1. The toggle pliers are used for a variety of clamping purposes. For the handle position given by a=10 o and for a handle grip P=150 N, calculate

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Homer Pearson
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2 1. The toggle pliers are used for a variet of clamping purposes. or the handle position given b a=10 o and for a handle grip P=150 N, calculate the clamping force C produced. Note that pins A and D are smmetric about the horizontal centerline of the tool.

3 2. The elements of a floor jack are shown in the figure. CD forms a parallelogram. Calculate the force in the hdraulic clinder AB corresponding to the 10 kn load. What is the force in link?

4 3. The elements of a rear suspension for a front-wheel-drive car are shown in the figure. Determine the magnitude of the force at each joint if the normal force eerted on the tire has a magnitude of 3600 N.

5 4. Determine the horizontal and vertical components of force that the pins at A, B, and D eert on the A-frame m C 1 m B D 0.75 m 1600 N 1 m 1200 N A 0.5 m 0.5 m 0.5 m 0.5 m

6 5. The motion of the backhoe bucket shown is controlled b the hdraulic clinders AD, CG and. As a result of an attempt to dislodge a portion of a slab, a 13-kN force P is eerted on the bucket teeth at J. Determine the force eerted b each clinder.

7 6. A basketball hoop whose rim height is adjustable is shown. The supporting post ABCD weighs 400 N with the center of gravit at point C, and backboard-hoop assembl weighs 220 N with the center of gravit at point G. The height of the rim is adjustable b means of the screw and hand crank IJ, where the screw is vertical. If a person with 800 N weight hangs on the rim, determine the support reactions at D and the forces supported b all members. Hint: Member IJ is a two-force member.

8 7. The mechanism in the figure is used to raise the bucket of a bulldozer. The bucket and its contents weigh 10 kn and have a center of gravit at H. Arm ABCD has a weight of 2 kn and a center of gravit at B, arm DG has a weight of 1 kn and a center of gravit at. The weights of the hdraulic clinders can be neglected. Determine the forces in the hdraulic clinders CJ, B and I and also determine all the forces acting at arm DG.

Two-force members: CJ, B, I. BD of bucket I G G 10 kn M G 0 0 0 10 G G 0. 3 1.

9 Two-force members: CJ, B, I. BD of bucket I G G 10 kn M G G G cos 30 I I G G I kn kn 10 kn BD of hdraulic clinder I I I I

10 BD of DG D D D 30 o 1 kn D I B a 19 o 30 o 30 o B G G G B sina sin sin 60 cos 60 a 41 o, 79 o B m M D I 0. 6cos sin 30 B sin cos 30 B cos sin 30 G 1. 8cos 30 G 1. 8sin B kn G G D D B 1 cos19 B I sin D D kn kn

BD of entire sstem P= CJ A 2 kn 1 kn 10 kn A M CJ A 0 1. 8sin 60100. 3 1. 8sin 30 2.

11 BD of entire sstem P= CJ A 2 kn 1 kn 10 kn A M CJ A sin sin sin sin sin sin 30 CJ 18 kn A CJ A A A kn kn

12 20 kn 15 kn 8. The figure shows a special rig designed to erect vertical sections of a construction tower. The assembl A has a weight of 15 kn and is elevated b the platform B, which itself has a weight of 20 kn. The platform is guided up the fied vertical column b rollers and is activated b the hdraulic clinder CD and links D and H. or the particular position shown, calculate the force eerted b the hdraulic clinder at D and the magnitude of the force supported b the pin at.

13 3 m Two-force members: CD, H. 15 kn ( H ) BD of H 20 kn H ( H ) =35 kn a 1.25 m a o 35 H H kn

16 43 o M CD 0 cos 1 sin 0. 75 cos a3 sina 2.

14 3 m 0.75 m BD of D o. H a , kn 1 m D CD H a C sin o M CD 0 cos 1 sin cos a3 sina CD H H 0 CD kn 0 0 H H sina cos a CD CD sin 0 cos kn kn

15 9. The elements of a stump grinder with a total mass (eclusive of the hdraulic clinder D and arm C) of 300 kg with mass center at G are shown in the figure. The mechanism for articulation about a vertical ais is omitted, and the wheels at B are free to turn. or the nominal position shown, link C is horizontal and the teeth of the cutting wheel are even with the ground. If the magnitude of the force eerted b the cutter on the stump is 400 N, determine the force P in the hdraulic clinder and the magnitude of the force supported b the pin at C.

