Question

A, B, C and D are four masses carried by a rotating shaft at radii 100 mm, 125 mm, 200
mm and 150 mm respectively. The planes in which the masses revolve are spaced 600
mm apart and the mass of B, C and D are 10 kg, 5 kg and 4 kg respectively. Find the
required mass A and relative angular settings of the four masses so that the shaft shall be
in complete balance. Solve by analytical method. ( How to find angles A, B, C, D)

Answer 1

0.1m r = 0.125m ma= m kg (let) mg = lokg 0.2.1 me = 5kg mo = 4kg Y: 0.15m Let plane of mass A is the refrence reference plane. Then, position of blane can be drawn as:- R.P 600 600 X 600 Now find out mir and more using the Data tasulated in the following table. plane Mall Radio Coat for pistoare Couple we mir (kg-rn) from plamen nord) (kg only ACR.P) MA Olma B 0.125 0.6 5 1:2 1.8 (1) 0 10 1.25 0 0.75 C 0.2 1.2 D 4 0.15 1.08 Now drew Couple polygon using scale 0.75 kg:n Tomm. (o'b). 1.2 lcg.m. 80 mm 1. of = 72 mm

Couple polygon Now, draw angular position diagram of reference plane. By drawing lines Couple diagram direction. Malte parallel to 125mm me 2.00 Tokg Measure angle made by each masses aris with hapo mo will be anfulan position of me & mo. 0 me big

Angelor position of Mo = 100° anticlocklue of MB and angular position of Mo: 24o". anticlockwise of MB. Now angular position of MA Can be find But by drowning force polygon as angular position of mo and my is known direction of forces will be in the same direction as that of couple. 1.25 Scale eredi- 1.25 50 mm d 21.08 do & 30mm = 1.25x30 = 0.75kgam. -0.75kg.m.olmA Ma= 7.5 kg. OD makes an angle 155 with the horizontal hence. Ma = 7.5kg is at arsular position 155 with the horizontal

The analytical method involves the resolution of force component into a three-dimensional system, which will lead to following the matrix method for the solution and that result will always in terms of the characteristic equation of Eigenvectors. while the used method, the graphical method involves just tricky rules which have been explained at each level in case if you feel still uncomfortable at any point. feel free to put that problem to the discussion in comment section here.