机械类外文翻译【FY188】KHV分度凸轮机构：一种新的间歇性机制【PDF+WORD】【中文4300字】
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KHV 分度凸轮机构：一种新的间歇性机制 Hao Wang1 , Ce Zhang2, and Guanlong Chen1 1机械工程学院，上海交通大学，上海，中华人民共和国 2机械工程学院，天津大学，天津，中华人民共和国 摘要： KHV分度凸轮机构是一种新型的间歇机构，它具有 KHV行星齿轮传动装置（一种类型的行星传动的结构类似少齿差，其中 K表示太阳齿轮， H 表示的枢转臂，和 V表示的输出机制）。本文重点介绍的是在这样一个新的机制中，间距曲线和一个凸轮轮廓的生成。对 KHV分度凸轮机构的三种类型进行比较和讨论，得出 凸轮的曲线方程。对凸轮的节距曲线的偏移量进行布尔运算，然后得出凸轮的轮廓曲线。在此之后，被消除凸轮轮廓上的尖点，由一个特定的厄米曲线取代。 下文将展示这三种类型的动画，并呈现这样一个机制的原型。 关键词：间歇机构，分度凸轮机构，行星传动 1、介绍： 分度凸轮机构在工业中被广泛使用。平行分度凸轮机构，弧面分度凸轮机构，圆柱分度凸轮机构，这三种传统类型的机构在今天广为人知 81 。 近年来，一些新的索引的类型的凸轮机构也有报道，例如，冈萨 雷斯 -帕拉西奥斯 和洛杉矶报道的凸轮和从动件之间直接接触的合成的球形分度凸轮机构 9 。这个类型的球面分度凸轮机构，包括 滚筒 10 。 冈萨雷斯 -帕拉西奥斯 和洛杉矶 11 还提出了统一的方法，目的在于分度凸轮的合成机制与直接接触传递 。西冈和西村报道了一类新型的有内部凸轮的平行分度凸轮机 构 12 。张 13 14 对于分度凸轮机制，创建了一个新的概念 -行星分度凸轮机构，并提出了两种类型的这种机构。在本文中，这个概念延伸到 KHV分度凸轮机构，这是一个间歇运动机中构具有 KHV行星齿轮变速器的布局。新的机制适合某些需要大量停止的工作环境。在该机制中由于大部分的滚子可以与 凸轮接合，所以可以得到更高的强度和更紧凑的设计。这一新的机制的索引驱动器的适用范围将扩大到更广泛的行业应用。 2、设备结构： 一个 KHV分度凸轮机构的结构是类似一个摆线针轮减速机，其计划描绘在图 1。 摆线减速机由一个行星齿轮，有偏心率的输入轴 H（旋转手臂）和固定在太阳齿轮 b上的一些 滚 子组成。对于纯旋转运动的输出轴 V行星齿轮 g的偏心摆动 被一个平行四边形机构的设备 w滤出。 作为一个 KHV分度凸轮机构的布局是类似的摆线减速机，图。 1也被用来作为该计划的新机制。在这样的机制中，行星齿轮 g和在太阳齿轮 b上的辊将被取代 ，由一个凸轮 -辊机构来进行间歇运动。在运动过程中，输入轴 H将在一个恒定的速度旋转，而旋转的行星齿轮 g则是间歇性的。行星齿轮 g的旋转运动也被输出装置 w滤出到轴五。 根据凸轮 -滚子的布局， KHV分度凸轮机构可以被设计为两种不同的类型，即， I型，其中的行星齿轮 g是一个凸轮，而滚子被固定在太阳齿轮 b上，和型，其中滚子被固定在行星齿轮 g上，而太阳轮齿 b是一个内部的凸轮。当输出轴的太阳齿轮 b和 V是固定的，该机制是不再是一个行星齿轮机构，而是从一个行星齿nts轮机构倒退变为一个普通齿轮传动机构。（图 2）因为这样的退变机制也能 完成间歇运动的任务。这被叫做退变型的 KHV索引机制。关于型机构的研究工作在先前已经被张报道过了。在本文中，都集中在所有这三种类型的合成。 3.1、凸轮的节距曲线： 根据前面提到的对于该机制的布局和其组成部分的相对运动，在图 3 构造出了坐标系统和型机构的参数。考虑三个结构： g是行星凸轮， b是有滚子的太阳齿轮， H是有偏心作用的输入轴。 Ob和 Og分别表示太阳齿轮 b和行星凸轮 g的中心。固定坐标系 ObXbYb被刚性地固定在太阳齿轮 b上，输入轴 H以一个恒定的角速度绕点 Ob旋转。与行星凸轮有关 的相对坐标系统 OgXgYg也建立起来了，并且Og也代表了行星凸轮 g的旋转中心。我们假设， e表示输入轴的偏心，与太阳齿轮 b的半径（ Ob与滚子的中心之间的距离 Mi）为 Rz。在太阳齿轮 b 中滚子的数目是 z。输入轴 H的角位移是 H，行星凸轮的角位移是 g。分别让 Mi（ i= 1， .，z）代表各滚子的中心。 三个位置向量， RZI， H和 RTI， 也示于图 3中，其中 RZI被固定在太阳齿轮 b并且面向各个滚子的中心和点 Ob。 H被固定于输入轴并且面向行星凸轮的中心与点Ob。 RTI表示点 Og作凸轮节距曲线运动的位置 . nts他们之间的关系是： 对于 II 型，坐标系和参数的构造如图 4 所示，在这样的类型里， g 所扮演的角色的行星滚子齿轮， b 是一个内部的凸轮，和 H 是有偏心率的输入轴。 Ob 与 Og 分别表示太阳齿轮 b 和滚子齿轮 g 的中心。固定坐标系 ObXbYb 也刚性地连接到凸轮 b 的内部，输入轴 H 以一个恒定的角速度绕点 Ob 旋转。移动坐标系统OgXgYg 被刚性地连接到滚子子齿轮 g， Og 是滚子齿轮 g 的旋转中心。此外， e表示的偏心，滚子齿轮 g 的半径为 Rz。在太阳齿轮 b 中的滚子的数目是 z。 输入轴 H的角位移是 H，行星凸轮的角位移是 g，分别让 Mi（ i= 1， .， z）代表各滚子的中心。