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購(gòu)買設(shè)計(jì)請(qǐng)充值后下載，資源目錄下的文件所見即所得，都可以點(diǎn)開預(yù)覽，資料完整，充值下載可得到資源目錄里的所有文件?！咀ⅰ浚篸wg后綴為CAD圖紙，doc,docx為WORD文檔，原稿無水印，可編輯。具體請(qǐng)見文件預(yù)覽，有不明白之處，可咨詢QQ:12401814 機(jī)0405 11號(hào) 馬吟川 指導(dǎo)老師：許寶杰THE DESIGN OF PARALLEL KINEMATIC MACHINETOOLS USING KINETOSTATIC PERFORMANCECRITERIAhttp:/arxiv.org/ftp/arxiv/papers/0705/0705.1038.pdf1. INTRODUCTIONMost industrial machine tools have a serial kinematic architecture, which means thateach axis has to carry the following one, including its actuators and joints. High SpeedMachining highlights some drawbacks of such architectures: heavy moving parts requirefrom the machine structure high stiffness to limit bending problems that lower themachine accuracy, and limit the dynamic performances of the feed axes.That is why PKMs attract more and more researchers and companies, because theyare claimed to offer several advantages over their serial counterparts, like high structuralrigidity and high dynamic capacities. Indeed, the parallel kinematic arrangement of thelinks provides higher stiffness and lower moving masses that reduce inertia effects. Thus,PKMs have better dynamic performances. However, the design of a parallel kinematicmachine tool (PKMT) is a hard task that requires further research studies before wideindustrial use can be expected.Many criteria need to be taken into account in the design of a PKMT. We pay specialattention to the description of kinetostatic criteria that rely on the conditioning of theJacobian matrix of the mechanism. The organisation of this paper is as follows: nextsection introduces general remarks about PKMs, then is explained why PKMs can beinteresting alternative machine tool designs. Then are presented existing PKMTs. Anapplication to the design of a small-scale machine tool prototype developed at IRCCyNis presented at the end of this paper.2. ABOUT PARALLEL KINEMATIC MACHINES2.1. General RemarksThe 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 flightsimulators and robotic applications2 because of their low moving mass and high dynamicperformances. Since the development of high speed machining, PKMTs have becomeinteresting alternative machine tool designs3, 4.Figure 1. The Gough platformIn a PKM, the tool is connected to the base through several kinematic chains or legsthat are mounted in parallel. The legs are generally made of either telescopic struts withfixed node points (Figure 2a), or fixed length struts with gliding node points (Figure 2b).Along with high-speed cuttings 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 beds manufacture and the inventory cost are much lower than the same functions 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 quantitys 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 tools 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 beds 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 parts 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 PKMFigure 2b. A biglide PKM2.2. SingularitiesThe singular configurations (also called singularities) of a PKM may appear insidethe workspace or at its boundaries. There are two types of singularities5. A configurationwhere a finite tool velocity requires infinite joint rates is called a serial singularity. Aconfiguration where the tool cannot resist any effort and in turn, becomes uncontrollable,is called a parallel singularity. Parallel singularities are particularly undesirable becausethey 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 thetool though actuated joints are locked.Figures 3a and 3b show the singularities for the biglide mechanism of Fig. 2b. InFig. 3a, we have a serial singularity. The velocity amplification factor along the verticaldirection is null and the force amplification factor is infinite.Figure 3b shows a parallel singularity. The velocity amplification factor is infinitealong the vertical direction and the force amplification factor is close to zero. Note that ahigh velocity amplification factor is not necessarily desirable because the actuatorencoder resolution is amplified and thus the accuracy is lower.Figure 3a. A serial singularityFigure 3b. A parallel singularity2.3. Working and Assembly ModesA 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 fora given tool position (each leg node point can be to the left or to the right of theintermediate position corresponding to the serial singularity, Fig. 4a) and two assemblymodes for a given actuator joint input (the tool is above or below the horizontal linecorresponding to the parallel singularity, Fig. 4b). The choice of the assembly mode andof the working mode may influence significantly the behaviour of the mechanism5.Figure 4a. The four working modesFigure 4b. The two assembly modes3. PKMs AS ALTERNATIVE MACHINE TOOL DESIGNS3.1. Limitations of Serial Machine ToolsToday, newly designed machine tools benefit from technological improvements ofcomponents such as spindles, linear actuators, bearings. Most machine tools are based ona 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 dynamicperformances, like feed rates or accelerations. That is why machine tools manufacturershave started being interested into PKMs since 1990.3.2. PKMs Potentialities for Machine Tool DesignThe low moving mass of PKMs and their good stiffness allow high feed rates (up to100 m/min) and accelerations (from 1 to 5g), which are the performances required byHigh Speed Machining.PKMs are said to be very accurate, which is not true in every case4, but anotheradvantage is that the struts only work in traction or compression. However, there aremany structural differences between serial and parallel machine tools, which makes ithard to strictly compare their performances.3.3. Problems with PKMsa) The workspace of a PKM has not a simple geometric shape, and its functionalvolume is reduced, compared to the space occupied by the machine7, as we can see onFig. 