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/Engineering ScienceEngineers, Part C: Journal of Mechanical Proceedings of the Institution of Mechanical /content/219/7/687The online version of this article can be found at: DOI: 10.1243/095440605X31508687 2005 219:Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering ScienceHao Wang, Ce Zhang and Guanlong ChenKHV Indexing Cam Mechanism: A New Intermittent Mechanism Published by: On behalf of: Institution of Mechanical Engineers can be found at:ScienceProceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical EngineeringAdditional services and information for /cgi/alertsEmail Alerts: /subscriptionsSubscriptions: /journalsReprints.navReprints: /journalsPermissions.navPermissions: /content/219/7/687.refs.htmlCitations: What is This? - Jul 1, 2005Version of Record at ZHEJIANG UNIVERSITY on January 5, 2013Downloaded from KHV indexing cam mechanism:a new intermittent mechanismHao Wang1?, Ce Zhang2, and Guanlong Chen11School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, Peoples Republic of China2School of Mechanical Engineering, Tianjin University, Tianjin, Peoples Republic of ChinaThe manuscript was received on 13 September 2004 and was accepted after revision for publication on 5 April 2005.DOI: 10.1243/095440605X31508Abstract: The KHV indexing cam mechanism is a new type intermittent mechanism that hasa structure similar to the KHV planetary gear transmission (one type of the planetary drivewith small teeth difference, where K indicates the sun gear, H indicates the pivoted arm, andV indicates the output mechanism). This paper focuses on the generation of a pitch curveand a cam profile in such a new mechanism. Three types of the KHV indexing cam mechanismare compared and discussed, and the equations of cams pitch curves are derived. The camsprofile is generated by Boolean operations on the offsets of the cams pitch curve.After this, the cusps on the cam profile are eliminated and replaced by a particular Hermitecurve. The animations of all three types are illustrated, and a prototype of such mechanism isreported.Keywords: intermittent mechanism, indexing cam mechanism, planetary transmission1INTRODUCTIONIndexing cam mechanisms are widely used in theindustry. Three types of such mechanisms, the paral-lel indexing cam mechanism, the Ferguson indexingcam mechanism, and the barrel indexing cammechanism, are the traditional types well knowntoday 18. In recent years, some new types ofindexing cam mechanisms have also been reported,e.g. the synthesis of the spherical indexing cammechanism with direct contact between cam andfollower was reported by Gonzalez-Palacios andAngeles 9. They extended this concept to thespherical indexing cam mechanism including rollers10. Gonzalez-Palacios and Angeles 11 also pro-posed a unified approach aiming at the synthesisof indexing cam mechanisms with direct contacttransmission. A new type of parallel indexing cammechanism with an internal cam was reported byNishioka and Nishimura 12. Zhang 13, 14 createda new concept of indexing cam mechanisms theplanetary indexing cam mechanism and presentedtwo types of it. In this paper, the concept is extendedto the KHV indexing cam mechanism, which is anintermittent mechanism that has a layout of KHVplanetary gear transmission.The new mechanism is suitable for the workingconditions where a large number of stops areneeded. As most of the rollers can be engaged withthe cam in the mechanism, a higher strength andmore compact design can be obtained. This newmechanism could expand the applicable ranges ofthe indexing drivers to wider industry applications.This paper focuses on the generation of the pitchcurve and the profile of the cam in such a mechan-ism. The structure of this paper is as follows. First,section 2, discusses three types of the KHV indexingcam mechanism, namely, type I, type II, and theretrogressed mechanism; then the generation of thecams pitch curve and cam profile are explained andtheanimationofthemechanism(typeIandtypeII) isillustrated in sections 3, 4, and 5, respectively, after abrief introduction of the retrogressed mechanism insection 6. Finally a prototype of the mechanism ispresented in section 7.?Corresponding author: Auto-body Manufacturing TechnologyCentre, School of Mechanical Engineering, Shanghai Jiao TongUniversity, Shanghai 200030, Peoples Republic of China.687C16204#IMechE 2005Proc. IMechE Vol. 219 Part C: J. Mechanical Engineering Science at ZHEJIANG UNIVERSITY on January 5, 2013Downloaded from 2STRUCTURE OF THE DEVICEThe structure of a KHV indexing cam mechanism issimilar to a cycloid speed reducer, whose schemeis depicted in Fig. 1. A cycloid speed reducer is com-posed of an epitrochoid planet gear g, an input shaftH (pivoted