三个位置向量， RZI， H和 RTI，也用在这里，具有与类型 I相同的意义。在 II型中，他们有着不同的关系： 方程（ 1）和（ 2）应满足 从等式（ 3）和（ 4）中，根据 I 型，得到下面的表达式： 然后，输入轴和输出轴的位移是由下面的等式定义的： 对于 II 型，可以获得另一种表达方式： 在 II 型中的输入轴和输出轴的位移有不同的定义： 3.2、机构的输入和输出之间的关系 从方程（ 1）和（ 2），可以看出，两种类型的节距曲线由它们相应的组中的每个方程所确定的几个曲线构 成。每个曲线彼此连接，以确保该节距曲线的凸轮是连nts续的。然后，图 5 和 6 中的参数分别提供了 I 型和 II 型机构的节距曲线。在这两种类型中， RZ=100 中， n=12，改性的正弦运动用于生成节距曲线。图 5 还显示了每一块曲线之间的带有星号的连接点，其中 d=0.83 和 K1=1.2，图 6 中， d= 1，K1=1.92。 4、 凸轮的轮廓： 4.1、布尔运算 虽然星轮的凸轮曲线的间距是一个闭合曲线，但是由于曲线互相相交（图 5 和图6），所以它不是一个简单的平面曲线。鉴于作为电机曲线的平面分析曲 线 RTi，到 RTi 的偏移量 Rz 在曲线中被定义为： 其中， ni 分别表示到 RTI、 RII 和 ROI 内部和外部偏移的单位法线矢量，如果行星凸轮的间距曲线是一个简单的曲线，行星凸轮的轮廓将变成内部偏移曲线 RLi（ I 型），或外部偏移曲线 ROi（ II 型）。因为节距曲线上某些地方发生互相相交，行星凸轮的轮廓就由内部和外部的偏移量上的若干处组成。 要确定的行星凸轮的轮廓，就要在由简单的曲线围成的区域上引入一个布尔算法。假设 Ac1 是曲线 C1 包围的区域， Ac2 是曲线 C2 包围的区域。在这里，三种布尔运算互相联系：合并 AC1， AC2，表示为 AC1 AC2； 让 AC1， AC2 相交，表示为 AC1 AC2； 让 AC1 和 AC2 相减，表示为 AC1 AC2。 LOBO（循环布尔运算）的算法用来计算凸轮的轮廓。这里应用的 LOBO 算法是 Rohmfeld 15.首先提出的。 通过采用布尔运算，我们得到了各类型的凸轮轮廓的表达。由于相交也会引起节距曲线的偏移，我们首先将偏移量分成两部分：一个是由自相交部分包围的区域，我们称为 SI（内部偏移曲线）和 SO（外部偏移曲线）。另一个是由不相交部分包围的区域，我们称为 AI（内部偏移曲线）和 AO（外部偏移曲线） 。 nts对于型，用 AI 和 AO 的交集减去 SI 和 SO 的并集来表示凸轮轮廓围出的面积TI.: 对于 II 型，凸轮轮廓围成的面积 TII 由 AI， AO， SI 和 SO 的并集来表示： 图 7 和图 8 分别表示类型 I 和类型 II 生成的凸轮轮廓，由经过布尔运算的图 5和图 6 中获得。另外，在如图 7 所示，滚子的半径计算中 Kz=0.6，在图 8 中，KZ=0.5。 4.2、凸轮轮廓的平整度 在凸轮轮廓上，连接两个偏移量的点，即， RIi 和 ROi 的交点，成为一个尖点。 这样的尖点是在轮廓中的一个弱点，它的曲率是无穷大的，容易折断。为了消除尖点 ，尖点附近的曲线替换为一个 Hermite 曲线。由于几个滚子与凸轮同时啮合，更换不会影响机构的输出。图 9 示出了的一个尖点附近的局部区域，其中 P0 和P1 是位于尖点 P 两侧的点。鉴于结束点 P0 和 P1，还有在这些点上的凸轮轮廓的切线向量， Hermite 曲线可以很容易地被定义。因此，曲线 P0P 和 PP1 可以从凸轮轮廓上除去，用 Hermite 曲线嵌入来代替。每个轮廓上的尖点可以被除去，取而代之的是一个特定的 Hermite 曲线。在此之后，凸轮轮廓就变成一个简洁，流畅，连续的曲线。图 10 表示的是前面提到的改变之后的凸轮轮廓。 nts 5、 机构的运动图片 图 11 和 12 分别显示了行星索引机制的动画（ I 型和 II 型），（ a）显示一个间歇运动期间的开始，（ b） (c)和（ d）是在运动期间的相位，（ e）是运动期间的结束，也是停留时间的开始，（ f）和（ g）是在停留期间内，（ h）是这个间歇运动周期的结束和下一个的开始。 nts 6、 倒退机构 考虑 V 被固定（图 2），输出轴是太阳齿轮 b，这个机构是一个行星齿轮机构的退变机构，与内部平行索引机构相比，在这样的退变机构中输入轴是 H，而不是凸轮 g，凸轮 g 在任何运动期间都没有角位移，在运动过程中，输入轴 H 以均匀的速度转 动，行星凸轮没有角位移，滚子齿轮 b 的旋转是一种间歇运动。对行星齿轮机构来说也一样。图 13 显示出了 I 型（图 11）的一个运动期间中退变机构的动画，其中，（ a）表示间歇运动期间的开始，（ b） ,(c)和（ d）是运动期间的相位，（ e）是运动期间的结束，也是停留时间的开始，（ f）和（ g）是在停留期间内，（ h）是这个间歇运动周期的结束和下一个的开始。 nts 7、 机构的原型 用已取得的原型机构（ I 型）来验证其该机制的可行性，图 14 分别显示出了行星凸轮，凸轮和滚子的组装，以及原型外观的照片。凸轮是用一个线性切割机，而不是 NC 铣削制造的，因为在凸轮轮廓上有一些槽。用线切割制造的凸轮并不十分准确，但是用以测试该机构的可行性是足够的。该原型机构通过驱动马达皮带链实现了 250 转 /分的速度。