully PKMT with six variable length struts are called hexapods. Hexapods are
inspired by the Gough Platform. The first PKMT was the hexapod “Variax” from
Giddings and Lewis presented in 1994 at the IMTS in Chicago. Hexapods have six
degrees of freedom. One more recent example is the CMW300, a hexapod head designed
by the Compagnie Mécanique des Vosges (Figure 7)
.
Figure 7. Hexapod CMW 300 (perso.wanadoo.fr/cmw.meca.6x/6AXES.htm)
Fully parallel machine tools with fixed length struts can have three, four or six legs.
The Urane SX (Figures8 and 13) from Renault Automation is a three leg machine,
whose tool can only move along X, Y and Z axes, and its architecture is inspired from
the Delta robot9, designed for pick and place applications. The Hexa M from Toyoda is a
PKMT with six fixed length struts (Figure 9).
Figure 8. Renault automation Urane SX (from “Renault
Automation Magazine”, n° 21, may 1999)
Figure 9. Toyoda Hexa M (www.toyodakouki.
co.jp)
4.2. Other Kinds of PKMT
The Tricept 805 is a widely used PKMT with three variable length struts (Figures 5
and 10). The Tricept 805 has a hybrid architecture: a two degrees of freedom wrist
serially mounted on a tripod architecture.
Another non fully parallel MT is the Eclipse (Figure 11) from Sena Technology10, 11.
The Eclipse is an overactuated PKM for rapid machining, capable of simultaneous five
faces milling, as well as turning, thanks to the second spindle.
Figure 10. Tricept 805 from Neos robotics
(www.neosrobotics.com)
Figure 11. The Eclipse, from Sena Technology
(macea.snu.ac.kr/eclipse/homepage.html)
5. DESIGNING A PKMT
5.1. A Global Task
Given a set of needs, the most adequate machine will be designed through a set of
design parameters like the machine morphology (serial, parallel or hybrid kinematic
structure), the machine geometry (link dimensions, joint orientation and joint ranges), the
type of actuators (linear or rotative motor), the type of joints (prismatic or revolute), the
number and the type of degrees of freedom, the task for which the machine is designed.
These parameters must be defined using relevant design criteria.
5.2. Kinetostatic Performance Criteria are Adequate for the Design of PKMTs
The only way to cope with problems due to singularities is to integrate kinetostatic
performance criteria in the design process of a PKMT. Kinetostatic performance criteria
evaluate the ability of a mechanism to transmit forces or velocities from the actuators to
the tool. These kinetostatic performance criteria must be able to guaranty minimum
stiffness, accuracy and velocity performances along every direction throughout the
workspace of the PKMT.
To reach this goal, we use two complementary criteria: the conditioning of the
Jacobian matrix J of the PKMT, called conditioning index, and the manipulability
ellipsoid associated with J12. The Jacobian matrix J relates the joint rates to the tool
velocities. It also relates the static tool efforts to the actuator efforts. The conditioning
index is defined as the ratio between the highest and the smallest eigenvalue of J. The
conditioning index varies from 1 to infinity. At a singularity, the index is infinity. It is 1
at another special configuration called isotropic configuration. At this configuration, the
tool velocity and stiffness are equal in all directions. The conditioning index measures
the uniformity of the distribution of the velocities and efforts around one given
configuration but it does not inform about the magnitude of the velocity amplification or
effort factors.
The manipulability ellipsoid is defined from the matrix (J JT)-1. The principal axes of
the ellipsoid are defined by the eigenvectors of (J JT)-1 and the lengths of the principal
axes are the square roots of the eigenvalues of (J JT)-1. The eigenvalues are associated
with the velocity (or force) amplification factors along the principal axes of the
manipulability ellipsoid.
These criteria are used in Wenger13, to optimize the workspace shape and the
performances uniformity of the Orthoglide, a three degree of freedom PKM dedicated to
milling applications (Figure 12).
Figure 12. A section of Orthoglide’s optimised workspace
5.3. Technical Problems
If the struts of the PKMT are made with ballscrews, the PKMT accuracy may suffer
from struts warping due to heating caused by frictions generated by ballscrews. This
problem is met by hexapods designers that use ballscrews. Thus, besides manufacturing
inaccuracies, the calibration of a PKMT will have to take into account dimensions
variations due to dilatation. A good thermal evacuation can minimise the effects of
heating.
In case PKMT actuators are linear actuators, magnetic pollution has to be taken into
account so that chips clearing out is not obstructed. One technique, used by Renault
Automation for the Urane SX, is to isolate the tool from the mechanism.
At last, choosing fixed length or variable length struts influence the behaviour of the
machine. Actuators have to be mounted on the struts in case of variable length struts,
which increases moved masses. Fixed length struts do not have this problem, and
furthermore allow the use of linear actuators, that bring high dynamic performances.
6. CONCLUSIONS
The aim of this article was to introduce a few criteria for the design of PKMTs, which
may become interesting alternatives for High Speed Machining, especially in the milling
of large parts made of hard material, or for serial manufacturing operations on
aeronautical parts.
Kinetostatic criteria seem to be well adapted to the design of PKMTs, particularly for
the kinematic design and for the optimisation of the workspace shape, with regard to
performances uniformity.
The kinetostatic criteria have been used for the design of the Orthoglide, a three-axis
PKMT developed at IRCCyN. A small scale prototype is under development. A five-axis
PKMT will be derived from the Orthoglide.
11