Question

Q3. 1 Figure Q3 For the four bar linkage shown in Figure Q3, assume the diagram is drawn to scale and that crank link 2 has a length of 0.2m and an angular velocity of 20rad/s clockwise driven by an input torque of 5Nm. a) Find the positions with respect to the crank origin at A of the instant centre of velocity between the coupler link 3 and the ground link 1 and between the crank link 2 and the follower link 4. (5 marks] b) Find the magnitude and direction of: the angular velocity of the output link 4, the velocity of the cg of link 3 as shown and the output torque in the current configuration. Clearly state any assumptions made. [12 marks] c) Explain what is meant by mechanical advantage of a mechanism, and for the four bar linkage shown above, sketch a configuration in which the mechanical advantage is high and explain why this is the case. State two different ways in which the mechanical advantage could be computed throughout the working cycle of the crank. [8 marks]

Answer 1

solution! Given = AB=0.2m W2 = с 20 Hads clockwise В. 4 Tinput 5 N-m AR 1 TTTT (a) Number of instantaneous centers, 44-1) = 6 N= n(n.) 2 AB=0.2m , W2= 20 radys =) V2 = 0.2x20 4 ms Instant centre of velocity between the coupler link 3 and the ground link 1 is 113 Instant centre of velocity between the crank link 2 and the follower link 4 is 124 'I 13 ' I34 123, Izy II4 3 I12 4 12, 23 14,34 23,34 135,1 21,14 Scanned with CamScanner

solution! Given = AB=0.2m W2 = с 20 Hads clockwise В. 4 Tinput 5 N-m AR 1 TTTT (a) Number of instantaneous centers, 44-1) = 6 N= n(n.) 2 AB=0.2m , W2= 20 radys =) V2 = 0.2x20 4 ms Instant centre of velocity between the coupler link 3 and the ground link 1 is 113 Instant centre of velocity between the crank link 2 and the follower link 4 is 124 'I 13 ' I34 123, Izy II4 3 I12 4 12, 23 14,34 23,34 135,1 21,14 Scanned with CamScanner

(b) W4= ? According to Theorem of Angular velocity! Any instantan tous center Imn ✓ Can be treated on link m can be treated on link n VImn = Wm ( Imn Ilm) Wn (Imm Ien) I24: W2 l Izu I12) Wy (Inu Igy) Wy=20 wy 20 20 [ 124 122 لا I24 112 I24 Isy and w Since Iss and Ily lie at the same dire ction of Isy then the wh is also clockwise. The velocity of C.G. ob link 3 is zero due to kure rotation. CScanned with CamScanner

Mechanical Advantage (MA) The M. A. of a linkage is the ratio of the output torque exerted by the driven link to the required inkut torque at the drivere link. 2 с ld 2 by NRESAS. a 1 MA for above 4- bar linkage mechanism! It can be proved that the MA is directly proportional to Sin (B), the angle between the coupler link (c) and the driven link (d) and is inversely proportional to the sind, the angle between the driver link (b) and coupler (c). The angles were not constant so it is clear that MA is constantly changing. the linkage position with an angle 2 = 0° and 180° have "Infinite mechanical advantage'. - These positions are retferred to as toggle position. C B B 2=180° a 7777 2= 0° Q = 180° aned with CamScanner

Example! Slider Grank Mechanism s brank 3k & Slider Mechanical Advantage Torque Joudkust (Tueque Jinpuit MA Winput Woutput x Nmechanism Because nmechanism (Power output (Power) input = folpx Voir X VIIA fslp Tolp X Wolp Tilpx X Wilf In the above mechanismi MA = Will Wale ما Wolp Wolpe =o due to pure reciprocation MA نیا Let assume nmech = 1 MA CSScanned with CamScanner