这个原型机构证明， KHV 分度凸轮机构的概念是可行的，成功的。另一个样机已经被制造用来对这种机构的定位精度，最高速度，振动和噪音等性能的测试，第二个原型机构的性能测试报告将在后面提交。 8、 总结 KHV 分度凸轮机构的布局采用了类似于摆线减速器的结构，根据凸轮的滚子对的不同布局，该机制可以被设计成两个不同的类型（ I 型和 II 型）。把输出轴 V转换成一个固定的元件 ，这样得到的一个退变机构，也是一个间歇运动机构。由于节距曲线自的相交，异常的凸轮轮廓就由若干节距曲线内部和外部的偏移区域组成。这一机制的原型证明 KHV 分度凸轮机构的概念是可行的，并在工业上拥有极大的潜力。 参考文献 : 1、 Jacobs, R. J. Indexing with concave barrel camsJ. Mach.Des., 1949, 93 96 2、 Neklutin, C. N. Designing cams. Mach. DesM., 1952,143 160 nts3、 Jensen, P. W. Cam Design and Manufacture,M 1965(Industrial Press, New York). 4、 Bickford, J. H. Mechanisms for Intermittent Motion,J1972 (Industrial Press, New York). 5、 Chakraboty, J. and Dhande, S. G. Kinematics and Geometry of Planar and Spatial Cam MechanismM, 1977(John Wiley and Sons, Inc., New York). 6、 Rees Jones, J. Cams and Cam MechanismsJ, 1978(Mechanical Engineering Publications Ltd. for the Institution 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. Unified optimal design of external and internal parallel indexing cam mechanisms. Mech. Mach. Theory, 1988,23(4), 313 318. 9、 Gonzalez-Palacios, M. A. and Angeles, J. The generation of contact surfaces of indexing cam mechanisms a unified approach. In Proceedings of ASME Design Automation Conference on Advances in Design Automation,1990. Vol. 2, pp. 359364 10、 Synthesis of contact surface of spherical cam oscillating roller-follower mechanisms: a general approach. J. Mech. Des.T. ASME, 1994, 116, 315 319 11、 Gonzalez-Palacios, M. A. and Angeles, J. Gonzalez-Palacios, M. A. and Angeles, J. The generation of contact surface of indexing cam mechanisms: a unified approach. J. Mech. Des. T. ASME, 1994, 116,369 374. 12、 Nishioka, M. and Nishimura, T. Synthesis of the internal parallel cam mechanism. Proc. Instn Mech.Engrs, Part C: J. Mechanical Engineering Science, 1998,212, 577585. 13、 Zhang, C. A new type of intermittent mechanism planetary indexing cam mechanism. Mech. Sci.Technol., 1995, 15, 871 873 (in Chinese). 14、 Wang, H. and Zhang, C. Synthesis of the planetary indexing cam mechanism. Chinese J. Mech. Eng., 2003,39, 13 16. 