The document discusses static force analysis and equilibrium of mechanisms. It covers topics like static equilibrium, equilibrium of two and three force members, members with two forces and torque, free body diagrams, and the principle of virtual work. Examples of static force analysis of four bar and slider-crank mechanisms are presented. Methods to determine the forces and torques required for static equilibrium are demonstrated through graphical techniques like force triangles and the principle of virtual work.
The various forces acts on the reciprocating parts of an engine.
The resultant of all the forces acting on the body of the engine due to inertia forces only is known as unbalanced force or shaking force.
Unit 6- spur gears, Kinematics of machines of VTU Syllabus prepared by Hareesha N Gowda, Asst. Prof, Dayananda Sagar College of Engg, Blore. Please write to hareeshang@gmail.com for suggestions and criticisms.
The various forces acts on the reciprocating parts of an engine.
The resultant of all the forces acting on the body of the engine due to inertia forces only is known as unbalanced force or shaking force.
Unit 6- spur gears, Kinematics of machines of VTU Syllabus prepared by Hareesha N Gowda, Asst. Prof, Dayananda Sagar College of Engg, Blore. Please write to hareeshang@gmail.com for suggestions and criticisms.
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When the inertia forces are considered in the analysis of the mechanism, the analysis is known as dynamic force analysis.
Now applying D’Alembert principle one may reduce a dynamic system into an equivalent static system and use the techniques used in static force analysis to study the system.
Garcia and Bayo (1994), Wang and Wang (1998), Shi and Mc Phee (2000) were interested in the analytical and
experimental study of the dynamic response of these mechanisms
Unit 4- balancing of rotating masses, Dynamics of machines of VTU Syllabus prepared by Hareesha N Gowda, Asst. Prof, Dayananda Sagar College of Engg, Blore. Please write to hareeshang@gmail.com for suggestions and criticisms.
Unit 5- balancing of reciprocating masses, Dynamics of machines of VTU Syllabus prepared by Hareesha N Gowda, Asst. Prof, Dayananda Sagar College of Engg, Blore. Please write to hareeshang@gmail.com for suggestions and criticisms.
Whirling of shafts occurs due to rotational imbalance of a shaft, even in the absence of external loads, which causes resonance to occur at certain speeds, known as critical speeds.
Design of flywheel theory and numericals prof. sagar a dhotareSagar Dhotare
1. Introduction.
2. Coefficient of Fluctuation of
Speed.
3. Fluctuation of Energy.
4. Maximum Fluctuation of
Energy.
5. Coefficient of Fluctuation
of Energy.
6. Energy Stored in a Flywheel.
7. Stresses in a Flywheel Rim.
8. Stresses in Flywheel Arms.
9. Design of Flywheel Arms.
10. Design of Shaft, Hub and
Key.
11. Construction of Flywheel.
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Belt is a Flexible Mechanical element that transmit power from one shaft to another
Belt is a Flexible Mechanical element that transmit power from one shaft to another
Gear Train
Ex: Automobile, engines etc.
Chain Drive
Ex : Bi-cycle , Motor cycle etc.
Belt Drive
Ex: Rice mills, sewing machine etc.
Rope Drive
Ex: lift, crane etc
This presentation contains basic idea regarding spur gear and provides the best equations for designing of spur gear. One can Easily understand all the parameters required to design a Spur Gear
Unit 6- Governers , Dynamics of machines of VTU Syllabus prepared by Hareesha N Gowda, Asst. Prof, Dayananda Sagar College of Engg, Blore. Please write to hareeshang@gmail.com for suggestions and criticisms.
Unit-6: Gyroscope, of Dynamics of machines of VTU Syllabus prepared by Hareesha N Gowda, Asst. Prof, Dayananda Sagar College of Engg, Blore. Please write to hareeshang@gmail.com for suggestions and criticisms.
BEST PPT FOR DOWNLOADING & SUBMISSION
INFORMATION IN POINTS
When the inertia forces are considered in the analysis of the mechanism, the analysis is known as dynamic force analysis.
Now applying D’Alembert principle one may reduce a dynamic system into an equivalent static system and use the techniques used in static force analysis to study the system.
