F

1. 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.

FTwo-force member: CD

FBD of member EDF

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

ax

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

FCDFCD

Wheel + BC

NA

NAFAF

NAFAF

NF

F

M

yEFyy

xEFxx

EF

EF

A

455013844330

138404000sin0

433001856cos0

5920

0)350(4000)260(sin

0

22

Bx

By

x

y

30.65200

435tan 1

FEF

EF

FEF

FEF

Ax

Ay

AEB

3. 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. For the position shown, when the dumpster just fully

lifts off the ground, determine the force hydraulic cylinder CF. Roller at G is 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

E

68.118724

0)450(45cos)45cos900900(450)45cos900()1950(900

0

4. 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 =60o, 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

FCFB

A B C

BCCBCBy

ADADx

FW

FW

FFW

FFF

FFFx

220

20

000

Pulley CFC

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

FBCFBC

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

aEy

FBC

FDH

0.7 m

0.61 m

1.4 m

Cosine theorem:

Sine theorem:

5. 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

6. 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