5Figure 5. Workspace sections of Tricept 805b) For a serial mechanism, the velocity and force transmission ratios are constant inthe workspace. For a parallel mechanism, in contrast, these ratios may vary significantlyin the workspace because the displacement of the tool is not linearly related to thedisplacement of the actuators. In some parts of the workspace, the maximal velocitiesand forces measured at the tool may differ significantly from the maximal velocities andforces that the actuators can produce. This is particularly true in the vicinity of THE DESIGN OF PKMT USING KINETOSTATIC PERFORMANCE CRITERIA 5singularities. At a singularity, the velocity, accuracy and force ratios reach extremevalues.c) Calibration of PKMs is quite complicated because of kinematic modelscomplexity8.4. EXISTING PKMT DESIGNSIn this section will be presented some existing PKMTs.4.1. Fully Parallel Machine ToolsWhat we call fully parallel machine tools are PKMs that have as many degrees offreedom as struts. On Fig. 7, we can see a 3-RPR fully parallel mechanism with threestruts. Each strut is made of a revolute joint, a prismatic actuated joint and a revolutejoint.Figure 6. 3-RPR fully parallel mechanismFully PKMT with six variable length struts are called hexapods. Hexapods areinspired by the Gough Platform. The first PKMT was the hexapod “Variax” fromGiddings and Lewis presented in 1994 at the IMTS in Chicago. Hexapods have sixdegrees of freedom. One more recent example is the CMW300, a hexapod head designedby the Compagnie Mcanique 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 fromthe Delta robot9, designed for pick and place applications. The Hexa M from Toyoda is aPKMT with six fixed length struts (Figure 9).Figure 8. Renault automation Urane SX (from “RenaultAutomation Magazine”, n 21, may 1999)Figure 9. Toyoda Hexa M (www.toyodakouki.co.jp)4.2. Other Kinds of PKMTThe Tricept 805 is a widely used PKMT with three variable length struts (Figures 5and 10). The Tricept 805 has a hybrid architecture: a two degrees of freedom wristserially 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 fivefaces 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 PKMT5.1. A Global TaskGiven a set of needs, the most adequate machine will be designed through a set ofdesign parameters like the machine morphology (serial, parallel or hybrid kinematicstructure), the machine geometry (link dimensions, joint orientation and joint ranges), thetype of actuators (linear or rotative motor), the type of joints (prismatic or revolute), thenumber 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 PKMTsThe only way to cope with problems due to singularities is to integrate kinetostaticperformance criteria in the design process of a PKMT. Kinetostatic performance criteriaevaluate the ability of a mechanism to transmit forces or velocities from the actuators tothe tool. These kinetostatic performance criteria must be able to guaranty minimumstiffness, 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 theJacobian matrix J of the PKMT, called conditioning index, and the manipulabilityellipsoid associated with J12. The Jacobian matrix J relates the joint rates to the toolvelocities. It also relates the static tool efforts to the actuator efforts. The conditioningindex is defined as the ratio between the highest and the smallest eigenvalue of J. Theconditioning index varies from 1 to infinity. At a singularity, the index is infinity. It is 1at another special configuration called isotropic configuration. At this configuration, thetool velocity and stiffness are equal in all directions. The conditioning index measuresthe uniformity of the distribution of the velocities and efforts around one givenconfiguration but it does not inform about the magnitude of the velocity amplification oreffort factors.The manipulability ellipsoid is defined from the matrix (J JT)-1. The principal axes ofthe ellipsoid are defined by the eigenvectors of (J JT)-1 and the lengths of the principalaxes are the square roots of the eigenvalues of (J JT)-1. The eigenvalues are associatedwith the velocity (or force) amplification factors along the principal axes of themanipulability ellipsoid.These criteria are used in Wenger13, to optimize the workspace shape and theperformances uniformity of the Orthoglide, a three degree of freedom PKM dedicated tomilling applications (Figure 12).Figure 12. A section of Orthoglides optimised workspace5.3. Technical ProblemsIf the struts of the PKMT are made with ballscrews, the PKMT accuracy may sufferfrom struts warping due to heating caused by frictions generated by ballscrews. Thisproblem is met by hexapods designers that use ballscrews. Thus, besides manufacturinginaccuracies, the calibration of a PKMT will have to take into account dimensionsvariations due to dilatation. A good thermal evacuation can minimise the effects ofheating.In case PKMT actuators are linear actuators, magnetic pollution has to be taken intoaccount so that chips clearing out is not obstructed. One technique, used by RenaultAutomation 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 themachine. 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, andfurthermore allow the use of linear actuators, that bring high dynamic performances.6. CONCLUSIONSThe aim of this article was to introduce a few criteria for the design of PKMTs, whichmay become interesting alternatives for High Speed Machining, especially in the millingof large parts made of hard material, or for serial manufacturing operations onaeronautical parts.Kinetostatic criteria seem to be well adapted to the design of PKMTs, particularly forthe kinematic design and for the optimisation of the workspace shape, with regard toperformances uniformity.The kinetostatic criteria have been used for the design of the Orthoglide, a three-axisPKMT developed at IRCCyN. A small scale prototype is under development. A five-axisPKMT will be derived from the Orthoglide.11