Garcia and Bayo (1994), Wang and Wang (1998), Shi and Mc Phee (2000) were interested in the analytical and
experimental study of the dynamic response of these mechanisms
Unit 4- balancing of rotating masses, Dynamics of machines of VTU Syllabus prepared by Hareesha N Gowda, Asst. Prof, Dayananda Sagar College of Engg, Blore. Please write to hareeshang@gmail.com for suggestions and criticisms.
Unit 5- balancing of reciprocating masses, Dynamics of machines of VTU Syllabus prepared by Hareesha N Gowda, Asst. Prof, Dayananda Sagar College of Engg, Blore. Please write to hareeshang@gmail.com for suggestions and criticisms.
Whirling of shafts occurs due to rotational imbalance of a shaft, even in the absence of external loads, which causes resonance to occur at certain speeds, known as critical speeds.
Design of flywheel theory and numericals prof. sagar a dhotareSagar Dhotare
1. Introduction.
2. Coefficient of Fluctuation of
Speed.
3. Fluctuation of Energy.
4. Maximum Fluctuation of
Energy.
5. Coefficient of Fluctuation
of Energy.
6. Energy Stored in a Flywheel.
7. Stresses in a Flywheel Rim.
8. Stresses in Flywheel Arms.
9. Design of Flywheel Arms.
10. Design of Shaft, Hub and
Key.
11. Construction of Flywheel.
Like Comment and download
Belt is a Flexible Mechanical element that transmit power from one shaft to another
Belt is a Flexible Mechanical element that transmit power from one shaft to another
Gear Train
Ex: Automobile, engines etc.
Chain Drive
Ex : Bi-cycle , Motor cycle etc.
Belt Drive
Ex: Rice mills, sewing machine etc.
Rope Drive
Ex: lift, crane etc
This presentation contains basic idea regarding spur gear and provides the best equations for designing of spur gear. One can Easily understand all the parameters required to design a Spur Gear
Unit 6- Governers , Dynamics of machines of VTU Syllabus prepared by Hareesha N Gowda, Asst. Prof, Dayananda Sagar College of Engg, Blore. Please write to hareeshang@gmail.com for suggestions and criticisms.
Unit-6: Gyroscope, of Dynamics of machines of VTU Syllabus prepared by Hareesha N Gowda, Asst. Prof, Dayananda Sagar College of Engg, Blore. Please write to hareeshang@gmail.com for suggestions and criticisms.
Unit 3- friction and belt drives, Dynamics of machines of VTU Syllabus prepared by Hareesha N Gowda, Asst. Prof, Dayananda Sagar College of Engg, Blore. Please write to hareeshang@gmail.com for suggestions and criticisms.
Energy Conversion Engineering laboratory manual prepared by Hareesha N G, Asst. Prof., Dept of Aerospace, DSCE, Bangalore, for BE Students under VTU. Sub code:10AEL57
Unit 8-cams, Kinematics of machines of VTU Syllabus prepared by Hareesha N Gowda, Asst. Prof, Dayananda Sagar College of Engg, Blore. Please write to hareeshang@gmail.com for suggestions and criticisms.
Unit 7-gear trains, Kinematics of machines of VTU Syllabus prepared by Hareesha N Gowda, Asst. Prof, Dayananda Sagar College of Engg, Blore. Please write to hareeshang@gmail.com for suggestions and criticisms.
Unit 2- mechanisms, Kinematics of machines of VTU Syllabus prepared by Hareesha N Gowda, Asst. Prof, Dayananda Sagar College of Engg, Blore. Please write to hareeshang@gmail.com for suggestions and criticisms.
Unit 1-introduction to Mechanisms, Kinematics of machines of VTU Syllabus prepared by Hareesha N Gowda, Asst. Prof, Dayananda Sagar College of Engg, Blore. Please write to hareeshang@gmail.com for suggestions and criticisms.
Unit-3 - Velocity and acceleration of mechanisms, Kinematics of machines of VTU Syllabus prepared by Hareesha N Gowda, Asst. Prof, Dayananda Sagar College of Engg, Blore. Please write to hareeshang@gmail.com for suggestions and criticisms.
