16-48 - *1648 Peg B mounted on hydraulic cylinder BD slides freely along the slot in link AC If the hydraulic cylinder extends at a constant rate of 0.5

16-48 - *1648 Peg B mounted on hydraulic cylinder BD slides...

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B C D A 0.5 m / s u 0.6 m *16–48. Pe g B mounted on hydraulic cylinder BD s lide s freely alon g the s lot in link A C . If the hydraulic cylinder e x tend s at a con s tant rate of , determine the an g ular v elocity and an g ular acceleration of the link at the in s tant . u = 45° 0.5 m > s SOLUTION Position Coordinate: From the g eometry s hown in Fi g . a , Time Derivatives: Takin g the time deri v ati v e, (1) Here, s ince act s in the po s iti v e s en s e of . When , E q . (1) g i v e s Ans. The time deri v ati v e of E q . (1) g i v e s (2) Since i s con s tant, .Thu s , E q . (2) g i v e s d Ans. The ne g ati v e s i g n indicate s that act s counterclockwi s e. a AB a AB = u $ = - 0.3472 rad > s 2 = 0.347 rad > s 2 = u $ + 2 tan 45° A 0.4167 2 B a C = v C a C = 0.6 s ec 2 u A u $ + 2 tan uu # 2 B a C = y $ C = 0.6 A s ec 2 uu $ + 2 s ec u s ec u tan uu # 2 B v AB = u # = 0.4167 rad > s = 0.417 rad > s 0.5 = A 0.6 s ec 2 45° B u # u = 45° y C v C v C = 0.5 m > s v C = y # C = (0.6 s ec 2 uu # ) m > s y C = 0.6 tan u m

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