EXERCISES. Let us see an example of graphical methods for solving static analysis associated with numerical evaluation of the results. 2 1 E 3 P=?

Transcription

1 Let us see an example of graphical methods for soling static analysis associated with numerical ealuation of the results.? ϑ D A

2 ? ϑ D A

3 R ( ) a ( ) R sin π ϑ R sinϑ a R R R? π ϑ R R ϑ R D

4 R ( D) ( D) R D sin π π ϑ D sin π D sin ϑ R π D sin R sinϑ π ϑ ϑ ϑ R π D sinϑ D π sin ϑ π sin D

5 Nm.5 m D m.5 m ϑ 45 deg π ϑ R R R deg R R D sinϑ D π sin ϑ π sin π ϕ R D

6 Nm.5 m D m.5 m ϑ 45 deg π ϑ R R R deg R R ( ) ( ) ( ) sin sin 45.5sin N.5sin(6) π ϕ R D

7 Let us see an example of graphical application of the V for soling static analysis associated with numerical ealuation of the results.? A γ D

8 Let us assume a elocity for the slider: we want to compute the angular elocity of the other members in term of. Let us start with ω c ω c c c c c D sinγ A D cosγ AD A sinγ AD cosγ c A AD tgγ A ω AD tgγ c c γ D c

9 We search now the expression of ω in terms of. π sin ( π γ) Asin c ω A AD tgγ ( ) ( ) ( ) ( ) Asin π / AD tgγ sin π / sin ω ω ω D π γ sin π γ ( ) ( π γ) AD tgγ sin π / D sin A c c π c π γ γ ω D c

10 ω AD tgγ c ω ω ω ( ) ( π γ) AD tgγ sin π / D sin ω ( ) ( ) AD tgγ sin π / AD tgγ D sin π γ ( π ) ( π γ) sin / D sin A c π c π γ γ ω D c c

11 V N F N F + ω j j j j j j In order to ealuate the power associated with the torque we must assume a direction for it: + ω ω ( π ) ( π γ) sin / D sin A ω γ? D ( ) ( π γ) sin π / + D sin D ( π γ) ( π ) sin sin /

12 N D. m 45 deg γ 45 deg D sin sin ( π γ) ( π ) A γ D ( ) ( ) ( ) ( ).sin π π 4 π 4 sin π sin π / π 4 sin π 4 The negatie alue for the amplitude tell us we chose the wrong direction Nm 8. Nm

13 ONTRIUTION OF A STUDNT Another possibility is to directly relate the motions of the slider and the crank ω ( ) c c c c c c D AD tg c ω ADtg AD tg A c c ω γ D c

14 7? Let us now study the kinematics of the lifting platform. We will see how introducing some simple considerations on the mechanism geometry may greatly simplify its analysis D 4 A

15 7 7? 6 6 For the symmetry of the system, the platform can only translate ertically. Its elocity will be equal to the ertical component of the absolute elocity of the point, that may be computed once the angular elocity of body is known. In fact: ω ( ) D 4 A 6 π /

16 cos 7 ω D ω? D 5 4 A After some considerations, we may restrict our analysis to the motion induced on by the piston -, thus studying a simpler system

17 In order to determine we may compute and exploit the relation ω ω ω ω ω? + D A ω ω ω

18 We need now only to determine the position of D A

19 Since is an improper point (at infinite), the body translate. Thus ω ω D D D A cos D 7 cos

20 7 7 D cos 7 6 D. m 5 D 45 m D 4 A. m s 7. cos ( 45 ).7. m s

21 Q 7 6 Let us now sole the static analysis of the lifting platform? 5 D 4 A

22 7 Q 6 a + b + R67 Q a b R57 Q a b R 67 R 57 Q a b

23 R 75 c 5 d R R 5 75 R45 R75 d c+ d d c 4 R 45 R R 75 5

24 R 5 S R 6 S R5 + R6 e + f S R5 f R 6 R 5? e f D

25 S S R5 + R6 e + f S R5 f? R S D

26 7 7 Q 6 It is worth to notice that we could determine, when known Q, by means of the V directly after the kinematic analysis. 7 D cos 5? Q7 + D Q cos D 4 A

27 76 It is possible to determine the motion of the member 7 also by means of its instantaneous absolute center of rotation