Civil Engineering is the Branch of Engineering.The Civil engineering field requires an understanding of core areas including Mechanics of Solids, Structural Mechanics - I, Building Construction Materials, Surveying - I, Geology and Geotechnical Engineering, Structural Mechanics, Building Construction, Water Resources and Irrigation, Environmental Engineering, Transportation Engineering, Construction and Project Management. Ekeeda offers Online Mechanical Engineering Courses for all the Subjects as per the Syllabus Visit us: https://ekeeda.com/streamdetails/stream/civil-engineering
Ekeeda Provides Online Civil Engineering Degree Subjects Courses, Video Lectures for All Engineering Universities. Video Tutorials Covers Subjects of Mechanical Engineering Degree.
Learn Online Courses of Subject Engineering Mechanics of First Year Engineering. Clear the Concepts of Engineering Mechanics Through Video Lectures and PDF Notes. https://ekeeda.com/streamdetails/subject/Engineering-Mechanics
This presentation gives the information about introduction to control systems
Subject: Control Engineering as per VTU Syllabus of Aeronautical Engineering.
Notes Compiled By: Hareesha N Gowda, Assistant Professor, DSCE, Bengaluru-78.
Disclaimer:
The contents used in this presentation are taken from the text books mentioned in the references. I do not hold any copyrights for the contents. It has been prepared to use in the class lectures, not for commercial purpose.
This template was created for DSCE, Aeronautical students. You have to replace the institution details.
Create a separate document for each chapter, so that under numbering, you can change the sequence of chapter main heading according to chapter wise. i.e., 2.1, 2.2 etc.
Same procedure is applicable to Figure caption and Table caption.
This template can be used to generate, BE seminar report, M.Tech and Ph.D thesis also.
This template is created to assist UG students in generating their thesis without much hassle.
Contents are taken from VTU website. I don’t hold any copyright for this document.
Hareesha N G
Assistant Professor
DSCE, Bengaluru
This document is an Instruction manual for Computer aided machine drawing
Subject: Computer aided machine drawing (CAMD)
Syllabus contest is as per VTU, Belagavi, India.
Notes Compiled By: Hareesha N Gowda, Assistant Professor, DSCE, Bengaluru-78.
This document gives the class notes of Unit-8: Torsion of circular shafts and elastic stability of columns. Subject: Mechanics of materials.
Syllabus contest is as per VTU, Belagavi, India.
Notes Compiled By: Hareesha N Gowda, Assistant Professor, DSCE, Bengaluru-78.
This document gives the class notes of Unit-8: Torsion of circular shafts and elastic stability of columns. Subject: Mechanics of materials.
Syllabus contest is as per VTU, Belagavi, India.
Notes Compiled By: Hareesha N Gowda, Assistant Professor, DSCE, Bengaluru-78.
This document gives the class notes of Unit 6: Bending and shear Stresses in beams. Subject: Mechanics of materials.
Syllabus contest is as per VTU, Belagavi, India.
Notes Compiled By: Hareesha N Gowda, Assistant Professor, DSCE, Bengaluru-78.
This document gives the class notes of Unit 5 shear force and bending moment in beams. Subject: Mechanics of materials.
Syllabus contest is as per VTU, Belagavi, India.
Notes Compiled By: Hareesha N Gowda, Assistant Professor, DSCE, Bengaluru-78.
This document gives the class notes of Unit 3 Compound stresses. Subject: Mechanics of materials.
Syllabus contest is as per VTU, Belagavi, India.
Notes Compiled By: Hareesha N Gowda, Assistant Professor, DSCE, Bengaluru-78.
This document gives the class notes of Unit 2 stresses in composite sections. Subject: Mechanics of materials.
Syllabus contest is as per VTU, Belagavi, India.
Notes Compiled By: Hareesha N Gowda, Assistant Professor, DSCE, Bengaluru-78.
This document contains: Mechanics of Materials: Question bank from old VTU Question papers ; Pprepared by Hareesha N G, DSCE, Bengaluru. These questions are picked from last 06 years of old VTU question papers.
This presentation was prepared for a seminar. I have shared this with you. This is not related to curriculam. Please writre your criticisms to: hareeshang@gmail.com.
This presentation gives the information about Screw thread measurements and Gear measurement of the subject: Mechanical measurement and Metrology (10ME32/42) of VTU Syllabus covering unit-4.
This presentation gives the information about Force, Pressure and Torque measurements of the subject: Mechanical measurement and Metrology (10ME32/42) of VTU Syllabus covering unit-6.
