Question

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) 12 in 10 in 10 nads AAAAAAAA |VR બનતા 6 in 16. in

Answer 1

B (2-2) (90-a) k 90-d) bin Vc 190-cord 2980 llain loin 16 in lorad see Apo Y V VR (90-la-e Gin > Gin the velocity of point B (ve must be perpendi- link (AB) (since point (A) is fined] [ the length of the link cannot be changed as it is cular to the W 2 VB ? rx w AB lored/see RAB length of link AB AB 12 m NB 12x102 120 in /see B 90-60+8) VB VC 90-(x-4) 90-(2-d] с where o is (< BAY) in DABY , & is <CDZ in a CDZ , dis <KBC in AKBC /

CA?. where 'Y is the point of intersection of vectical lince [imaginary from B and horisontel line Limaginary] pom point 2 is the intersection of vectical line [imaginery] from and horizontal line (imaginary] from Do point k) is the intersection of horizontal line [imaginary from B and veetical line Cimarinary] from 'e. B A (90-(0 to VB Vc è rão (-2] Now for sigid link BC, the velocity of point & along the link ( component of up along B2] must be egnel to velocity of point & along BC [ component of velocity Vc, along B2] Vi bo0 (10-1840) - V C09 (90-(6-4] -0 From A (ABY) tano 2 tan [2] tas (2 N N 63.4349°

from (z CD) Jand To 6 2 -> La ten' ( 10% 59.0362 N From DBK() tand (12-10) 16 e tan (17/ 2 dz ☺ 2 16. dan [/s 7.125 2 in applying Vie cos [90-(63-4549+ 7-125] - vecs (90-159.0342 - 7. 125] We found out that Visa [ 19.4401] Vc cos [38.0888 8888] 120 in /see 120x cos Vc z 120x ces (19.4401) 143.77483 cos (38.0888] in/see Now consideing the sin components of Vo and Yc in tes to the link B?

Voter B EL (90-1044) Veter 98 Vc V ro-(2-4) Veter (compon ro 1 С rc since voter C component Veten and voter are moving opposite directions the instantaneous Centre link Bê is inside the link be one chelzWBL) We know the link has only of the WBC VB ter Vcter 2 2 & B re 2 Vota 120x sin(19.4401) z VB sin (90-(0+ 0 39.9385 in/see z Veter. Ve sin( 90- (2-0) 2 143.77483 sin (38.088 88-6921 in /see //

39.9385 88. 6921 N &B lu BC فيما هاج rothea from A B K C) hypotenuse BC 2 VOK) ² + (KC) ? V (16) 2+ (12-10)' 2 16.1245 in 2 hea (16-1245-26 39.9385 2 88-6921 ( 6 - 8 -83) RB 88.6921 ro 39.9385 (16-1245-23): 88.692183 643.9883- 39.9385&B 643. 9883 2 88.69211B + 3909385&B ? RB 2 643.9885 5.00 6 ws Voter (88.6921 +39-9385) 39.9385 5.06 649 2 N 7.977 had (see rB

None for the link 'Do the velocity ke zigid is tes to the link as the link is Vc 143.77483 WDC 2. D C (DC) From A (CZD) DC 2 hypotenu tenuse ✓0z)2+(ZD) 2 v (10) 2+ (672 2 Z 11- 6619 in こ 12.3285 aad/see WDC 143.77483 ll-6619 h pinion x (distence pom D to (of woongeer) the Jack) on (DC) (distance pon D torack) a radius of pinion Gin VR Wax redius & pinion 12.3285 X6 73.971 in/see