Force analysis is a fundamental tool used to understand how forces affect the motion and behavior of objects. It involves identifying all forces acting on an object, determining their magnitudes and directions, and applying Newton's laws of motion. Force analysis is used across various engineering fields to predict how structures and systems will perform under different loading conditions. It allows engineers to design structures and machines that can withstand anticipated forces safely and efficiently. Force analysis considers both static systems at rest as well as dynamic systems in motion. Computer modeling has enhanced force analysis by enabling complex systems to be simulated.

1. FORCE ANALYSIS

2. 1
Force Analysis
Introduction:
If the acceleration of moving links in a mechanism is running with
considerable amount of linear and/or angular accelerations, inertia forces
are generated and these inertia forces also must be overcome by the
driving motor as an addition to the forces exerted by the external load or
work the mechanism does.
Force analysis is a fundamental concept in physics and engineering that
involves the study of forces acting on objects. Forces can be defined as
interactions that cause a change in the motion or shape of an object.
Understanding and analyzing forces are crucial in various fields, including
mechanics, civil engineering, biomechanics, and many others.
In physics, force is described by Sir Isaac Newton's famous second law,
which states that the force acting on an object is equal to the mass of the
object multiplied by its acceleration (F = ma). This law forms the basis for
force analysis in classical mechanics and is essential for predicting the
motion of objects under the influence of external forces.
Force analysis involves determining the magnitude, direction, and point of
application of forces in a system. Engineers and scientists use force
analysis to design structures, machines, and systems that can withstand or
generate specific forces. It is a crucial step in ensuring the safety,
efficiency, and functionality of various devices and structures.
There are different types of forces, including gravitational forces, frictional
forces, tension forces, compression forces, and more. Each type of force
has unique characteristics, and understanding how they interact is essential
for accurate force analysis.

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In engineering, force analysis is often applied to static and dynamic
systems. Static force analysis deals with objects at rest or in a state of
equilibrium, where the sum of all forces and torques is zero. Dynamic
force analysis, on the other hand, considers objects in motion and involves
the study of how forces affect acceleration and velocity.
Computer-aided tools and simulations have become invaluable in modern
force analysis, allowing engineers to model complex systems and predict
their behavior under different conditions. Overall, force analysis is a
fundamental and indispensable tool for understanding the physical world
and designing structures and systems that meet specific performance
requirements.
Newton’s Law: First Law:
Everybody will persist in its state of rest or of uniform motion (constant
velocity) in a straight line unless it is compelled to change that state by
forces impressed on it. This means that in the absence of a non-zero net
force, the center of mass of a body either is at rest or moves at a constant
velocity. Second Law A body of mass m subject to a force F undergoes an
acceleration a that has the same direction as the force and a magnitude that
is directly proportional to the force and inversely proportional to the mass,
i.e., F = ma. Alternatively, the total force applied on a body is equal to the
time derivative of linear momentum of the body. Third Law The mutual
forces of action and reaction between two bodies are equal, opposite and
collinear. This means that whenever a first body exerts a force F on a
second body, the second body exerts a force −F on the first body. F and −F
are equal in magnitude and opposite in direction. This law is sometimes

4. 3
referred to as the action-reaction law, with F called the "action" and −F the
"reaction".
Types of force Analysis:
 Equilibrium of members with two forces.
 Equilibrium of members with three forces.
 Equilibrium of members with two forces and torque.
 Equilibrium of members with two couples.
 Equilibrium of members with four forces.
Graphical Force Analysis:
Graphical force analysis employs scaled free-body diagrams and vector
graphics in the determination of unknown machine forces. The graphical
approach is best suited for planar force systems. Since forces are normally
not constant during machine motion. analyses may be required for a
number of mechanism positions; however, in many cases, critical
maximum-force positions can be identified and graphical analyses
performed for these positions only. An important advantage of the
graphical approach is that it provides useful insight as to the nature of the
forces in the physical system. This approach suffers from disadvantages
related to accuracy and time. As is true of any graphical procedure, the
results are susceptible to drawing and measurement errors. Further, a great
amount of graphics time and effort can be expended in the iterative design
of a machine mechanism for which fairly thorough knowledge of force-
time relationships is required. In recent years, the physical insight of the
graphics approach and the speed and accuracy inherent in the computer-
based analytical approach have been brought together through computer
graphics systems, which have proven to be very effective engineering

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design tools. There are a few special types of member loadings that are
repeatedly encountered in the force analysis of mechanisms, These include
a member subjected to two forces, a member subjected to three forces, and
a member subjected to two forces and a couple. These special cases will be
considered in the following paragraphs, before proceeding to the graphical
analysis of complete mechanisms.
Analysis of a Two-Force Member:
A member subjected to two forces is in equilibrium if and only if the two
forces (1) have the same magnitude, (2) act along the same line, and (3)
are opposite in sense. Figure 1.2A shows a free-body diagram of a member
acted upon by forces F1 and F2 where the points of application of these
forces are points A and B. For equilibrium the directions of F1 and F2
must be along line AB and F1 must equal F2 graphical vector addition of
forces F1 and F2 is shown in Figure 1.2B, and, obviously, the resultant net
force on the member is zero when F1 = - F2 The resultant moment about
any point will also be zero. Thus, if the load application points for a two-
force member are known, the line of action of the forces is defined, and it
the magnitude and sense of one of the forces are known, then the other
force can immediately be determined. Such a member will either be in
tension or compression.

