空间轮系综合实验台的设计运用运动学分析锥齿轮轮系的曲线图英文翻译与英文文献

空间轮系综合实验台的设计运用运动学分析锥齿轮轮系的曲线图英文翻译与英文文献内容摘要：

he nonoriented and the oriented graph techniques. The nonoriented graph technique was first introduced by Freudenstein [1]. The method utilizes the concept of fundamental circuits. It was elaborated in more detail by Freudenstein and Yang [2] and then a puter algorithm and a canonical representation of the mechanisms were developed by Tsai [3]. The oriented linear graph technique has been used since the early sixties [4]–[7] for electrical works and other types of lumped physical systems including mechanical systems in onedimensional motion. Chou et al. [8] have extended these techniques to threedimensional systems by using the same approach. The most significant work with the derivation of a general and pact mathematical model of a multiterminal rigid body in threedimensional motion was that of Tokad in 1992 [9]. In this derivation, a systematic approach, the socalled Network Model Approach, is developed for the formulation of threedimensional mechanical systems. The work model approach was elaborated for a kinematic and dynamic analysis of spatial robotic bevelgear trains by Uyguroglu and Tokad [10], [11]. In [11], a new oriented graph technique was used for the relation of relative angular velocities of bevelgear trains. In this paper, a parison of the nonoriented and oriented linear graph techniques for kinematic analysis of bevelgear trains is carried out and the advantages of the oriented graph technique over the nonoriented graph technique are shown. The theory is demonstrated by the kinematic analysis of the articulated robotic mechanism used by the Cincinnati Milacron T3。 2 Robotic bevelgear trains Often a robot manipulator is an openloop kinematic chain since it is simple and easy to construct. However, it requires the actuators to be located along the joint axes which increases the inertia of the manipulator system. In practice many manipulators are constructed in a partially closedloop configuration to reduce the inertia loads on the actuators. For example,the Cincinnati Milacron T3 uses a three roll wrist mechanism which is made of a closedloop bevelgear train [12]. Functional representation Figure 1 shows the functional representation of mechanisms used by the Cincinnati Milacron T3,The mechanism has 7 links, 6 turning pairs and 3 gear pairs. The gearpairs are (7,3)(2) ,(6,5)(2) and (4,5)(3). In this notation, the first two numbers designate the gear pairs and the third one identifies the carrier arm maintaining the constancy of the center distance between the gears. Links 2, 6, and 7 are the inputs of the mechanism. The rotations of the input links are transmitted to the endeffector by the bevel gears 4, 5, 6 and 7. The endeffector is attached to link 4 and carried by link 3. The axis locations of the turning pairs are as follows: Axis a: pairs 1–2, 1–7 and 1–6. Axis b: pairs 2–5 and 2–3. Axis c: pair 3–4. The mechanism has three degrees of freedom. 3 Nonoriented graph representation In nonoriented graph representation, the following steps are performed: (1) On the functional schematic of the mechanical system: (i) Number each link (1, 2, 3,...). (ii) Label axes of coaxial turning pairs (a, b, c,...). (2) For the graph: (i) Represent each link by a correspondingly numbered node. (ii) Identify the fixed link (reference) by filling the corresponding node. Fig. 1. Functional schematic of the Cincinnati Milacron T3 (iii) A gear mesh between two links is represented by a heavy line connecting the corresponding nodes. (iv) A turning pair between two links is represented by a light line connecting the corresponding 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. Fundamental circuit equations Note that in Fig. 2, each geared edge is associated with a fundamental circuit. Each fundamental circuit consists of one geared edge (heavy line) and the turning edges (light lines) connecting the endpoints of the geared edge. The fundamental circuits 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 called the transfer 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 pair and k be the transfer node corresponding to the carrier arm (i, j)(k). Then links i,j, and k form a simple epicyclic gear train, and the following fundamental circuit equation can be derived as (i,j)(k), ωik=nji ωjk, (1) Where ωik and ωjk 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, ., nji = Nj/Ni where Nj and Ni deno。