【正文】 2]更詳細(xì)地闡述 ,而后由 Tsai [3]將 電腦算法 與 舊有的機(jī) 制融合，最終發(fā)展起來(lái) 的。這 種 圖 形 技術(shù)理論 是通過(guò)對(duì) Cincinnati Milacron 公司的 T3鉸接式機(jī)器人所應(yīng)用的運(yùn)動(dòng)學(xué)分析說(shuō)明 的。在這個(gè) 表示法中 ,前兩個(gè)編號(hào)指明齒輪副和第三 編號(hào) 識(shí)別載體 并保持 齒輪 之間 恒定的中心距。 圖 2 遵循圖 1 中所應(yīng)用的這些步驟的機(jī)理。 回 路 3:節(jié)點(diǎn) 2(軸副 a,b)。 ω 43=n54 ω 53, （ 3） (5,6)(2)。j和 k是三同軸 構(gòu)件 ,那么在這 3個(gè)構(gòu)件之間的 相對(duì)角速率可以表示為如下的 同軸條件 : ω ij = ω ik ω jk。 (ii) 通過(guò)填寫節(jié)點(diǎn)確定固定連接 (參考 )。在這條路 線 上的具有不同軸的標(biāo)簽 的 節(jié)點(diǎn) , 就 是相對(duì)兩邊齒輪副的轉(zhuǎn)移節(jié)點(diǎn)。 (a)如圖可知方程 在圖 5中 ,轉(zhuǎn)載 乘節(jié)點(diǎn)如下 : 路徑 I：節(jié)點(diǎn) 2個(gè)（軸副 a 和 b）。 (27) M43 = M,43: (28) 注意 公式 (17)(19)作為 同軸條件定理在 無(wú)導(dǎo)向圖形 技術(shù) 中已經(jīng) 給出了。 這是一個(gè)預(yù)期的結(jié)果 因?yàn)檩d體節(jié)點(diǎn)是相同的 : MTiω i +MT0ω 0 = 0. (44) 5 結(jié)論 通過(guò) 比較 無(wú)導(dǎo)向圖形 技術(shù) 和導(dǎo)向圖形技術(shù) 顯示 導(dǎo) 向 圖形 技術(shù) 的 優(yōu)勢(shì)。 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 con?guration 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 ?rst two numbers designate the gear pairs and the third one identi?es 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 ?xed link (reference) by ?lling 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 di?erent 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 denote the number of teeth on gears j and i, respectively. The gear ratio is nji = + Nj / Ni, if a positive rotation of gear j with respect to the arm k produces a positive rotation of gear i, andnji = Nj / Ni otherwise. By de?nition, ωij= ωji and nij=1/nji (2) for all i and j. The Cincinnati Milacron T3 shown in Fig. 1 contains three gear pairs. Therefore three fundamental circuit equations can be written as Fig. 2. Nonoriented graph representation of the Cincinnati Milacron T3 (4,5)(3)。 j and k be three coaxial links, then the relative angular velocities among these three links can be expressed by the following coaxial condition: ωij = ωik ωjk。 b). Path III (): Node 3 (pair axes b。 ω52 = n65(ω61 ω21) .