# tutorial_4 - Mechanics tutorial_4 1 In the mechanism shown...

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Mechanics tutorial_4.doc 1 1. In the mechanism shown in diagram, FED is an offset slider-crank chain, which is given an oscillatory motion by the rotation of crank AB. When B is vertically above A, the angular velocity of AB is 3.0rad/s anti-clockwise. Determine the corresponding velocity of slider D. All the lengths are given in mm. 30 A B C D E F 150 300 300 220 AB = 70 BC = 250 CD = 570 CE=ED=EF= 300 ans: 0.2m/s 2. Referring to the diagram, the linkage mechanism is called quick-return mechanism. Crank AB rotates about A and the slotted link CD rotates about C. Pin B on the end of AB engages in the slot of CD; AB=r and AC=l. The angular velocity of AB is k and its angular acceleration is k . If l/r=R, show that the angular velocity of CD is k R R R CD cos 2 1 ) cos 1 ( 2 and its angular acceleration is       k R R R R R R R CD cos 2 1 cos 1 cos 2 1 1 sin 2 2 2 2 if r=50mm, l=40mm, =1rad/s and = 2rad/s 2 , determine CD and CD if 30 . A B C D x y ans: -0.3571k rad/s, -0.1127k rad/s 2

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Mechanics tutorial_4.doc 2 3. The diagram shows a simple two speed epicyclic gearbox. The sun S 1 is keyed to input shaft I which is rotating at 1000rev/min. The sun wheel S 2 is keyed to the annulus A 1 . The planet carriers C 1 and C 2 are keyed to the output shaft O. The number of teeth on the annulus and the sun wheels are T A1 = T A2 = 80, T S1 =30 and T S2 =28. Determine the speeds of the output shaft O and the non-stationary annulus when (a) A 1 is fixed and (b) when A 2 is fixed. S S A A C C 1 1 2 2 2 1 1000 rpm Input Output ans: (a) 368.2 rev/min (b) -151.1 rev/min 4. A device for testing the resistance to wear between the material of a road (Y) and a shoe (X) is shown. The crank OA is rotating clockwise at 10rad/s and the shoe is loaded such that contact is always maintained between the test surfaces and B lies on the line OD. When the angle
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tutorial_4 - Mechanics tutorial_4 1 In the mechanism shown...

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