Problems (Motion Relative to Rotating Axes)

Transcription

1 1. The disk rolls without slipping on the roblems (Motion Reltie to Rotting xes) horizontl surfce, nd t the instnt represented, the center O hs the elocity nd ccelertion shown in the figure. For this instnt, the prticle hs the indicted speed u nd the time rte-of-chnge of speed u, ሶ both tie to the disk. Determine the bsolute elocity nd ccelertion of prticle.

2 . The disk rottes bout fixed xis through O with n ngulr elocity w=5 rd/s (ccw) nd n ngulr ccelertion =4 rd/s (cw) t the instnt represented. The prticle moes in the circulr slot with (ccw) nd ሶ β = rd/s ሷ β=3 rd/s (cw) when b=36.87 o. Determine the bsolute elocity nd ccelertion of t this instnt. / O / O 5k sin36. 87i 3 cos i O 0 / O 1. i 4. 6 b 4 cm / s 4cos36. 87i 4 sin i i 8. 4 /O

3 w=5 rd/s (ccw), =4 rd/s (cw), β ሶ = rd/s (ccw), β=3 ሷ rd/s (cw) b=36.87 o. w r w w r r w O / O / O 0 w r 5k 5 k 1. i 4. 6 / O / O 4k 30i i i 4. 8 w 5 t n k 3. i. 4 4i 3 b 3 t 6cos t 4. 8i 3. 6 t b n 8 sin36. 87i n 4. 8i 6. 4 n 8i cm / s i 6 sin cm / s 8cos α r /O ω ω ω r /O re

4 3. For the instnt represented, link B roblems (Motion Reltie to Rotting xes) is rotting ccw t constnt rte N = 4 rd/s nd its pin cuses cw rottion of the slotted member ODE. Determine the ngulr elocity w nd ngulr ccelertion of ODE for this instnt.

5 4. Link 1, of the plne mechnism shown, rottes roblems (Motion Reltie to Rotting xes) bout the fixed point O with constnt ngulr speed of 5 rd/s in the cw direction while slider, t the end of link, moes in the circulr slot of link 1. Determine the ngulr elocity nd the ngulr ccelertion of link t the instnt represented where BO is perpendiculr to O. The rdius of the slot is 10 cm o o B 16 cm w 1 =5 rd/s O BO O

6 5. The mechnism shown consists of disk, slotted rm D nd br EF. The disk rottes bout fixed xis through with n ngulr elocity of 3 rd/s (ccw) nd ngulr ccelertion of 6 rd/s (ccw). The slotted rm D, which is pinned t is free to turn bout this point. The br EF cn oscillte within the guides t E nd F. in B is fixed on the disk. s the disk rottes, the pin B moes within the slotted rm. Determine the ngulr elocity nd ngulr ccelertion of the slotted rm D nd the elocity nd ccelertion of the br EF t the instnt shown.

7 B B B w D r B / B / 3k 0. 1i 0. 3 wdk D D (1)=() w 0 6 rd / s m / s 0. 1i 0. 4 D i 0. i 0. 1w 0. w i i B B / (1) 3 k 0. 1i 6k 0. 1i 0. 9i k (3) () w k 0. 1i k B D B 0. 6k 0. 6k 0. 1i i B wd rb / D rb / wd 0. 1i 0. 4 D 0. 34i i i (4) D D (3)=(4) D. 305 rd / s m / s ccelertion of br EF EF i 0.67i

8 roblems (Motion Reltie to Rotting xes) 6. The Gene wheel is mechnism for producing intermittent rottion. in in the integrl unit of wheel nd locking plte B engges the rdil slots in wheel, thus turning wheel one-fourth of reolution for ech reolution of the pin. t the enggement position q = 45. For constnt clockwise ngulr elocity w 1 = rd/s of wheel, determine the ngulr ccelertion of wheel for the instnt when q = / mm 0 o O 1 00 mm Lw of cosines: d d 8.77 mm 00 d O cos sin 0 Lw of sines: sin o 35.76

9 constnt clockwise ngulr elocity w 1 = rd/s, determine the ngulr ccelertion when q = 0. lte : w r O Velocity 1 O lte B: O 1 w1 r / O1 k cos qi sin q i i wk 8.77cosi 8.77sin cosi sin O / O 67.17i w 48.37wi i d mm 0 o o mm 1 1 = w 1.93 rd / s 34.5 mm / s

10 d mm 0 o o O 1 00 mm O ccelertion lte B: w w r i O1 1 1 / O1 3 w w r r w 1.93k 1.93k 67.17i k 67.17i k 34.5cosi 34.5sin cosi sin lte : O / O / O 50.7i i 59.5i i = 4.59 rd / s 68.1 mm / 16 s

11 roblems (Motion Reltie to Rotting xes) 7. For the instnt shown, prticle hs elocity of 1.5 m/s towrds point tie to the disk nd this elocity is decresing t the rte of 7.5 m/s ech second. The disk rottes bout B with ngulr elocity w=9 rd/s nd ngulr ccelertion =60 rd/s in the directions shown in the figure. The ngle b remins constnt during the motion. Telescopic link hs elocity of 5 m/s nd n ccelertion of.5 m/s. Determine the bsolute elocity nd ccelertion of point for the position shown.

12 8. The pin in the bell crnk OD is guided by the flnges of the collr B, which slides with constnt elocity B of 0.9 m/s long the fixed shft for n interl of motion. For the position q=30 o determine the ccelertion of the plunger E, whose upper end is positioned by the rdil slot in the bell crnk.

13 Velocity nlysis 30 o B =( ) x B m / s cos 30 cos wod w rd / s 60 o 30 o 19.9 mm r 6. 98k 0. 5i cos 30i sin 30 O w / O i i 0. 5 (1)=() =1.039 m/s c =.079 m/s

14 ccelertion nlysis n w O m / s cos 30 sin m / s ( ) n 30 o t OD ( ) t n V B =constnt So must be erticl. 3 r O w w k rd / m / s r w s t OD O 60 o 30 o 6. 98k 0. 5i k 0. 5i k cos 30i sin 30 cos 30i sin i i (3)=(4) 19.9 mm =4.9 m/s =7.9 m/s