15、 Rohmfeld, R. F. Classification of Curve Curve Intersections from the CAD/CAM Viewpoint, 1996, Vol. VII,pp. 230 239 (IEEE Computer Society Press, Los Alamitos, CA, USA). nts /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: 10.1243/095440605X315086872005 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 MechanismPublished by:On behalf of:Institution of Mechanical Engineerscan 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 ntsKHV indexing cam mechanism:a new intermittent mechanismHao Wang1C3, 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 transmission1 INTRODUCTIONIndexing 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.C3Corresponding author: Auto-body Manufacturing TechnologyCentre, School of Mechanical Engineering, Shanghai Jiao TongUniversity, Shanghai 200030, Peoples Republic of China.687C16204#IMechE 2005 Proc. IMechE Vol. 219 Part C: J. Mechanical Engineering Scienceat ZHEJIANG UNIVERSITY on January 5, 2013Downloaded from nts2 STRUCTURE 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.The KHV indexing cam mechanism can bedesigned 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.3 PITCH CURVE OF THE CAM3.1 Equation 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)isRz. The number of rollers in the sun gear bis z. The angular displacement of the input shaft His uH, and that of the planet cam g is ug. 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. 1 Scheme of a KHV indexing cam mechanism(type I and type II)Fig. 2 SchemeofaKHVindexingcammechanism(theretrogressed mechanism) Fig. 3 Coordinate system of type I688 Hao Wang, Ce Zhang, and Guanlong ChenProc. IMechE Vol. 219 Part C: J. Mechanical Engineering Science C16204#IMechE 2005at ZHEJIANG UNIVERSITY on January 5, 2013Downloaded from ntsTheir relationship yieldsRTi(t) RziH Rzej(aiC0ug(t)C0 eej(uH(t)C0ug(t)t 0, TC138, 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,bis 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 is ug. 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, TC138, i 1,2, .,z (2)3.2 Relations 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)iHgC0(z C0 1) (6)Then, the displacement of the input shaft and theoutput shaft are defined by the following equationuH(t) uH(0) 2(n C0 1)ptnT(7)ug(t) C02pSn(8)For type II, another expression is obtainedn z (9)iHgC0z (10)the displacement of the input shaft and the outputshaft in type II has a different definitionuH(t) uH(0) 2ptT(11)ug(t) C02pSn(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. 