the design of parallel kinematic machine

1、<p>　　THE DESIGN OF PARALLEL KINEMATIC MACHINE</p><p>　　TOOLS USING KINETOSTATIC PERFORMANCE</p><p><b>　　CRITERIA</b></p><p>　　http://arxiv.org/ftp/arxiv/papers/070

2、5/0705.1038.pdf</p><p>　　1. INTRODUCTION</p><p>　　Most industrial machine tools have a serial kinematic architecture, which means that</p><p>　　each axis has to carry the following

3、one, including its actuators and joints. High Speed</p><p>　　Machining highlights some drawbacks of such architectures: heavy moving parts require</p><p>　　from the machine structure high stiffn

4、ess to limit bending problems that lower the</p><p>　　machine accuracy, and limit the dynamic performances of the feed axes.</p><p>　　That is why PKMs attract more and more researchers and compa

5、nies, because they</p><p>　　are claimed to offer several advantages over their serial counterparts, like high structural</p><p>　　rigidity and high dynamic capacities. Indeed, the parallel kinem

6、atic arrangement of the</p><p>　　links provides higher stiffness and lower moving masses that reduce inertia effects. Thus,</p><p>　　PKMs have better dynamic performances. However, the design of

7、 a parallel kinematic</p><p>　　machine tool (PKMT) is a hard task that requires further research studies before wide</p><p>　　industrial use can be expected.</p><p>　　Many criteria

8、need to be taken into account in the design of a PKMT. We pay special</p><p>　　attention to the description of kinetostatic criteria that rely on the conditioning of the</p><p>　　Jacobian matrix

9、 of the mechanism. The organisation of this paper is as follows: next</p><p>　　section introduces general remarks about PKMs, then is explained why PKMs can be</p><p>　　interesting alternative m

10、achine tool designs. Then are presented existing PKMTs. An</p><p>　　application to the design of a small-scale machine tool prototype developed at IRCCyN</p><p>　　is presented at the end of this

11、 paper.</p><p>　　2. ABOUT PARALLEL KINEMATIC MACHINES</p><p>　　2.1. General Remarks</p><p>　　The first industrial application of PKMs was the Gough platform (Figure 1),</p>&

12、lt;p>　　designed in 1957 to test tyres1. PKMs have then been used for many years in flight</p><p>　　simulators and robotic applications2 because of their low moving mass and high dynamic</p><p&g

13、t;　　performances. Since the development of high speed machining, PKMTs have become</p><p>　　interesting alternative machine tool designs3, 4.</p><p>　　Figure 1. The Gough platform</p><

14、;p>　　In a PKM, the tool is connected to the base through several kinematic chains or legs</p><p>　　that are mounted in parallel. The legs are generally made of either telescopic struts with</p><

15、;p>　　fixed node points (Figure 2a), or fixed length struts with gliding node points (Figure 2b).</p><p>　　Along with high-speed cutting's unceasing development, the traditional tandem type organizatio

16、n 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

17、 was opposite in the tandem engine bed, the parallel working platform had the following characteristic and the merit:</p><p>　　(1) structure is simple, the price is low The engine bed mechanical spare part n

18、umber 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 compos

19、ed, 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 assemb</p>

20、<p>　　(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 decomp

21、oses 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 s

22、ides inserted the (build-in) next best, came is again both sides Jan supports (</p><p>　　(3) processing speed is high, the inertia is low If the structure withstands the strength will change the direction, (

23、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

24、actuating units, therefore machine very easy high speed, and will have the low inertia. </p><p>　　(4) working accuracy is high Because it for the multiple spindle parallel organization composition, six expan

25、dable 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 ph

26、enomenon, 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</p><p>　　(5) multi-purpose flex

27、ible 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, wi

28、th 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

29、 application and the market prospect, has </p><p>　　(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 th

30、e iron filings either the refrigerant enters the guide rail interior to cause it to scratch, the attrition or the corrosion phenomenon. </p><p>　　(7) Stewart platform suits in the modular production Regardin

31、g 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 param

32、eter input. </p><p>　　(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 de

33、pend on the software to complete completely, is convenient. </p><p>　　When the Stewart platform applies in the engine bed and the robot, may reduce the static error (, because high rigidity), as well as dyna

34、mic 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 mee

35、ts time the singular point, accountant will figure out the actuation order which the drive is unable to achieve to create the ning error, but t</p><p>　　Figure 2a. A bipod PKM</p><p>　　Figure 2b

36、. A biglide PKM</p><p>　　2.2. Singularities</p><p>　　The singular configurations (also called singularities) of a PKM may appear inside</p><p>　　the workspace or at its boundaries.

