Assemblies forParallel Kinematics

Frank Dürschmied

INA reprint from “Werkstatt und Betrieb”Vol. No. 5, May 1999Carl Hanser Verlag, München

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Assemblies for Parallel KinematicsFrank Dürschmied

Joints and struts are importantmechanical assemblies in machinedesigns that are based on parallelstructures. These assemblies arethe critical components that deter-mine the precision and performancecapability of such machines.

1 IntroductionTwo years ago, industrial sources claimedthat parallel kinematics technology mightwell be the future of the machine tool.Very few people thought the new concepthad a chance, but now it seems that noone wants to be left out. The future isalready here!

A development like this has also been achallenge for manufacturers of machinecomponents. The rolling bearing industryrecognized this two years ago and drewa lot of attention when the first of the newcomponents were introduced. It began

with developments in mechanical jointsand was followed by the design andproduction of telescopic strut assemblies. Currently such components are beingtested by INA applications engineersalong with engineering partners fromuniversities and the industry. Besidespractical tests, extensive testing isunderway to validate performance data.On the basis of the positive resultsrecorded so far, INA is presentingproduction-ready standardized productsnow. These products will surely have aneffect on the development of parallelkinematics.

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2 Heavy demands on jointsJoints are not new. They are standardcomponents in both automobiles andagricultural machinery. However, therequirements in these areas are quitedifferent from those in machine tooldesign and construction. In the context of parallel kinematics, the requirementsthat joints must meet are:• high rigidity • high static load-carrying capacity• long service life• pivot angle suitable for the design• low mass• high precision• clearance-free bearing arrangements,

preloaded systems• smooth running, stick and slip free• defined, measurable joint crosspoint• low wear.

For tripods and hexapods, a parallelstructure requires joints having both twoand three degrees of freedom. Bothversions were thus developed in each ofthe respective joint types.The specific requirements of differentapplication areas led to further types.For example, a joint in a cutting machinemust have maximum rigidity and precision.In handling technology and in cuttingprocesses, large workspaces are traversedvery quickly. This means large pivotangles and low joint mass.Three different joint designs have beendeveloped to meet these requirements.These will be discussed below.

2.1 Ball joints with three degreesof freedom

Ordinarily, ball-to-ball contact is a poorrolling-contact match in terms of surfaceloading. However, in the course of proto-type development, this yielded highlyfavorable conditions in this application(Fig. 1).Because a large number of small balls areused, the Hertzian pressure between thecup and the rolling element and betweenthe rolling element and the inner ballremains low. However, favorableconditions can only be utilized if thegeometric accuracy of the contacting ballsurfaces is very high. Testing allowedmanufacturing processes to be improved,and good results were achieved in termsof both shape and surface quality. Besidesa high load rating, rigidity of joints isabsolutely essential in a cutting machine.Despite point contact, high rigidity isachieved under preloading because ofthe favorable load distribution.

Fig. 1 Ball joint with three degrees of freedom

➀ Seal carrier

➁ Ball with pin

➂ Rolling elements

➃ Ball cup

➄ Centering seat

Pivot angle:Axis I 30°Axis II 30°Axis III 360°

➀

➁

➂

➃

➄

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Of all joints, the ball joint offers the bestratio of load carrying capacity and rigidityin terms of design space. The surroundingseal carrier provided a complete sealingeffect. With these characteristics and withpivot angles up to about 20°, this joint willmainly be used in cutting machines andheavy handling equipment.

2.2 Universal joints with two orthree degrees of freedom

The universal joint (Fig. 2) is ideal forapplications in the handling sector. Its lowmass and large pivot angles allow struc-tures to be designed that are subjectedto high accelerations and speeds in largeworkspaces. In order to keep design sizeand rigidity within an appropriate range,the pivot angle was limited in the endpositions (Fig. 3). The pivot angle diagramshows the permissible pivot positions ofthe axes to one another. Because ofsmall support width and the use ofangular-contact needle roller bearings,rigidity values are significantly belowthose of the ball joint, despite preloading.However, they are sufficient for theapplications mentioned above. The advantage clearly lies in the low 2.7 kg mass and the large pivot angles.