4 Coordinate system of type II Fig. 5 Pitch curve of type IKHV indexing cam mechanism 689C16204#IMechE 2005 Proc. IMechE Vol. 219 Part C: J. Mechanical Engineering Scienceat ZHEJIANG UNIVERSITY on January 5, 2013Downloaded from nts4 PROFILE OF THE CAM4.1 Boolean operationAlthoughthepitchcurveoftheplanetcamisaclosedcurve, 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)C0rzni(t)ROi(t) RTi(t)rzni(t)t 0, TC138, 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: one is the area enclosed by the self-intersection pieces, we called as SI(in the interioroffset curve) and SO(in the exterior offset curve)the other is the area enclosed by the non-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 (AIAO)n(SISO) (14)For type II, the area enclosed by the cam profile TIIis expressed by the union of AI, AO, SI, and SO.TO AIAOSISO(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. 6 Pitch curve of type IIFig. 7 Cam profile (type I)Fig. 8 Cam profile (type II)690 Hao Wang, Ce Zhang, and Guanlong ChenProc. IMechE Vol. 219 Part C: J. Mechanical Engineering Science C16204#IMechE 2005at ZHEJIANG UNIVERSITY on January 5, 2013Downloaded from nts4.2 Smoothness of the cam profileInthecam profile,thepoint 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.As several rollers are engaging with the camsimultaneously, 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.5 MOTION 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. 11 Animation of the mechanism (type I)Fig. 9 Locality of a cusp Fig. 10 Cam profile after the smoothing procedureKHV indexing cam mechanism 691C16204#IMechE 2005 Proc. IMechE Vol. 219 Part C: J. Mechanical Engineering Scienceat ZHEJIANG UNIVERSITY on January 5, 2013Downloaded from nts6 THE 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. 12 Animation of the mechanism (type II)Fig. 13 Animation of the retrogressed mechanism692 Hao Wang, Ce Zhang, and Guanlong ChenProc. IMechE Vol. 219 Part C: J. Mechanical Engineering Science C16204#IMechE 2005at ZHEJIANG UNIVERSITY on January 5, 2013Downloaded from nts7 PROTOTYPE 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, assembled pair of cam and rollers, 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 m
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