Question

Question 1 (40 points): The figure shows a rigid rod of length t = 1 m whose end B is connected to a roller by a pin joint which is in a vertical guide and the other end, A, is controlled by a piston whose cylinder is fixed to the ground. There is a pin connection between the piston and rod at A. For the instant when s = 0.293 m, is increasing at a rate s = 0.2 m/s and second rate 5 = 0.4 m/s, a. by using absolute motion analysis, determine y, y and y of point B at this instant, b. by using instant center of zero velocity verify your Ý (i.e. VB) obtained in part a and also determine the angular velocity of the rod at this instant, c. by using relative motion analysis, verify y and y (i.e. Vo and as) you have determined in part a, verify the angular velocity of the rod you have determined in part b and determine its time rate (i.e. angular acceleration of the rod) at this instant. P= 1 m A S 1 m

Answer 1

ㅈ B So. 293 0 ac =에 gmlb 6 니mb 0 A 누 -S X 707 Im ( coso 2017 의 2 Cos(o-707) cus' So, J = 0-707

NB scosus mingi re Velocity of link AB would be same at A & B along the link lingth. gcosus VB cosus £go- g A YB = 3 oʻ2 mln anys VB = =0 o'z mis s similarly acceleration off 8 GB) ab groses ag cosus' - j costs AB= y = 0ium? scosus šsinus"

b Instant centre of zero xelocity. VB I fconise of zen velocity) 0707 نه 0.707 Ч”, Now, .y 8 xo for VB X 8769 VB = ті ý = o amis angulos velocity of rod. A verified wrod 2 0.982 roolo. 0707 0707

TVB Cadd velocity of A to point B inopposite direct relowy of B relative to Now. A 1 хв LA VB coses A ticosys' acceleration of B worth B 'Brodes is cosys Ye = s =* OA CB cosus' ca acosus' ak felative toda) a Brda j ro'u mlsz B • VB sinus for calculation of angular velocity only tangential velocity be counted. Im ܝܘܒܝ w = VBsinust is sinus lm a š sinus 0.28a rad/ Verified گیا

AB/A 98 7 "absinus Arrangential Le şarron gerrlial I'm = 98 Sinus tacosus 2x0.4 x S2 ao K TACOSUS d 0.365 rad free? angular acceleration of mod.
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