2.3 Cardan jointsCardan joints usually serve to transmittorques and to offset misalignment inshaft connections. In parallel structures,tensile and compressive forces must betransmitted and high rigidity must beensured. For this reason the spider wasoptimized for tensile-compressive loadingby a finite element program. In particular,the spider and the yoke was improved.The rolling bearings to be used arepreloaded axial-radial needle rollerbearings. These bearings offer thegreatest possible rigidity relative to space,are completely sealed and represent thetechnical standard in the rolling bearingsector. The cardan joint closes the gap betweenball joint on the one hand and universaljoint on the other. At very high rigidities,this joint permits large pivot angles. Alsonote the pivot angle diagram in Fig. 3. Its limitations in relation to the relativemovement of axis I and axis II are alsoapply to the cardan joint. This makes the cardan joint ideal for applications inwhich large workspaces are traversedand rigidity is required (Fig. 4).

Fig. 2 Universal joint with two or three degrees of freedom

Fig. 3 Pivot angle diagram

Pivot angle diagram

45°

I

II

30°

15°

0°0° 15° 30° 45° 60° 75° 90°

➀

➁

➂

➃

➀ Angular contactneedle bearings

➁ Pin with degreeof freedom II /45°

➂ Optional degreeof freedom III /360°,axial-radial needle bearing

➃ Baseplate withrolling element raceway,degree of freedom I / 90°

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3 Telescopic strutsTwo years ago INA presented the firsttelescopic struts as machine componentsat the EMO in Hanover. In contrast to thestruts machine builders had developedfor their own projects, these were the firststruts to become commercially available.After further design enhancements, twodiameter sizes are now available. Startingfrom the basic dimensions, the design ismatched to customer requirements withregard to stroke path, rigidity and thereactive forces expected. Stroke length,the second suspension point and the

type of joint are also variable and can bedesigned to meet customer requirements. The functional structure of a telescopicstrut, with outer tube and inner tube, is similar to that of a hydraulic cylinder.To ensure clearance-free guidance of theinner tube during extension, a preloadedlinear guidance system is provided in theouter tube and patented, embeddedINA KUVS raceway in the inner tube.Depending on rigidity requirements, feeddrive is either a ball or roller screw drive.The drive spindle has a DKLFA seriesthrust angular-contact ball bearing.

At a maximum speed of 2000 min–1 andspindle pitch of 20 mm, feed speeds of0.8 m/s are possible (Fig. 5).Stresses on the platform are converted totensile-compressive loads by the jointkinematics. A transverse force on thelinear guidance system occurs onlybecause of the accelerated mass of thetelescopic strut. The decisive rigidity factor is thereforethe rigidity of the axis of the telescopicstrut. Rigidity is thus a function of strokelength when the diameter remainsconstant.

