Post on 04-Apr-2018
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).
A multi force member supports three or more forces
or at least two forces and one or more couples.
In contrast with a truss, the force or moment can be
exerted to any point on the frame member; it does
not have to be applied the joint as in the trusses.
Machines are structures which contain moving parts and are
designed to transmit input forces or couples to output forces or
couples.
Therefore a machine is an assembly of rigid and sturdy members
that are capable of generating work by means of some kind of
motion.
A mechanism is a term used to describe the physical devices which
enable the parts of a machine to conduct the intended movements.
A machine may contain several mechanisms.
Machines are designed to change forces, enhance and
amplify their magnitudes and transmit them.
Whether a machine is as simple as a hand tool or as
complex as an airplane, the main aim is to convert input
forces into output forces.
The main difference between a frame and a
machine is that although frames are rigid
structures, machines are not. Machines may be
fixed to some supporting surface or body, but
they will always consist moving parts.
The forces acting on each member of a connected system are
found by isolating the member with a FBD and applying the
equations of equilibrium.
The principle of action and reaction must be carefully observed
when we represent the forces of interaction on the separate FBDs.
It would be appropriate to identify the two forces members in the
frame, if there is any, before starting with the solution.
In order to determine the forces in a frame or machine,
it is divided into a sufficient number of members or
groups of members, but initially the support forces to
be used in the analysis must generally be determined
from the equilibrium of the whole frame.
The structure is then, dismembered and the equilibrium of
each member is considered separately.
The equilibrium equations for the several parts will be related
through the terms involving the forces of interaction.
It should be kept in mind that when going from one member to
the other, the direction of the interaction force must be
changed in accordance with Newton’s third law.
In general the FBDs of pins in the structures are not drawn;
pins are considered as a complementary part of one of the
two members it connects. It must be clearly decided which
member the pin will belong to. Whereas, the FBD of a pin
will be considered if:
It connects three or more members,
It connects a support and two or more members,
A load is directly applied to the pin.
Machines are considered as “ideal machines” when the work
output is equal to the energy input. It is impossible to build such
machines. In a real machine friction forces always generate
useless work which causes loss of energy, therefore, work output
is always less than the energy input. In other words, the
mechanical efficiency is always less than one, h<1.
inputenergy
utputo workh
Mechanical advantage is the ratio of the output force of a
machine to the input force necessary to work the machine.
This concept is totally different from the mechanical
efficiency and should not be mixed with it. Mechanical
advantage is generally greater than one.
ForceInput
ForceOutputAdvantageMechanical
Small bolt cutter operated by hand for cutting small bolts and rods is shown. For
a hand grip P=150 N. Determine the force Q developed by each jaw on the rod
to be cut.
Mechanical advantage
The forces acting on the two parts of the bolt cutter behave as mirror images of each other with respect to
x-axis. Thus, we can not have an action on one member in the +x direction and its reaction on the other
member in the –x direction. Consequently the forces at E and B have no x-components and CD is a two-
force member.
1. The clamp shown in the figure is frequently used in welding operations.
Determine the clamping force on the two metal pieces at E and the magnitudes of
the forces supported by pins A, B and D.
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.
3. Determine the force P exerted on the twig G. Note that there is a
horizontal line of symmetry for the handles, but there is no line of
symmetry for the jaws.
4. Calculate the x- and y-components of all forces acting on each member
of the loaded frame.
5. The truck shown is used to deliver food to aircraft. The elevated unit weighs
1000 kg with center of gravity at G. Determine the required force in the hydraulic
cylinder AB.
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.
F
7. 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.
8. In the frame shown determine the forces acting at pins A, B and D.
9. 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 gravity at H. Arm ABCD has a weight of 2 kN and a center of gravity
at B, arm DEFG has a weight of 1 kN and a center of gravity at E. The weights of the hydraulic cylinders
can be neglected. Determine the forces in the hydraulic cylinders CJ, BF and EI and also determine all
the forces acting at arm DEFG.
10. 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
11. 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 q=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
q=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
q=60o
FBD of CG
C
G
FCG
q=60o 30
30
cos
FF
sin
FF
CCG
BCCG
FBD of BC
FCG
FBC FBC
30tanF
F
C
BC
30o
q=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
q=60o
Ex
o.sin
.
sin
.
m.DHcosEHDEEHDEDH
021260
91270
912602222
D
H
Ey
FBC
FDH
0.7 m
0.61 m
1.4 m
Cosine theorem:
Sine theorem:
12. 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
13. 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