Question

For the machine element shown, locate the z coordinate of the center of gravity.

For the machine element shown, locate the z coordinate of the center of gravity. y 2 in. 1 in. 2 in. 3 in. 2 in. r= 1.25 in. r= 1.25 in. 0.75 in. 2 in. 2 in. 4

Answer 1

Solution plate Step 1 Calculate the distance of the centroid of greetergelee along di z ancis Z. 2 ho length of rectanguliece plate li 3 +2 +2 7 ln 2 Vi î of = com 76 .:. Za 7 = 3.5 ln lib,hi Volume of sectangulies plate length sectangular low plete bi - wielth of rectangutas plate height of the rectangulos plade 20.4519 di 4 ln bi 3 :: Vi = 7 vitin X 4 X 0.75 = 21 In Step-2 Consicles the Wertical rectangular plate. Iz Centeroidal clutance, Ž. 2 b = 4 In 4 2 In .. Z 2

Calculate the volume of Vertical rectangular plate. V2 2 lab.hu l 4 ln I In be hi 2 In :: V2 = 4x1x2 = 818? Step 3 Calculate the distance of centroid of the hall Cylindrical bole along z axis 23 2 ln Volume of half cylinder V3 = I a 2 be 83 1.25 10 by = 1 in 3 i Vz= X 1.25 x1 = 3.067 in 3 2 step of Calculate the clistance of Centroiel of the half cylindriced Yaxis plate along Zn 7+ 484 31 9,7 radus of half oy uncloucas plate Nu = 2

.: Zy- 7+ 6 xH v& 7.848 in volume of half cywnclouced place Vua 2.hu N4 2 Nu = 2 in hy 6.75 3 Vu T x 2'x0.75 4.712 In 2 Step 5 Calculate the distance of the Centroid of cy Welsical hole along 2. Goci's. Z - 7 in hol. Calculate the Volume of the eylundrual VE т","h, No 1.25 In by = 0.75 ln Vg =7 x 1.25 10.75 2.945 int

Step 6. Calculate the folal nblume of machine element EV = V, + V2 - 113 + Vy - V5 le ŹV 21 +8 3.067 +4.712 - 2.945 3 24.7 In Calculate the product of Centroid and volume of the machine element { žu = Evi + ZzV2 - Ž V + Zn V4 - Zsvo (3.5% 21) + (2x8) - (2x 3.067) +(7.848 X 4.412) - x 2.9465) 99.73 in 4 Step 1 Calculate the clustance of the centroid of the machine element along Z-axis Ž EV = į žv x 27.7 99.73 NI 99.73 3.6 10 27.7 3.6 In .:: The Centcold of the machinebo element is along Z-axis.