Two-force member: D. BD of entire machine 20 o M B cos 200. 6 sin 202. 25 B 1. 55 300 9.

16 Two-force member: D. BD of entire machine 20 o M B cos sin B B N 0 0 cos 20 0 B sin N N

17 230 mm BD of DC D P a C C C D a 1300 mm 230 tan a a o M C P cos a P sina P N 0 0 C C P P cos a 0 sina 0 C C N N

18 10. If the forces shown in the figure are applied to the digger at point G, find the forces in the hdraulic clinders HB and CD.

19 (1) BD of entire digger (2) BD of bucket+k+c+cd+cj HB CD 15 o A K K A (1) (2) 5 5 M cos sin M A K 0 0 HB cos sin 70 sin cos kn CD HB CD 0 HB CD kn

20 11. The linkage shown is used on a garbage truck to lift a 9000 N dumpster. Points A-G are pins, and member ABC is horizontal. or the position shown, when the dumpster just full lifts off the ground, determine the force hdraulic clinder C. Roller at G is contact with the dumpster.

21 A A G BD of dumpster N A A N A A N M G G G G A sin cos (600) 9000(1500) 0

22 CD G BD of member DG M (1500) CD 22500cos cos cos 45 (300) sin 45 0 G N N N

23 C rom equilibrium of whole sstem; B B M 900(1950) C N (900cos 45) 450 ( cos 45) C cos 45(450) 0

24 12. A hdraulic lift-table is used to raise a 1000 kg crate. It consists of a platform and two identical linkages on which hdraulic clinders eert equal forces. In the figure onl one linkage and one clinder are shown. Members DB and CG are each of length 2a and member AD is pinned to the midpoint of DB. If the crate is placed on the table, so that half of its weight is supported b the sstem shown, determine the force eerted b each clinder in raising the crate for q=60 o, a=0.70 m and L=3.20 m. Show that the result obtained is independent of the distance d.

25 Two-orce Members: AD, BC, CG, DH. BD of Platform W/2 A B C 30 o q=60 o AD B C 0 0 AD B 0 C W 2 0 AD 0 B C W 2 C W 2 B Pulle C C BC C 0 0 CG CG sin 30 cos 30 BC C 0 0 C CG cos o CG

26 BD of CG C CG G CG CG BC sin 30 C q=60 cos 30 o q=60 o 30 o CG BD of BC BC C tan 30 BC BC

27 BD of DB B B BC 30 o 1.4 m D 0.7 m 0.61 m q=60 o a DH H q=60 o Cosine theorem: Sine theorem: M DH 0 DH DH DH 0. 7 sina B DH cos DH sin B 0. 7 BC tan N B C W / 2 D sin 60 C 2 BC 0 H 2 2DH cos 60 DH m a o 0

28 13. The mechanism is designed to keep its load level while raising it. A pin on the rim of the 80 cm diameter pulle fits in a slot on arm ABC. Arm ABC and D are each 80 cm long and the package being lifted weighs 80 kn. The mechanism is raised b pulling on the rope that is wrapped around the pulle. Determine the force P applied to the rope and all the forces acting on arm ABC when the package has been lifted 80 cm as shown.

29 SOLUTION BD of Platform Two force member: D BD of D mm

30 BD of ABC BD of the pulle

31 14. A simple folding chair comprised of two identical frames, one on each side, is shown in the figure. The half frame shown carries half the weight of a 70 kg person. Determine all the forces acting on member B. Neglect the weights of the connecting elements (not shown) and the seat, and also the friction at points A, B and. Detail of contact at Dimensions in mm

32 Geometr of the Chair

33 SOLUTION Two force member: G quilibrium of the whole sstem: BD of DC

34 G two force member BD of B

Similar to trusses, frames are generally fixed, load carrying structures.

Similar to trusses, frames are generally fixed, load carrying structures. The main difference between a frame and a truss is that in a frame at least one member is a multi force member (çoklu kuvvet elemanı).