This presentation gives the information about mechanical measurements and measurement systems of the subject: Mechanical measurement and Metrology (10ME32/42) of VTU Syllabus covering unit-5.
This CIM and automation laboratory manual covers the G-Codes and M-codes for CNC Turning and Milling operations. Some concepts of Robot programming are also introduced.
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Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
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This will be used as part of your Personal Professional Portfolio once graded.
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Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
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2. Unit 1: Static Force Analysis
• Static force analysis
– Introduction
– Static equilibrium
– Equilibrium of two and three force members
– Members with two forces and torque
– Free body diagrams
– principle of virtual work
• Static force analysis of
– four bar mechanism
– slider-crank mechanism with and without friction.
6/19/2015 Hareesha N G, Dept of Aero Engg, DSCE, Blore 2
3. STATIC EQUILIBRIUM
• A body is in static equilibrium if it remains in its state of rest or
motion.
• If the body is at rest, it tends to remain at rest and if in motion, it
tends to keep the motion.
• In static equilibrium,
– the vector sum of all the forces acting on the body is zero and
– the vector sum of all the moments about any arbitrary point is zero.
• Mathematically,
• In a planer system, forces can be described by two-dimensional
vectors and therefore,
6/19/2015 Hareesha N G, Dept of Aero Engg, DSCE, Blore 3
4. EQUILIBRIUM OF TWO AND THREE-FORCE MEMBERS
• A member under the action of two forces will be in
equilibrium if
– the forces are of the same magnitude,
– the forces act along the same line, and
– the forces are in opposite directions.
• Figure shows such a member.
• A member under the action of three forces will be in
equilibrium if
– the resultant of the forces is zero, and
– the lines of action of the forces intersect at a point (known as
point of concurrency).
6/19/2015 Hareesha N G, Dept of Aero Engg, DSCE, Blore 4
5. EQUILIBRIUM OF TWO AND THREE-FORCE MEMBERS (Contd….)
• Figure (a) shows a member acted upon by three forces F1, F2 and F3
and is in equilibrium as the lines of action of forces intersect at one
point O and the resultant is zero.
• This is verified by adding the forces vectorially [Fig.(b)].
• As the head of the last vector F3 meets the tail of the first vector F1,
the resultant is zero.
• Figure (d) shows a case where the magnitudes and directions of the
forces are the same as before, but the lines of action of the forces do
not intersect at one point.
• Thus, the member is not in equilibrium.
6/19/2015 Hareesha N G, Dept of Aero Engg, DSCE, Blore 5
6. • Consider a member in equilibrium in which force F1 is completely
known, F2 known in direction only and F3 completely unknown.
• The point of applications of F1 , F2 and F3 are A, B and C respectively.
• To solve such a problem, first find the point of concurrency O from the
two forces with known directions, i.e. from F1, and F2.
• Joining O with C gives the line of action of the third force F3.
• To know the magnitudes of the forces F2 and F3, take a vector of proper
magnitude and direction to represent the force F1.
• From its two ends, draw lines parallel to lines of action of the forces F2
and F3 forming a force triangle [Fig.].
• Mark arrowheads on F2 and F3 so that F1 , F2 and F3 are in the same
order.
6/19/2015 Hareesha N G, Dept of Aero Engg, DSCE, Blore 6
7. MEMBER WITH TWO FORCES AND A TORQUE
• A member under the action of two forces and an applied torque will
be in equilibrium if
– the forces are equal in magnitude, parallel in direction and opposite in sense
and
– the forces form a couple which is equal and opposite to the applied torque.
• Figure shows a member acted upon by two equal forces F1, and F2
and an applied torque T for equilibrium,
where T, F1 and F2 are the magnitudes of T, F1 and F2 respectively.
• T is clockwise whereas the couple formed by F1, and F2 is counter-
clockwise.
6/19/2015 Hareesha N G, Dept of Aero Engg, DSCE, Blore 7
8. FORCE CONVENTION
• The force exerted by member i on member j is represented
by Fij
6/19/2015 Hareesha N G, Dept of Aero Engg, DSCE, Blore 8
9. FREE BODY DIAGRAMS
• A free body diagram is a sketch or diagram of a part isolated from the
mechanism in order to determine the nature of forces acting on it.