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Analysis of a Three-Force Member:
A member subjected to three forces is in equilibrium if and only if (1) the
resultant of the three forces is zero, and (2) the lines of action of the forces
all intersect at the same point. The first condition guarantees equilibrium
of forces, while the second condition guarantees equilibrium of moments.
The second condition can be under-stood by considering the case when it
is not satisfied.If moments are summed about point P, the intersection of
forces F1 and F2 , then the moments of these forces will be zero, but F3
will produce a nonzero moment, resulting in a nonzero net moment on the
member.
A typical situation encountered is that when one of the forces, F1 , is
known completely, magnitude and direction, a second force, F2 , has
known direction but unknown magnitude, and force F3 has unknown
magnitude and direction. First, the free-body diagram is drawn to a
convenient scale and the points of application of the three forces are
identified. These are points A, B, and C. Next, the known force F1 is
drawn on the diagram with the proper direction and a suitable magnitude
scale. The direction of force F2 is then drawn, and the intersection of this
line with an extension of the line of action of force F1 is the concurrency
point P. For equilibrium, the line of action of force F3 must pass through
points C and P and is therefore as shown in Figure 1.4A. The force
equilibrium condition states that: F1+F2+F3=0

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Static-force analysis of a slider crank mechanism is discussed. Consider
the slider crank linkage shown in Figure 1.5A, representing a compressor,
which is operating at so low a speed that inertia effects are negligible. It is
also assumed that gravityforces are small compared with other forces and
that all forces lie in the same plane.The dimensions are OB = 30 mm and
BC == 70 mm, we wish to find the required crankshaft torque T and the
bearing forces for a total gas pressure force P = 40N at the instant when
the crank angle  45 degrees?
Solution:
The graphical analysis is shown in Figure 1.5B. First, consider connecting
rod 2. In the absence of gravity and inertia forces, this link is acted on by
two forces only, at pins B and C. These pins are assumed to be frictionless
and, therefore, transmit no torque. Thus, link 2 is a two-force member
loaded at each end as shown. The forces F12 and F32 lie along the link,
producing zero net moment, and must be equal and opposite for
equilibrium of the link. At this point, the magnitude and sense of these
forces are unknown. Next, examine piston 3, which is a three-force
member. The pressure force P is completely known and is assumed to act
through the center of the piston (i.e., the pressure distribution on the piston
Problem:

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face is assumed to be symmetric). From Newton's third law, which states
that for every action there is an equal and opposite reaction, it follows that
F23=-F32 , and the direction of F23 is therefore known. In the absence of
friction, the force of the cylinder on the piston, F03 , is perpendicular to
the cylinder wall, and it also must pass through the concurrency point,
which is the piston pin C. Now, knowing the force directions, we can
construct the force polygon for member 3 (Figure 1.5B). Scaling from this
diagram, the contact force between the cylinder and piston is F03=12.7 N
acting upward, and the magnitude of the bearing force at C is
F23=F32=42N . This is also the bearing force at crankpin B, because
F12=-F32 Further, the force directions for the connecting rod shown in the
figure are correct, and the link is in compression However these forces are
not collinear, and for equilibrium, the moment of this couple must be
balanced by torque T. Thus, the required torque is clockwise and has
magnitude:
It should be emphasized that this is the torque required for static
equilibrium in the position shown in Figure 1.10A.

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Summary:
Force analysis is a fundamental tool used to understand and predict the
behavior of objects under the influence of forces. It involves identifying all
the forces acting on an object, determining their magnitudes and
directions, and applying Newton's laws of motion to calculate the object's
acceleration and velocity.
Force analysis is used in a wide range of applications, including structural
engineering, mechanical engineering, aerospace engineering, robotics, and
biomechanics.
In conclusion, force analysis is a powerful technique that allows engineers
and scientists to predict the behavior of objects under the influence of
forces. It is used to design a wide range of structures and systems, from
buildings and bridges to aircraft and robots. Force analysis is an essential
tool for understanding and shaping the physical world around us.
References:
1- Meriam, J. L., & Kraige, L. G. (2017). Engineering mechanics:
Statics. John Wiley & Sons.
2- Hibbeler, R. C. (2018). Engineering mechanics: Statics & dynamics.
Pearson Education.
3- Beer, F. P., Johnston, E. R., Mazurek, D. F., & Cornwell, P. J.
(2017). Vector mechanics for engineers: Statics and dynamics.
McGraw-Hill Education.
4- Bedford, A., & Fowler, W. (2017). Engineering mechanics: Statics.
Pearson Education.
5- Shames, I. H., & Pitarresi, J. M. (2017). Introduction to solid
mechanics. Pearson Education.