arm) with an eccentricity, and a numberof rollers fixed in sun gear b. For pure rotationalmotion of the output shaft V, the eccentric wobbleof the planet gear g is filtered out by device W,which is a parallelogram mechanism.As the layout of a KHV indexing cam mechanism issimilar to the cycloid speed reducer, Fig. 1 is alsoused as the scheme of the new mechanism. In sucha mechanism, the pair of planet gears g and the roll-ers in sun gear b are replaced by a camroller pair toimplement the intermittent motion. In the motionprocess, the input shaft H rotates at a constantspeed, while the rotation of the planet gear g isintermittent. The rotational motion of the planetgear g is also filtered out by device W to outputshaft V.TheKHVindexingcammechanismcanbedesigned as two different types according to thelayout of the camrollers pair, namely, type I, inwhich planet gear g is a cam and the rollers arefixed in sun gear b, and type II, in which the rollersare fixed in the planet gear g and the sun gear b isan internal cam. When the output shaft is the sungear b, and V is fixed, the mechanism is no longer aplanetary mechanism, but an ordinary gear trainretrogressed from the planetary mechanism (Fig. 2).Because such a retrogressed mechanism could alsofulfill the task of an intermittent motion, it is catalo-gued as the retrogressed type of the KHV indexingmechanism. Research work has been reported earlieron type II of the mechanism by Zhang 13. In thispaper, attention is focused on the synthesis of allthree types.3PITCH CURVE OF THE CAM3.1Equation of the pitch curveOn the basis of the layout of the mechanismmentioned earlier and the relative motion of its com-ponents, the coordinate system and the parametersin type I are constructed as in Fig. 3. Consider threebodies: g, playing the role of the planet cam, bbeing the sun gear with rollers, and H being theinput shaft with an eccentricity. Oband Ogdenotethe centre of sun gear b and planet cam g, respect-ively. The fixed coordinate system ObXbYbis rigidlyfixed on the sun gear b, and the input shaft H rotatesaround the point Obwith a constant angular velocity.A relative coordinate system OgXgYgrigidly con-nected to the planet cam g is also set up, and Ogalso represents the rotational centre of the planetcam g. We assume that e represents the eccentricityin the input shaft, and the radius of the sun gear b(the distances between Oband the centre of rollersMi) is Rz. The number of rollers in the sun gear bis z. The angular displacement of the input shaft HisuH, and that of the planet cam g isug. Let Mi(i 1,.,z) represent the centre of the rollers,respectively.Three position vectors, Rzi, H, and RTi, are alsoshown in Fig. 3, where Rziis fixed on the sun gear band oriented towards the centre of the roller Miwith the origin Ob, H is fixed on the input shaft andoriented towards the centre of the planet cam Ogwith the origin Obalso, and RTirepresents theposition of the cam pitch curve with the origin Og.Fig. 1Scheme of a KHV indexing cam mechanism(type I and type II)Fig. 2Scheme of a KHV indexing cam mechanism (theretrogressed mechanism)Fig. 3Coordinate system of type I688Hao Wang, Ce Zhang, and Guanlong ChenProc. IMechE Vol. 219 Part C: J. Mechanical Engineering ScienceC16204#IMechE 2005 at ZHEJIANG UNIVERSITY on January 5, 2013Downloaded from Their relationship yieldsRTi(t) Rzi H Rzej(ai?ug(t)? e ej(uH(t)?ug(t)t 0, T?,i 1, 2,.,z(1)For type II, the coordinate system and the par-ameters are as constructed in Fig. 4. In such type, gplays the role of the planet roller gear, b is an internalcam, and H is the input shaft with an eccentricity.Oband Ogdenote the centre of sun gear b androller gear g, respectively. The fixed coordinatesystem ObXbYbis also rigidly connected to theinternal cam b, and the input shaft H rotates aboutthe point Obwith a constant angular velocity.The moving coordinate system OgXgYgis rigidly con-nected to the roller gear g, and Ogis the rotationcentre of the roller gear g. Also, e representsthe eccentricity, and the radius of the roller gear gis Rz. The number of rollers in the sun gear b is z.The angular displacement of the input shaft H isuH, and that of the planet cam g isug. Let Mi(i 1,.,z) represent the centre of the rollers,respectively. Three position vectors, Rzi, H, and RTi,are also used here and have the same denotionas with type I. In type II, they yield a differentrelationship asRTi(t) H Rzi eejuH(t) Rzej(aiug(t)t 0, T?,i 1,2,.,z(2)3.2Relations between the input and theoutput of the mechanismFrom equations (1) and (2), it is seen that the pitchcurve of either type is composed of several curvesthat are determined by every equation in the setcorrespondingly. Every curve has to be connectedto each other to make sure that the pitch curve ofthe cam is continuous. Then, the parameters inequations (1) and (2) should satisfyRTi(T) RTi1(0)(3)RTn(T) RT1(0)(4)From equations (3) and (4), for type I, the followingexpression is obtainedn z(5)iHg ?