【導(dǎo)讀】中，輪系運(yùn)動(dòng)的齒輪結(jié)構(gòu)都是由一個(gè)圖像來(lái)表示的。繪，它們僅用于確定的基本電路的載波節(jié)點(diǎn)。供更多的信息，因?yàn)槊恳粋€(gè)有向圖行代表一對(duì)互補(bǔ)的變數(shù)。在本文中，對(duì)這兩。式機(jī)構(gòu)進(jìn)行的運(yùn)動(dòng)學(xué)分析，已經(jīng)證明了導(dǎo)向圖形技術(shù)的優(yōu)點(diǎn)。在近年來(lái)，圖理論對(duì)機(jī)器人的錐齒輪傳動(dòng)的應(yīng)用已經(jīng)建立起來(lái)。是由Freudenstein[1]首先提出的，該技術(shù)利用了基本電路的概念。的機(jī)制融合，最終發(fā)展起來(lái)的。系統(tǒng)一維運(yùn)動(dòng)在內(nèi)的其他類型的集總物理系統(tǒng),。要求致動(dòng)器位于尾軸,因此這也增加了關(guān)節(jié)機(jī)械臂系統(tǒng)的慣性。手是建立在一種半閉環(huán)配置的執(zhí)行機(jī)構(gòu)來(lái)降低慣性載荷。lacronT3使用的由閉環(huán)錐齒輪傳動(dòng)裝置構(gòu)成的三轉(zhuǎn)動(dòng)腕關(guān)節(jié)。機(jī)器人有7個(gè)構(gòu)件,6個(gè)轉(zhuǎn)動(dòng)副和3個(gè)齒輪副。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。輸入構(gòu)件的旋轉(zhuǎn)通過齒輪4、5、6和7傳到末端手爪。它被稱為轉(zhuǎn)移節(jié)點(diǎn)

　　

【正文】 （ 16） From the thin lines in Fig. 5, we ?nd the following fundamental circuit equations: Fig. 5. The oriented graph representation of the Cincinnati Milacron T3 ω,72,= ω71ω21 （ 17） ω,62=ω61ω21 （ 18） ω,53=ω52ω32 （ 19） ω,52=ω52 （ 20） ω,32=ω32 （ 21） ω,43=ω43 （ 22） From the nodes the following fundamental cutset equations may be derived: M71 = M,72。 (23) M61 = M,62。 (24) M21 = M,72+ M,62。 (25) M52 = M,52+ M,53。 (26) M32 = M,32+ M,53。 (27) M43 = M,43: (28) Note that Eqs. (17)–(19) are given as coaxial conditions theorem in nonoriented graph technique. (b) Kinematic analysis Substituting Eqs. (17) and (21) into Eq. (14) yields ω,32= n73ω,72。 ω32 = n73(ω71 ω21) . (29) Substituting Eqs. (18) and (20) into Eq. (15) yields ω,52= n65 ω,62。 ω52 = n65(ω61 ω21) . (30) And substituting Eqs. (19) and (22) into Eq. (16) yields ω,43= n54ω,53。 ω43 = n54(ω52 ω32 ). (31) Using Eqs. (29) and (31) we can writeω43 as ω43 = n54(ω52 ω32)= n54 (n65 (ω61 ω21) n73(ω71 ω21)) =n54(n73 n65) ω21 + n54n65ω61 n54n73ω71. (32) Hence, in matrix form 。 (33) or in more pact form, ω0 = Nωi。 (34) where ω0 =[ x32 x43 x52]T summarizes the output angular velocities, ωi = [ω21 ω61 ω71]T represents the input angular velocities and N is the teethratios coe?cient matrix. (c) Static moment analysis Substituting Eq. (14) into Eq. (23) yields M71 = M,72=M,32/n37=n73 M,32. (35) Now, substituting Eq. (27) into Eq. (35) yields M71 = n73 (M,53 M32). （ 36） Then substituting Eqs. (16) and (28) into Eq. (36) yields M71 = n73 (M,32n54 M,43)=n73(M32+n54 M43). (37) Similarly, from Eqs. (24) and (15) we can write that: M61 = M,62= n65 M,52. (38) Substituting Eq. (26) into Eq. (38) yields M61 = n65(M52 M,53). (39) And using Eqs. (16), (28) and (39), M61 can be written as M61 = n65 (M52 + n54 M,43)=n65(M52n54 M43). (40) Similarly, using Eqs. (23)–(25) and the expressions in Eqs. (37) and (40), M21 is obtained as M21 = M,72+ M,62=n73 (M32 + n54M43) n65 (M52 n54M43), M21 = (n73) M32+(n73 + n65)n54M43 + n65M52. (41) Equations (37), (39), and (41) can be written in matrix form as . (42) or in more pact form, Mi = KM0, (43) where Mi = [M21 M61 M71]Tare the input moments, M0 = [M32 M43 M52]T are the output moments and K= NT is the teethratios coe?cient matrix. This is an expected result since the transferred power has to be identical: MTiωi +MT0ω0 = 0. (44) 6 Conclusion A parison of the nonoriented and oriented graph techniques shows advantages of the oriented graph technique. In nonoriented graph technique a heavy line represents the gear pair and a light line represents the turning pair. Only the transfer node can be obtained from the nonoriented graphs and then the fundamental circuit equations are written. On the other hand, in the oriented graph technique each directed line between the nodes indicates where a pair of meters are connected to measure a pair a plementary terminal variables (angular velocity and moment) which describes the physical behavior of the ponent. Besides the coaxial conditions and the transfer node, all the kinematic and static moment equations can be obtained from the oriented graph directly. The advantages of the oriented graph technique are demonstrated by the kinematic analysis of the articulated robotic mechanism used by the Cincinnati Milacron T3.