Question

No hand writing please!

(4) Problem: ( the velocity of the collar at Cand the angular velocity of link CB at the instant shown. Link CB is horizontal at this instant. _/ 25 points) The link AB is rotating with angular velocity AB = 4 rad/s. Determine 400 mm 450 WAB = 4 rad/s %3! 650 mm 50° Solution:

Answer 1

Velocity of the collar = 2.817 m/s

Angular velocity of link CB = 9.157 rad/s

Posilue &- direction in in Bhrointing pul of the Page 1 500 DAB = 5 - Express relevant quantities in vector form: WAB = WAS WAB =. 4Ř Here Was Angular velocity vector of link AB Woc = WBC Hone Wsce and WBC are Angular velocity vector and magnitude of link AB Term=- 0065/cos5lit sim soj).m BIA = (0.4178î 1.0.49797)m Holl rom is position vector of B with respect to A = = 0oA Here there is position vector of c relative to B. e Us = . (0845ê + sin asi ū6 = 0.707 +01707 Here us is unit vector along slider bar

0 0 4 Calculation of velocity of Bi To = ( Who x Righ ) Here To is velocity vector of froint B, Sudsletile Wang = AŃ and Tram = 0.4178 î +0-4979 Vo = FAÂ ] x [0-4178 î+0.49799] = { x las costume of 1.478 014979 0 ] Ve = (-1.9917Â +1672h) → Calculale Velocity of slider loy selalive velocity analysis of leiska CB : Je = J + CWoc x. 918) Here To is velocity vector of collar - Sulollite Vo = -109917 û +167124, Wac - Wec K and KOB = -0.4 V = -109917 îl 106712 À + [CWec R)x(-0-41)]. Chol Product of 2 verton Ve = -19917 î + 1067199 -0.9War Vc = -1-9917î +(16712-0•4 Wec) î. —> 0 → @Using the conbraint to write velocity of collag? The collar is constramt lo move along the slider bar. Therefore the collar can have velocity only ts vector, Ve = V (Cs). Here Ve is magnitude of velocety of collar Sublitule us = 0•707 + 0.7079. 7 (0-70%) + (n+101420 (2) -> Equalung RHS of Equalien D and © because they represent same veclay: (01 707 V2 + (0-707V) =--1-9917î +( 1•6H 2–0-AWQc) î

comparing î components of LHS and RHS of Equation : 06 707 Ve = -109917 Ve --2-817 Velocity of Collag - 1Vel = 2.8177 K Velocity of Collar Comfaring component of L1HS and RHS of Equalcon a®: 00707 Vc = 10 6712 - 0•4WBC Sulstelule Ve= - 2.817 00707X(- 2.817) – 16712-0.4Wec 0.4 Wee = 1.6712.+ 1• 9917 Wee = 9:15.7 rad - Angular velocity of linke. BC