外文翻譯--運用運動學(xué)分析錐齒輪輪系的曲線圖（英文）

1、Kinematic analysis of bevel-gear trains using graphsM. Uygurog ? lu and H. Demirel, Gazimag ? usa, T.R.N.C.Received February 3, 2004; revised November 22, 2004 Published online: May 4, 2005 ? Springer-Verlag 2005Summary.

2、 The non-oriented and oriented graph techniques are used for kinematic analysis of bevel- gear trains. In both techniques, the kinematic structure of the gear trains is represented by a graph. Although the non-oriented g

3、raphs are simple to draw, they are used only to determine the carrier nodes of the fundamental circuits. On the other hand, the oriented graphs carry more information than the non-oriented graphs since each line in an or

4、iented graph represents a pair of complementary variables. In this paper, these two techniques are compared and the advantages of the oriented graph technique are demonstrated by the kinematic analysis of an articulated

5、robotic mechanism used by the Cincinnati Milacron T3.1 IntroductionThe application of graph theory to the kinematic analysis of robotic bevel-gear trains hasbeen well established in recent years. Two different graph tech

6、niques are used for thekinematic analysis of robotic bevel-gear trains: the non-oriented and the oriented graphtechniques. The non-oriented graph technique was first introduced by Freudenstein [1]. Themethod utilizes the

7、 concept of fundamental circuits. It was elaborated in more detail byFreudenstein and Yang [2] and then a computer algorithm and a canonical representationof the mechanisms were developed by Tsai [3].The oriented linear

8、graph technique has been used since the early sixties [4]–[7]for electrical networks and other types of lumped physical systems including mechanicalsystems in one-dimensional motion. Chou et al. [8] have extended these t

9、echniques tothree-dimensional systems by using the same approach. The most significant work with thederivation of a general and compact mathematical model of a multi-terminal rigid body inthree-dimensional motion was tha

10、t of Tokad in 1992 [9]. In this derivation, a systematicapproach, the so-called Network Model Approach, is developed for the formulation of three-dimensional mechanical systems. The network model approach was elaborated

11、for a kine-matic and dynamic analysis of spatial robotic bevel-gear trains by Uyguroglu and Tokad[10], [11]. In [11], a new oriented graph technique was used for the relation of relativeangular velocities of bevel-gear t

12、rains.In this paper, a comparison of the non-oriented and oriented linear graph techniques forkinematic analysis of bevel-gear trains is carried out and the advantages of the oriented graphtechnique over the non-oriented

13、 graph technique are shown. The theory is demonstrated by thekinematic analysis of the articulated robotic mechanism used by the Cincinnati Milacron T3.Acta Mechanica 177, 19–27 (2005)DOI: 10.1007/s00707-005-0212-8Acta M

14、echanicaPrinted in Austria(iii) A gear mesh between two links is represented by a heavy line connecting the corre-sponding nodes.(iv) A turning pair between two links is represented by a light line connecting the corre-s

15、ponding nodes: Label each turning edge according to its pair axis (a, b, c,. . .).Figure 2 is obtained by applying these steps to the mechanism shown in Fig. 1.3.1 Fundamental circuit equationsNote that in Fig. 2, each g

16、eared edge is associated with a fundamental circuit. Each funda-mental circuit consists of one geared edge (heavy line) and the turning edges (light lines)connecting the endpoints of the geared edge. The fundamental circ

17、uits in Fig. 2 are:Circuit 1: (4–5)(5–2)(2–3)(3–4).Circuit 2: (5–6)(6–1)(1–2)(2–5).Circuit 3: (7–3)(3–2)(2–1)(1–7).In each fundamental circuit, there is exactly one node connecting different pair axes. It is calledthe tr

18、ansfer node and represents the carrier arm. In Fig. 2, the transfer nodes are:Circuit 1: node 3 (pair axes b, c).Circuit 2: node 2 (pair axes a, b).Circuit 3: node 2 (pair axes a, b).Let i and j be the nodes of a gear pa

19、ir and k be the transfer node corresponding to the carrierarm (i; j)(k). Then links i,j, and k form a simple epicyclic gear train, and the following fun-damental circuit equation can be derived asði; jÞðk&

20、#222;; xik ¼ nji xjk; ð1Þwhere xik and xjk denote the angular velocities of gears i and j with respect to arm k, and nji denotes the gear ratio between gears j and i, i.e., nji ¼ Nj=Ni where Nj and Ni

21、 denote thenumber of teeth on gears j and i, respectively. The gear ratio is nji ¼ þNj=Ni, if a positiverotation of gear j with respect to the arm k produces a positive rotation of gear i, andnji ¼ ?Nj=Ni

22、otherwise. By definition,xij ¼ ?xji and nij ¼ 1nji ð2Þfor all i and j.The Cincinnati Milacron T3 shown in Fig. 1 contains three gear pairs. Therefore threefundamental circuit equations can be written