37、There are two types of singularities5. A configuration</p><p>　　where a finite tool velocity requires infinite joint rates is called a serial singularity. A</p><p>　　configuration where the tool

38、 cannot resist any effort and in turn, becomes uncontrollable,</p><p>　　is called a parallel singularity. Parallel singularities are particularly undesirable because</p><p>　　they induce the fol

39、lowing problems:</p><p>　　- a high increase in forces in joints and links, that may damage the structure,</p><p>　　- a decrease of the mechanism stiffness that can lead to uncontrolled motions o

40、f the</p><p>　　tool though actuated joints are locked.</p><p>　　Figures 3a and 3b show the singularities for the biglide mechanism of Fig. 2b. In</p><p>　　Fig. 3a, we have a serial

41、singularity. The velocity amplification factor along the vertical</p><p>　　direction is null and the force amplification factor is infinite.</p><p>　　Figure 3b shows a parallel singularity. The

42、velocity amplification factor is infinite</p><p>　　along the vertical direction and the force amplification factor is close to zero. Note that a</p><p>　　high velocity amplification factor is no

43、t necessarily desirable because the actuator</p><p>　　encoder resolution is amplified and thus the accuracy is lower.</p><p>　　Figure 3a. A serial singularity</p><p>　　Figure 3b. A

44、parallel singularity</p><p>　　2.3. Working and Assembly Modes</p><p>　　A serial (resp. parallel) singularity is associated with a change of working mode6</p><p>　　(resp. of assembly

45、 mode). For example, the biglide has four possible working modes for</p><p>　　a given tool position (each leg node point can be to the left or to the right of the</p><p>　　intermediate position

46、corresponding to the serial singularity, Fig. 4a) and two assembly</p><p>　　modes for a given actuator joint input (the tool is above or below the horizontal line</p><p>　　corresponding to the p

47、arallel singularity, Fig. 4b). The choice of the assembly mode and</p><p>　　of the working mode may influence significantly the behaviour of the mechanism5.</p><p>　　Figure 4a. The four working

48、modes</p><p>　　Figure 4b. The two assembly modes</p><p>　　3. PKMs AS ALTERNATIVE MACHINE TOOL DESIGNS</p><p>　　3.1. Limitations of Serial Machine Tools</p><p>　　Today,

49、newly designed machine tools benefit from technological improvements of</p><p>　　components such as spindles, linear actuators, bearings. Most machine tools are based on</p><p>　　a serial archit

50、ecture (Figure 5), whose advantage is that input/output relations are simple.</p><p>　　Nevertheless, heavy masses to be carried and moved by each axis limit the dynamic</p><p>　　performances, li

51、ke feed rates or accelerations. That is why machine tools manufacturers</p><p>　　have started being interested into PKMs since 1990.</p><p>　　3.2. PKMs Potentialities for Machine Tool Design<

52、/p><p>　　The low moving mass of PKMs and their good stiffness allow high feed rates (up to</p><p>　　100 m/min) and accelerations (from 1 to 5g), which are the performances required by</p>&l

53、t;p>　　High Speed Machining.</p><p>　　PKMs are said to be very accurate, which is not true in every case4, but another</p><p>　　advantage is that the struts only work in traction or compressio

54、n. However, there are</p><p>　　many structural differences between serial and parallel machine tools, which makes it</p><p>　　hard to strictly compare their performances.</p><p>　　3

55、.3. Problems with PKMs</p><p>　　a) The workspace of a PKM has not a simple geometric shape, and its functional</p><p>　　volume is reduced, compared to the space occupied by the machine7, as we c

56、an see on</p><p><b>　　Fig. 5</b></p><p>　　Figure 5. Workspace sections of Tricept 805</p><p>　　b) For a serial mechanism, the velocity and force transmission ratios are

