Question

2. In the mechanism shown, each of the two wheels has a mass of 30 kg and a centroidal radius of gyration of 100 mm. Each link OB has a mass of 10 kg and may be treated as a slender bar. The 7 - kg collar at B slides on the fixed vertical shaft with negligible friction. The spring has a stiffness k = 30 kN/m and is contacted by the bottom of the collar when the links reach the horizontal position. If the collar is released from rest at the position 8–45° and if friction is sufficient to prevent the wheels from slipping, determine (a) the velocity Vg of the collar as it first strikes the spring and (b) the maximum deformation x of the spring. 175 mm 150 mm 150 mm

Answer 1

Twheel For the interval O= 45 to Oz o > is zero because wheel starts from and momentarily comes to rest rest at 00 A1 = {214. Tow)-01 lo + links (1 mv - o] collar Scanned by TapScanner

X10X(0.375) 3 B t 0.375 7x V 2 6-83 VG The Collar at B distance is 0.375 ra 0-2 695 m AV Avg -> 2 x 10 x 9.81x0.265 2 7x9.81 x 0.265 -44.2 J => U-2 = O DTZ AV=0 6.83 VB 44.2 = 0 => Vo = 44.2./6.83 VB = 2.54m/s Scanned by TapScanner

For Maximums deformation (6) of the spring I all parts are at rest so AT = so ca ", -2 Attovg + Ave 2x10x.9-81 tx 2 ++ (30) 603 7x9.81* (0-265 +2 on solving Value of a We get x = 60.1 mm Scanned by TapScanner