Question

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8. In the Figure below, bar AB rotates with a clockwise angular velocity of 5 rad/s. Points A and D are fixed (VA= Vp=0). Find: a) The velocity of point B b) The angular velocity of BC and DC c) The vertical velocity VR of the rack in the rack-and-pinion gear (35 points) B 12 in 10 in 10 rad/s muna 6 in [VR -- 6 in- 16 in 4-6 in

Answer 1

The numerical data given in above problem has 2 values of angular velocity of crank AB i.e. 5 rad/s in written in question and 10rad/s given in diagram. I have solved the above problem for both the values of angular velocity. Kindly refer. If any doubts i will clear them in comments section. Thanks.

Scale Tinch=0.25cm (ICR diagram) liliom Hinh Road, Chennai - Izt * Уәөс B I 23 I34 3 VB 2 WAB * WDC Ø CD.-- I 13 De А. I12 1 114 6- tail (13) From above diagram of ICR. Ø = tan' () (I24B) = 3.75cm = 15 inch (from scale) i ø= 58.930 (I24 c)= 4.4cm = 17660 inch (from scale) ..0 = 63.43

considering & 5 sale} = 59330 in VB (67.08 15 a) AB = J[12]++(632 - 13-466inch. VB = (AB) WAB (13-46 (5) 67.08 YB = 67.08 in's Also; VB= (1 24 B) WBC b) : WBC - J = 4.474 124 B WBC=447 sadis Similarly; Vc = (Wgc)124C) Ve = 78.67 in7. Consider link 4 (CD) : Ve = (CD) WeDc = (11.66% WDC) WDC = VC = 6.74 rad j here : (DC = 11.66 inch) c) (Also; VR = (&gear) Wio V = 6X6.77 = 40.44 ins) (tangential velocity of rack and pinion remains, . Same hack pinon WDC DO rgear, VR

ch/s (WBC 8.94 Sad SOLUTION-2 given in diagram Considering w = (1 orals) a) AB = N(2)+(0)2 = 13.416 inch VB = (AB) WAB = 13.416X10 VB = 134.16 inchys b) Also: from ICR diagzam VB (124B) Similarly; Ve= (WBC) (I24C) :, Ive = 157.34 in/s Consider link 4 (CD): Ve = (CD) CDC Vc -]W WBC = 13.5 5 tad/s (DC) here: (DC=11.66 inch) Also; Tangential velocity of rack and pinion remains same .. Ve = ({ gear) Web • VR = 16 x 13.5 ) ) c) Ive = 81 in/sh