(z ? 1)(6)Then, the displacement of the input shaft and theoutput shaft are defined by the following equationuH(t) uH(0) 2(n ? 1)ptnT(7)ug(t) ?2pSn(8)For type II, another expression is obtainedn z(9)iHg ?z(10)the displacement of the input shaft and the outputshaft in type II has a different definitionuH(t) uH(0) 2ptT(11)ug(t) ?2pSn(12)Figures 5 and 6 provide examples of the pitchcurve of type I and type II, respectively. In bothtypes, Rz 100, n 12, modified sine motion isused to generate the pitch curve.Figure 5 also shows the connection point betweenevery piece of curve, with an asterisk, with d 0.83and K1 1.2, and in Fig. 6, d 1 and K1 1.92.Fig. 4Coordinate system of type IIFig. 5Pitch curve of type IKHV indexing cam mechanism689C16204#IMechE 2005Proc. IMechE Vol. 219 Part C: J. Mechanical Engineering Science at ZHEJIANG UNIVERSITY on January 5, 2013Downloaded from 4PROFILE OF THE CAM4.1Boolean operationAlthough the pitch curve of the planet cam is a closedcurve, it is not a simple plane curve because of itsself-intersection (Figs 5 and 6). Given the analyticalplane curve RTias the generator curve, the offsetsto RTiat distance rzare the curves defined byRIi(t) RTi(t) ? rzni(t)ROi(t) RTi(t) rzni(t)t 0, T?, i 1, 2,. ,z(13)where niis the unit normal vector to RTi, and RIiand ROirepresent the interior and exterior offset,respectively. If the pitch curve of the planet camwas a simple curve, the profile of the planet camwould be the interior offset curve RIi(in type I), orthe exterior offset curve ROi(in type II). Becauseself-intersection occurs in some pieces of the pitchcurve, the profile of the planet cam is composed ofcertain pieces on both the interior and exterioroffsets.To determine the profile of the planet cam, aBoolean algorithm on areas enclosed by simplecurves is introduced. Let AC1be the area enclosedby curve C1, and AC2be that of curve C2. Here,three types of Boolean operation are of interest:union of AC1and AC2, denoted as AC1AC2; andsubtraction of AC1and AC2, denoted as AC1AC2. Analgorithm called LOBO (loops of Boolean operation)is employed to calculate the profile of the cam.The LOBO algorithm applied here was reported byRohmfeld 15.By employing the Boolean operation, we derivethe expressions of the cam profile for each type. Asthe self-intersection also occurs in the offsets of thepitch curve, we first divide the offsets into twoparts:oneistheareaenclosedbytheself-intersection pieces, we called as SI(in the interioroffset curve) and SO(in the exterior offset curve)theotheristheareaenclosedbythenon-self-intersection pieces on the offsets, we called AI(in the interior offset curve) and AO(in the exterioroffset curve).For type I, the area enclosed by the cam profile TIis expressed by the subtraction of the union of SIand SOfrom the intersection of AIand AO.TI (AI AO)n(SI SO)(14)For type II, the area enclosed by the cam profile TIIis expressed by the union of AI, AO, SI, and SO.TO AI AO SI SO(15)Figures 7 and 8 show the cam profile of type Iand type II generated, respectively, from Figs 5 and6 by the Boolean operation mentioned earlier. InFig. 7, the radius of the rollers is calculated withKz 0.6 and in Fig. 8, Kz 0.5.Fig. 6Pitch curve of type IIFig. 7Cam profile (type I)Fig. 8Cam profile (type II)690Hao Wang, Ce Zhang, and Guanlong ChenProc. IMechE Vol. 219 Part C: J. Mechanical Engineering ScienceC16204#IMechE 2005 at ZHEJIANG UNIVERSITY on January 5, 2013Downloaded from 4.2Smoothness of the cam profileIn the cam profile, the point that connects two piecesof the offsets, namely, the intersection point of RIiand ROi, became a cusp. Such a cusp is a weaknessin the profile, for its curvature is infinite and easilybroken. To eliminate the cusps, a Hermite curveis employed to replace the curves near the cusps.Asseveralrollersareengagingwiththecamsimultaneously, the replacement will not affect theoutput of the mechanisms. Figure 9 shows thelocality of the areas near one of the cusps, in whichP0and P1are the points located in different sides ofthe cusp P. Given the end point P0and P1, and thetangent vector of the cam profile in these points, aHermite curve can be readily defined. Thus, thecurve P0P and PP1are removed from the cam profile,and the Hermite curve is embedded in it instead.Each cusp on the profile can be eliminated andreplaced by a particular piece of the Hermite curve.After this procedure, the cam profile is a simple,smooth, and continuous curve. Figure 10 shows thecam profile after the procedure mentioned earlier.5MOTION ANIMATION OF THE MECHANISMFigures 11 and 12 show the animations of the plane-tary indexing mechanism (type I and type II, respect-ively); (a) shows the beginning of an intermittentmotion period; (b), (c), and (d) are the phases inthe motion period; (e) is the end of motion periodand also the beginning of the dwell period; (f) and(g) are in the dwell period; (h) is the end of thisintermittent motion period and the beginning ofthe next one.Fig. 11Animation of the mechanism (type I)Fig. 9Locality of a cuspFig. 