Question

Question 2 Determine the coordinates x, y, z of the centroid of volume of this composite machine element. Volume of sphere is nr. 85 85 mm mm 125 mm 125 mm 95 mm 95 mm mm 50 mm 60 mm 150 mm ---200 mm

Answer 1

Complete solution is given below. Table of calculation is attached at the end.

into let us divide given machine element A different elements 1 2 3 4 cuboid large cylinder of lengthe 200 mm small cylinder of diameter 15 mm sphere. * volume of individual element V = Lxbxh = (125+125) x(85785) *(95+95) Vi= 8075000 mm Va= n xh = I x 60 x 200 TV2 = 22.61946.7 mm3)

V3 = ( 72 Jeth = Tix5° x f150-50) | V3 = 14671: 46 mm3 ] = 4 x Tix 503 IV 523598.78 mm? * Let us find centroidal distance of individual element with respect to x, y and a anis. - Element 1 x = 85 mm y = 125 mm z = 95 mm

= 270 mm → Element 2 X = 170 + Y = 125 mm Z = 95 mm Element 3 a X3=85mm 73 = 250+ (100) kg = 95 mm = 300 mm → Element 4 x = 85 mm Y = 250 + 100 + 50 = 400 mm Kera 24 = 95 mm

* Now let us find centroid of volume ī = VX, + 12 X2 + 133237 Vedly Vi +V2 + V3 + VA Substituting all the values ñ = 134 3108519 10878217 ē= 123,47 mm y = Vigit V2 Y₂ + V 343 + VM YA Vit V2 + V3 t V4 1506859288 10818217 17 = 138,52 mm)

2= Vizit V2 Z2 + V3 23 + VH ZA Ni + V2 + V3 + VA Ž = 10334 30609 10878217 Z = 95 mm] i controid of valume is (123.47,138.52,95)

2 2261 Component Volume 8075000 2261946.7 17671.46 523598.78 10878217 Xi 85 270 85 85 Yi 125 125 300 400 ZiL VX VY VZ 95 686375000 1009375000 767125000 610725609 | 282743337. 5214884936.5 95 1502074.1 5301438 1678788.7 95 | 44505896.3 209439512 49741884.1 13431085791506859288 1033430609 X'= Y'= Z'= 123.4677 138.5208 95