1. The toggle pliers are used for a variety of clamping

purposes. For the handle position given by a = 10° and for a

handle grip P = 150 N, calculate the clamping force FC

produced.

Note that pins

A and D are

symmetric

about the

horizontal

centerline of

the tool.

2. 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 F exerted on the tire has a magnitude of 3600 N.

magnitudes of forces at each joint

FCD

Bx

By

a

x

y

09.12280

60tan 1

a

NBFBF

NBFBF

NF

FF

M

yCDyy

xCDxx

CD

CDCD

B

400003600sin0

18560cos0

1898

0)70(sin)305(cos)165(3600

0

a

a

aa

NB 441040001856 22

CD

FCD

FCD

Wheel + BC

NA

NAFAF

NAFAF

NF

F

M

yEFyy

xEFxx

EF

EF

A

455013844330

138404000sin0

433001856cos0

5920

0)350(4000)260(sin

0

22

magnitudes of forces at each joint

Bx

By

x

y

30.65200

435tan 1

FEF

EF

FEF

FEF

Ax

Ay

AEB

3. The elements of a floor jack are shown in the figure. CDFE

forms a parallelogram. Calculate the force in the hydraulic

cylinder AB corresponding to the 10 kN load. What is the force

in link EF?

4. Determine the cutting force F applied by the blade DE to the

bar at G in terms of the force P applied to the handle of the

heavy-duty cutter.

Assume that

the cutting

force F is

perpendicular

to the lower

edge of the

blade DE.

cutting force F applied by the blade DE to the bar at G in terms of the force P applied to the handle, force F is perpendicular to the lower edge of the blade DE.

FBE

a

x

y

ABC

Ax

Ay

4

17

CPF

FFPM

BE

BEBEA

7.23

0)4(sin)17(cos)413(0

12.1028

5tan 1

aa

a

cutting force F applied by the blade DE to the bar at G in terms of the force P applied to the handle, force F is perpendicular to the lower edge of the blade DE.

FBE=23.7P

a

x

y

Blade DE

Dx

Dy

86

14°

PF

FFPPM D

4.45

0)5(14sin)48(14cos)13(sin7.23)86(cos7.230

60.886

13tan 1

aa

F

5. The design of a hoisting mechanism for the dump truck is shown in the enlarged view. Determine the compression P in the hydraulic cylinder BE and the magnitude of the force supported by the pin at A for the particular position shown, where BA is perpendicular to OAE and link DC is perpendicular to AC. The dump and its load together have a mass of 9 Mg with center of mass at G.

6. A basketball hoop whose rim height is adjustable is shown. The supporting post ABCD weighs 400 N with the center of gravity at point C, and backboard-hoop assembly weighs 220 N with the center of gravity at point G. The height of the rim is adjustable by 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 by all members. Hint: Member IJ is a two-force member.

800 N

24

7

mABCD= 400 N (at C), mhoop= 220 N (at G) IJ= two-force member, if a person with 800 N weight hangs on the rim, determine the support reactions at D and the forces supported by all members.

Dx

mNM

M

M

ND

D

F

ND

DF

D

D

D

y

y

y

x

xx

2.1867

0)35.1(768

)3(224)72.0(220

0

1388

0768220400

0

224

02240

220 N

400 N

Dy

MD

800 N

24

7

224 N

768 N

Entire frame

x

y

mABCD= 400 N (at C), mhoop= 220 N (at G) IJ= two-force member, if a person with 800 N weight hangs on the rim, determine the support reactions at D and the forces supported by all members.

FAE

NF

NF

FFF

NF

FFF

NF

NFF

F

NF

F

M

y

yAEyy

x

xAExx

AE

AEy

AEx

AEy

AEx

AEx

F

2243)1992()1031(

1992

07682200

1031

02240

1584)1004()1225(

1004,5

4

60.0

48.0

1255

0)75.0(768)12.0(22048.0

0

22

22

FAEx

220 N

FAEy

800 N

24

7

224 N

768 N

Fx

Fy

EFGH

x

y

mABCD= 400 N (at C), mhoop= 220 N (at G) IJ= two-force member, if a person with 800 N weight hangs on the rim, determine the support reactions at D and the forces supported by all members.

FIJ

NB

NBFBFF

NFBFBF

NF

FFF

M

yyyIJy

xxxxx

IJ

yxIJ

B

6740)6661()1031(

666100

103100

4669

0)60.0()48.0(15.0

0

22

Fx

Fy

IBF

Bx

By

IJ two force member

FIJ

FIJ

x

y

7. The figure shows a wheel puller which is designed to remove a V-belt pulley P from its tight-fitting shaft S by tightening of the central screw. If the pulley starts to slide off the shaft when the compression in the screw has reached 1.2 kN, calculate the magnitude of the force supported by the each jaw at A. The adjusting screws D support horizontal force and keep the side arms parallel with the central screw.

compression in the screw =1.2 kN, calculate the magnitude of the force supported by the each jaw at A, adjusting screws D support horizontal force