57、constant in</p><p>　　the workspace. For a parallel mechanism, in contrast, these ratios may vary significantly</p><p>　　in the workspace because the displacement of the tool is not linearly rela

58、ted to the</p><p>　　displacement of the actuators. In some parts of the workspace, the maximal velocities</p><p>　　and forces measured at the tool may differ significantly from the maximal veloc

59、ities and</p><p>　　forces that the actuators can produce. This is particularly true in the vicinity of THE DESIGN OF PKMT USING KINETOSTATIC PERFORMANCE CRITERIA 5</p><p>　　singularities. At a s

60、ingularity, the velocity, accuracy and force ratios reach extreme</p><p><b>　　values.</b></p><p>　　c) Calibration of PKMs is quite complicated because of kinematic models</p>

61、<p>　　complexity8.</p><p>　　4. EXISTING PKMT DESIGNS</p><p>　　In this section will be presented some existing PKMTs.</p><p>　　4.1. Fully Parallel Machine Tools</p><p

62、>　　What we call fully parallel machine tools are PKMs that have as many degrees of</p><p>　　freedom as struts. On Fig. 7, we can see a 3-RPR fully parallel mechanism with three</p><p>　　strut

63、s. Each strut is made of a revolute joint, a prismatic actuated joint and a revolute</p><p><b>　　joint.</b></p><p>　　Figure 6. 3-RPR fully parallel mechanism</p><p>　　Fu

64、lly PKMT with six variable length struts are called hexapods. Hexapods are</p><p>　　inspired by the Gough Platform. The first PKMT was the hexapod “Variax” from</p><p>　　Giddings and Lewis prese

65、nted in 1994 at the IMTS in Chicago. Hexapods have six</p><p>　　degrees of freedom. One more recent example is the CMW300, a hexapod head designed</p><p>　　by the Compagnie Mécanique des Vo

66、sges (Figure 7)</p><p><b>　　.</b></p><p>　　Figure 7. Hexapod CMW 300 (perso.wanadoo.fr/cmw.meca.6x/6AXES.htm)</p><p>　　Fully parallel machine tools with fixed length str

67、uts can have three, four or six legs.</p><p>　　The Urane SX (Figures8 and 13) from Renault Automation is a three leg machine,</p><p>　　whose tool can only move along X, Y and Z axes, and its arc

68、hitecture is inspired from</p><p>　　the Delta robot9, designed for pick and place applications. The Hexa M from Toyoda is a</p><p>　　PKMT with six fixed length struts (Figure 9).</p><

69、p>　　Figure 8. Renault automation Urane SX (from “Renault</p><p>　　Automation Magazine”, n° 21, may 1999)</p><p>　　Figure 9. Toyoda Hexa M (www.toyodakouki.</p><p><b>　

70、　co.jp)</b></p><p>　　4.2. Other Kinds of PKMT</p><p>　　The Tricept 805 is a widely used PKMT with three variable length struts (Figures 5</p><p>　　and 10). The Tricept 805 has

71、 a hybrid architecture: a two degrees of freedom wrist</p><p>　　serially mounted on a tripod architecture.</p><p>　　Another non fully parallel MT is the Eclipse (Figure 11) from Sena Technology1

72、0, 11.</p><p>　　The Eclipse is an overactuated PKM for rapid machining, capable of simultaneous five</p><p>　　faces milling, as well as turning, thanks to the second spindle.</p><p>

73、;　　Figure 10. Tricept 805 from Neos robotics</p><p>　　(www.neosrobotics.com)</p><p>　　Figure 11. The Eclipse, from Sena Technology</p><p>　　(macea.snu.ac.kr/eclipse/homepage.html)&l

74、t;/p><p>　　5. DESIGNING A PKMT</p><p>　　5.1. A Global Task</p><p>　　Given a set of needs, the most adequate machine will be designed through a set of</p><p>　　design param

75、eters like the machine morphology (serial, parallel or hybrid kinematic</p><p>　　structure), the machine geometry (link dimensions, joint orientation and joint ranges), the</p><p>　　type of actu

76、ators (linear or rotative motor), the type of joints (prismatic or revolute), the</p><p>　　number and the type of degrees of freedom, the task for which the machine is designed.</p><p>　　These p

