Question

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The differential gear system - differential train is shown in the figure 1. r =41, = 45 : a=30° Given data 3 & = 10 Figure 1 a) Determine Dof of system and analyze the motion of the rigid bodies of the mechanical system. b) Determine the angular velocity w of the 2nd gear and velocity of particle A on the 2nd gear. c) Determine the angular acceleration Ez of the 2nd gear and acceleration of particle A on the 2nd gear.

Answer 1

Given data © ri = 48 sto a=30 We 137 éc 3 we E, = 24 E

lod J3 à Dof of of system. We know dof 3(n. 1) - 2j-h-fr nt no of rigid body ja nool joint having dog one * with tinko both ha no of joint having of two link 2 8 rung gear 4 & conneeted so it Er & redundant degree of freedom is fomeny joint Biraning 314-1) - 2x3-1-0 = 343 - bol =9-7 2 = 3 1 joind F = ملل

De Angular velocity of gear 2 (M. * Taboration method Gom Arim Angular hear 2 Creart Arm velocity Angular vel Angular vel P2 Taking so i tve (x+y) ly cew rotation * Given arm rotation y = We • Alao given year rotation me x) \ لل

So gear Or, as we = (wet + x) Da, 4x = -3 we we on, 4x 3 we is rotate ow with on, x=-10 we angular velocity - lowe Velocity of particle A on the ano VÀ = VAD & Toso, (ruyooolt +rw zsinat + (3r we cosa h + (32 Wersona) (A) لل wo NBr -

D2, 5 VÀ = ( Lowa) singo) (?) + (3rwa Sinas) (îl + Pl_lowe) cos301 ) + +(Brwe) cos 30 a arwent (sigrwel +313 rw.)? 3.5 awe + 11.25 rue ITÀ la 11.78 rue 5owe -

Angular a acceleration Te te t Izeg + Ige=0 Considering Itafa Iz cow acceleration is the Eet egte=0 on E = -(ei tec) - Gi) elockwise a

afo2230 E2 P Acceleration of particle A Ona = war Na ano, 3rway 1 asta rez T Canda Ec (ano ya A la ol 2 an and anor ahoz + Roza ana cosaf-2) + (a) Asing (%) + (an Alsina ? + [ama) Casa (A) + (ato, cosa) a = (ao, sinajad) + 40, 6052 A) - (ano, bima)es) 4