Fig. 4 Cardan joint

Fig. 5 Telescopic strut

➀

➁

➂

➃

Inner tube with embedded patented INA KUVS raceway

Cardanic suspension

Outer tube

INA Linear guidance system KUVS

Ball screw or roller screw drive

INA thrust angular-contact ball bearingDKLFA

➀ Axial-radialneedle bearingoptional, degree offreedom III

➁ Spider

➂ Bearing support

➃ Axial-radialneedle bearing

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4 Determining rigidityJoints, particularly ball joints, can becompared to rolling bearings by calculatingcharacteristic values, but only to a limitedextent. Calculation methods must first bedeveloped in order to determine referencevalues for the design. These theoriesare then tested for plausibility and furtherdeveloped. To determine rigidity values, the jointswere calculated using a finite-elementprogram based on the 3-D CAD model.For cardan and universal joints, rigidityhere appears as series/parallel switchingof the individual components. The bearingsbehave like ordinary rolling bearings.Accordingly, deflection is clearly brokendown into rolling element compressionand the deformation of the spider.Determining the rigidity in ball joints isconsiderably more difficult. Basically, a finite-element model is also generatedhere. The rolling elements are replaced bynon-linear springs, and the geometricalaccuracy is captured by means of variousspring rigidities (Fig. 6). This is a justifiableprocedure since the deviation from theball shape nearly always occurs in thesame area as a result of the process.This modeling makes it possible toinclude in the calculation the inaccuracyof the components with respect togeometrical accuracy. In both the universal joint and the ball jointthere was a good correlation betweencalculation theory and the test. Figure 7gives a comparison of the rigidity valuescalculated for all joints.

5 Load ratings and rating lifeThe determination of load ratings incardan joints and universal joints is basedon classic rolling bearing theory. Finite-element calculations have demonstratedthat the connecting components are notcritical elements. For these types, a loadrating can thus also be defined by theload rating of the weakest rolling bearingmounted. As for the determination ofrating life, an analogy to oscillating bearingmovements can be seen here, i.e., thereis no fatigue in the conventional sense.The best characteristic number forquantifying probability of failure is thestatic load safety factor. Because of thehigh bearing load ratings, in normalapplications a static load safety factor ofat least four can be ensured. Empiricalvalues indicate that there is little tendencyfor the part to wear at these levels.These theoretical issues will be verifiedin the test.

Ball joints are a totally new design, andit is hard to compare them with rollingbearings. This type of joint is not aconventional rolling bearing type.INA is currently preparing calculationprocedures for ball joints.If a ball joint is pivoted, the roll-off move-ment of the rolling element occurs only atthe pivot level. Outside this level, i.e.,the case of about 95% of rolling elements,there is a movement about all three axes.Also, because of the full complementdesign, the effects of the balls on eachother must also be taken into account. In rolling bearing technology, a load thatoccurs in this joint, i.e. a pivoting move-ment with small pivot angles under load,cannot be calculated by conventionalmeans. Long-term testing must beconducted to determine the fatiguebehavior of these elements. Conclusionsconcerning possible calculation procedurescan be drawn from the test results.

Fig. 6 Ball joint, finite-element model

Force application

Inner ball

Rigid housing

Rolling bearingmodeled as elasticspring locationLocation

Pivot angle α = 0°-°α = 10°

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6 LubricationSwiveling motion or micro-oscillations inrolling elements place special demandson the lubricant. Greases designedespecially for this application can reducethe wear mechanisms commonly found inthese applications. More testing must beperformed in order reach final conclusionson whether fretting corrosion can beeliminated if special greases are used.Using protective coatings on critical partsis another means of preventing frettingcorrosion. Large-scale testing is alsounderway in this regard.

7 ConclusionWith the development of joints and teles-copic struts for parallel kinematics machinecomponents for this new generation ofmachine tools and handling equipmentare now available to the designer. Components have been designed tomeet the great number of demandsplaced on joints and telescopic struts. As for future developments, the resultsobtained from various research projectssuch as Dynamil II or from collaborationwith customers will point the way to newdirections.

Because of constant new developments,it is absolutely essential for designengineers to work closely with the manu-facturer when using these new machinecomponents. Further information on implementation,design criteria and the state-of-the-art ofdevelopment can be found in the detailedpublications supplied by rolling bearingmanufacturers or may be obtained bycontacting their Application EngineeringService.

Fig. 7 Comparison of rigidity values of the joints under investigation

Ball joint 40 mm(Tension load)

400

350

300

250

200

150

100

50

0

Rigidity valves calculated

N/m

icro

met

er

Ball joint 60 mm(Tension load)

Universal joint 2F Universal joint 3F Cardan joint 2F Cardan joint 3FF = Degree of freedom

Authors:Frank Dürschmied is an applicationsengineer in the Production Machinesand Systems Sector Management withINA Wälzlager Schaeffler oHGin Herzogenaurach (Germany).

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