10Cam profile after the smoothing procedureKHV indexing cam mechanism691C16204#IMechE 2005Proc. IMechE Vol. 219 Part C: J. Mechanical Engineering Science at ZHEJIANG UNIVERSITY on January 5, 2013Downloaded from 6THE RETROGRESSED MECHANISMConsidering that V is fixed (Fig. 2), and the outputshaft is the sun gear b, the mechanism is a retro-gressed mechanism of the planetary mechanism(Fig. 1). Compared with an internal parallel indexingmechanism, the input shaft in such a retrogressedmechanism is H rather than the cam g, and there isno angular displacement of the cam g in anymotion period. In the motion process, the inputshaft H rotates at a uniform speed, there is noangular displacement on planet cam g, the rotationof the roller gear b is an intermittent motion thatyields the same law as the planetary mechanism.Figure 13 shows the animation of the retrogressedmechanism of type I (Fig. 11) in a motion period, inwhich (a) shows the beginning of an intermittentmotion period; (b), (c), and (d) are sequences of themotion period; (e) is the end of motion period andthe beginning of the dwell period; (f) and (g) are inthe dwell period; (h) is the end of this intermittentmotion period and the beginning of the next one.Fig. 12Animation of the mechanism (type II)Fig. 13Animation of the retrogressed mechanism692Hao Wang, Ce Zhang, and Guanlong ChenProc. IMechE Vol. 219 Part C: J. Mechanical Engineering ScienceC16204#IMechE 2005 at ZHEJIANG UNIVERSITY on January 5, 2013Downloaded from 7PROTOTYPE OF THE MECHANISMA prototype of the mechanism (type I) has beenmade to test the feasibility of the mechanism.Figure 14 shows the photographs of the planetarycam,assembledpairofcamandrollers,andappearance of the prototype, respectively. The camis manufactured in a linear cutting machine, not anNC milling, as there are some grooves on the camprofile. The manufacture of the cam by linear cuttingis not very accurate, but it is enough to test themechanisms feasibility. The prototype achieved aspeed of 250 r/min driven by motor-belt chain.This prototype proved that the concept of theKHV indexing cam mechanism is feasible and suc-cessful. Another prototype has been manufacturedto test the performance of this mechanism such asthe positioning accuracy, highest speed, vibration,and noise. The report of the second prototypeperformance test will be presented later.8CONCLUSIONSThe layout of the KHV indexing cam mechanismemploys a structure similar to a cycloid speedreducer. The mechanism can be designed into twodifferent types (type I and type II) according to thedifferentlayoutofthecamrollerpair.Fromconverting the output shaft V to a fixed element, aretrogressed type can be obtained, such a mechan-ism is also an intermittent mechanism. Because ofself-intersection in the pitch curve, the unusualcam profile is composed of certain pieces on bothinterior and exterior offsets of the pitch curve. Theprototype of this mechanism proved that the conceptof the KHV indexing cam mechanism is feasibleand has potential in industry.ACKNOWLEDGEMENTSThe research work is supported by National NaturalScienceFoundationofChina(NSFC)Researchgrant no. 50175077. The authors are grateful toProfessor Yuhu Yang for his contribution in theprototype manufacturing.REFERENCES1 Jacobs, R. J. Indexing with concave barrel cams. Mach.Des., 1949, 9396.2 Neklutin, C. N. Designing cams. Mach. Des., 1952,143160.3 Jensen, P. W. Cam Design and Manufacture, 1965(Industrial Press, New York).4 Bickford, J. H. Mechanisms for Intermittent Motion,1972 (Industrial Press, New York).5 Chakraboty, J. and Dhande, S. G. Kinematics andGeometry of Planar and Spatial Cam Mechanism, 1977(John Wiley and Sons, Inc., New York).6 Rees Jones, J. Cams and Cam Mechanisms, 1978(Mechanical Engineering Publications Ltd. for theInstitution of Mechanical Engineers, London).7 Chen, F. Y. Mechanics and Design of Cam Mechanisms,1982 (Pergamon Press Inc., New York).8 GuoXun, P., Zhengyang, X., and Huimin, T. Unifiedoptimaldesignofexternalandinternalparallelindexing cam mechanisms. Mech. Mach. Theory, 1988,23(4), 313318.9 Gonzalez-Palacios, M. A. and Angeles, J. The gener-ation of contact surfaces of indexing cam mechanismsa unified approach. In Proceedings of ASME DesignAutomation Conference on Advances in Design Auto-mation, 1990. Vol. 2, pp. 359364.10 Gonzalez-P