Example 1.5 :Four masses 150 kg, 200 kg, 100 kg and 250 kg are attached to a shaft revolving at radii 150 mm, 200 mm, 100 mm and 250 mm; in planes A, B, C and D respectively. The planes B, C and D are at distances 350 mm, 500 mm and 800 mm from plane A. The masses in planes B, C and D are at an angle 105, 200 and 300 measured anticlockwise from mass in plane A. It is required to balance the system by placing the balancing masses in the planes P and Q which are midway between the planes A and B, and between C and D respectively. If the balancing masses revolve at radius 180 mm, find the magnitude and angular positions of the balance masses. TA = 150mm rB= 200mm rc = 100mm TD = 250 mm rx = ry= 180 mm mA = 150 kg MB = 200 kg mc = 100 kg mp = 250 kg -ve R.P. P -350 +ve 500 B 800 0A = 0 08 = 105 0c = 200 OD = 300