77、arameters must be defined using relevant design criteria.</p><p>　　5.2. Kinetostatic Performance Criteria are Adequate for the Design of PKMTs</p><p>　　The only way to cope with problems due to

78、singularities is to integrate kinetostatic</p><p>　　performance criteria in the design process of a PKMT. Kinetostatic performance criteria</p><p>　　evaluate the ability of a mechanism to transm

79、it forces or velocities from the actuators to</p><p>　　the tool. These kinetostatic performance criteria must be able to guaranty minimum</p><p>　　stiffness, accuracy and velocity performances a

80、long every direction throughout the </p><p>　　workspace of the PKMT.</p><p>　　To reach this goal, we use two complementary criteria: the conditioning of the</p><p>　　Jacobian matrix

81、 J of the PKMT, called conditioning index, and the manipulability</p><p>　　ellipsoid associated with J12. The Jacobian matrix J relates the joint rates to the tool</p><p>　　velocities. It also r

82、elates the static tool efforts to the actuator efforts. The conditioning</p><p>　　index is defined as the ratio between the highest and the smallest eigenvalue of J. The</p><p>　　conditioning in

83、dex varies from 1 to infinity. At a singularity, the index is infinity. It is 1</p><p>　　at another special configuration called isotropic configuration. At this configuration, the</p><p>　　tool

84、 velocity and stiffness are equal in all directions. The conditioning index measures</p><p>　　the uniformity of the distribution of the velocities and efforts around one given</p><p>　　configura

85、tion but it does not inform about the magnitude of the velocity amplification or</p><p>　　effort factors.</p><p>　　The manipulability ellipsoid is defined from the matrix (J JT)-1. The principal

86、 axes of</p><p>　　the ellipsoid are defined by the eigenvectors of (J JT)-1 and the lengths of the principal</p><p>　　axes are the square roots of the eigenvalues of (J JT)-1. The eigenvalues ar

87、e associated</p><p>　　with the velocity (or force) amplification factors along the principal axes of the</p><p>　　manipulability ellipsoid.</p><p>　　These criteria are used in Wenge

88、r13, to optimize the workspace shape and the</p><p>　　performances uniformity of the Orthoglide, a three degree of freedom PKM dedicated to</p><p>　　milling applications (Figure 12).</p>

89、<p>　　Figure 12. A section of Orthoglide’s optimised workspace</p><p>　　5.3. Technical Problems</p><p>　　If the struts of the PKMT are made with ballscrews, the PKMT accuracy may suffer<

90、/p><p>　　from struts warping due to heating caused by frictions generated by ballscrews. This</p><p>　　problem is met by hexapods designers that use ballscrews. Thus, besides manufacturing</p>

91、;<p>　　inaccuracies, the calibration of a PKMT will have to take into account dimensions</p><p>　　variations due to dilatation. A good thermal evacuation can minimise the effects of</p><p&g

92、t;<b>　　heating.</b></p><p>　　In case PKMT actuators are linear actuators, magnetic pollution has to be taken into</p><p>　　account so that chips clearing out is not obstructed. One t

93、echnique, used by Renault</p><p>　　Automation for the Urane SX, is to isolate the tool from the mechanism.</p><p>　　At last, choosing fixed length or variable length struts influence the behavio

94、ur of the</p><p>　　machine. Actuators have to be mounted on the struts in case of variable length struts,</p><p>　　which increases moved masses. Fixed length struts do not have this problem, and

95、</p><p>　　furthermore allow the use of linear actuators, that bring high dynamic performances.</p><p>　　6. CONCLUSIONS</p><p>　　The aim of this article was to introduce a few criter

96、ia for the design of PKMTs, which</p><p>　　may become interesting alternatives for High Speed Machining, especially in the milling</p><p>　　of large parts made of hard material, or for serial ma

97、nufacturing operations on</p><p>　　aeronautical parts.</p><p>　　Kinetostatic criteria seem to be well adapted to the design of PKMTs, particularly for</p><p>　　the kinematic design

98、and for the optimisation of the workspace shape, with regard to</p><p>　　performances uniformity.</p><p>　　The kinetostatic criteria have been used for the design of the Orthoglide, a three-axis