FCB

x

y

kNFF

kNFFFF

F

F

FFF

FF

FFF

EHCB

EHxCBxEHyCBy

CBx

CBy

EHxCBxx

EHyCBy

EHyCByy

85.0

6.0

145tan

0

2.1

02.10

1.2 kN

FEH

E

H

FEHx

FEHy

FCBx

FCBy

45°

45°

FCBy

FCBy

FCBx

FCBx

FCB

FCB

CB

EC

compression in the screw =1.2 kN, calculate the magnitude of the force supported by the each jaw at A, adjusting screws D support horizontal force

x

y

kNDF

kNAAA

kNA

A

AAFM

kNFF

kNFAF

xx

yx

x

x

xyCBxD

CBxCBy

CByyy

42.00

626.0

18.0

,)6.0(15)6.0(60150

0)150()15()60(0

6.0

6.00

22

FCBy

FCBy

FCBx

FCBx

FCB

FCB

Ax

Ay

FCBy

FCBx

FCB

45°

CB

Dx

ABD

F

8. The pruning mechanism of a pole saw is shown as it cuts a branch S. For

the particular position drawn, the actuating cord is parallel to the pole and

carries a tension of 120 N. Determine the shearing force P applied to the

branch by the cutter and the total force supported by the pin at E. The

force exerted by the light return spring at C is small and may be neglected.

9. A bag of potatoes is

sitting on the chair. The

force exerted by the

potatoes on the frame at

one side of the chair is

equivalent to horizontal and

vertical forces of 24 N and

84 N, respectively, at E and

a force of 28 N

perpendicular to member BH

at G. Find the forces acting

on member BH.

Dimensions are in centimeters

10. The elevation mechanism of a dumper-truck is comprised of two

identical systems of which one is shown in the figure and each

supports half of the load for the position depicted. Determine the

reactions in bars CD and HI and hydraulic cylinder BC. State

whether they work in

tension or compression.

Three members are

connected at pin B

(members EBD, ABH and

BC). Note that pins A and

D may not necessarily lie

along the same horizontal

line.

11. The linkage shown is used on a garbage truck to lift a 9000 N dumpster.

Points A to G are pins, and member ABC is horizontal. For the position shown,

when the dumpster just fully lifts off the ground, determine the force in

hydraulic cylinder CF. Roller at G is in contact with the dumpster.

Ax

Ay

FG

FBD of dumpster

NAFAF

NAFAF

NFFM

yGyy

xGxx

GGA

6910045sin90000

15910045cos0

225000)600()1500(90000

Ex

Ey

FCD

FG

FBD of member EDG

NEEF

NEEF

NFFM

yyy

xxx

GCDE

5.79549045sin2250045cos1125000

63640045cos11250045cos225000

1125000)300()1500(225000

Bx

By

FCF

Ex

Ey

From equilibrium of whole system;

NF

FEE

M

CF

CFyx

B

68.118724

0)450(45cos)45cos900900(450)45cos900()1950(9000

0

12. A hydraulic lift-table is used to raise a 1000 kg crate. It consists of a platform and two identical linkages on which hydraulic cylinders exert equal forces. In the figure only one linkage and one cylinder are shown. Members EDB and CG are each of length 2a and member AD is pinned to the midpoint of EDB. If the crate is placed on the table, so that half of its weight is supported by the system shown, determine the force exerted by each cylinder in raising the crate for =60°, a=0.70 m and L=3.20 m. Show that the result obtained is independent of the distance d.

FBD of Platform

Two-Force Members: AD, BC, CG, DH.

30o

=60o

FAD

W/2

FC FB

A B C

BCCBCBy

ADADx

FW

FW

FFW

FFF

FFFx

220

20

000

Pulley C FC

C

FCG

30o

FBC

300300

0300

cosFFFcosFF

FsinFF

CGCCCGy

BCCGx

30o

=60o

FBD of CG

C

G

FCG

=60o 30

30

cos

FF

sin

FF

CCG

BCCG

FBD of BC

FCG

FBC FBC

30tanF

F

C

BC

30o

=60o

N.F

FF.F.

.tanF.FF.

.F.F..sinF..cosFM

DH

/W

CBDH

F

CBDH

BCBDHDHE

BC

635124

070670

02113070670

021170350021261002120

2

FBD of EDB

B

E

FB

=60o

Ex

o.sin

.

sin

.

m.DHcosEHDEEHDEDH

021260

91270

912602222

aa

D

H

a

Ey

FBC

FDH

0.7 m

0.61 m

1.4 m

Cosine theorem:

Sine theorem:

13. The mechanism is designed to keep its load level while raising it. A pin

on the rim of the 80 cm diameter pulley fits in a slot on arm ABC. Arm ABC

and DE are each 80 cm long and the package being lifted weighs 80 kN.

The mechanism is

raised by pulling on

the rope that is

wrapped around the

pulley. 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.

SOLUTION

FBD of Platform Two force member: ED

69.28 mm

FBD of DE

FBD of ABC

FBD of the pulley

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 BF. Neglect the weights of the connecting elements (not shown) and the seat, and also the friction at points A, B and F.

Detail of contact at F

Dimensions in “mm”

Geometry of the Chair

SOLUTION

Two force member: EG

Equilibrium of the whole system:

FBD of DC

GE two force member

FBD of BF