• Figure (a) shows a four-link mechanism.
• The free-body diagrams of its members 2, 3 and 4 are shown in Figs.
(b), (c) and (d) respectively.
• Various forces acting on each member are also shown.
• As the mechanism is in static equilibrium, each of its members must
be in equilibrium individually.
6/19/2015 Hareesha N G, Dept of Aero Engg, DSCE, Blore 9
10. • Member 4 is acted upon by three forces F, F34 and F14.
• Member 3 is acted upon by two forces F23 and F43
• Member 2 is acted upon by two forces F32 and F12 and a torque T.
• Initially, the direction and the sense of some of the forces may not be
known.
• Link 3 is a two-force member and for its equilibrium F23 and F43 must
act along BC.
• Thus, F34 being equal and opposite to F43 also acts along BC.
6/19/2015 Hareesha N G, Dept of Aero Engg, DSCE, Blore 10
11. • Assume that the force F on member 4 is known completely.
• To know the other two forces acting on this member completely, the
direction of one more force must be known.
• For member 4 to be in equilibrium, F14 passes through the intersection
of F and F34 .
• By drawing a force triangle (F is completely known), magnitudes of
F14 and F34 can be known [Fig.(e)].
Now F34 = F43 = F23 = F32
• Member 2 will be in equilibrium if F12 is equal, parallel and opposite
to F32 and
6/19/2015 Hareesha N G, Dept of Aero Engg, DSCE, Blore 11
12. A four-link mechanism with the following dimensions is acted upon by
a force 80N at angle 1500 on link DC [Fig.(a)): AD = 50 mm, AB = 40 mm,
BC = 100 mm, DC = 75 mm, DE = 35 mm. Determine the input torque T
on the link AB for the static equilibrium of the mechanism for the given
configuration.
6/19/2015 Hareesha N G, Dept of Aero Engg, DSCE, Blore 12
As the mechanism is in static equilibrium, each of its
members must also be in equilibrium individually.
Member 4 is acted upon by three forces F F34 and F14.
Member 3 is acted upon by two forces F23 and F43
Member 2 is acted upon by two forces F32 and F12 and
a torque T.
Initially, the direction and the sense of some of the
forces are not known.
Force F on member 4 is known completely. To know the other two forces acting
on this member completely, the direction of one more force must be known. To
know that, link 3 will have to be considered first which is a two-force member.
13. • As link 3 is a two-force member [Fig.(b)], for its equilibrium, F23 and
F43 must act along BC (at this stage, the sense of direction of forces F23
and F43 is not known). Thus, the line of action of F34 is also along BC.
• As force F34 acts through point C on link 4, draw a line parallel to BC
through C by taking a free body of link 4 to represent the same. Now,
as link 4 is three force member, the third force F14 passes through the
intersection of F and F34 [Fig (c)].
• By drawing a force triangle (F is completely known), magnitudes of
F14 and F34 are known [Fig(d)].
6/19/2015 Hareesha N G, Dept of Aero Engg, DSCE, Blore 13
From force triangle, F34 = 47.8 N
14. • Now, F34 = -F43 =F23 = -F32
• Member 2 will be in equilibrium [Fig. (e)] if F12 is equal, parallel and
opposite to F32 and
T=-F32 x h = 47.8 x 39.3 = -1878.54 N.mm The input torque has to be
equal and opposite to this couple i.e. T= 1878.5 N/mm (clockwise)
h=Perpendicular distance between two equal and opposite forces.
6/19/2015 Hareesha N G, Dept of Aero Engg, DSCE, Blore 14
15. Figure shows a slider crank mechanism in which the resultant gas pressure 8x104 N/m2
acts on the piston of cross sectional area 0.1m2 The system is kept in equilibrium as a
result of the couple applied to the crank 2, through the shaft at O2. Determine forces
acting on all the links (including the pins) and the couple on 2. OA=100mm, AB=450mm.
6/19/2015
Hareesha N G, Dept of Aero Engg, DSCE,
Blore
15
16. 6/19/2015
Hareesha N G, Dept of Aero Engg, DSCE,
Blore
16
Force triangle for the forces acting on(4)is drawn to some suitable scale.
Magnitude and direction of P known and lines of action of F34 & F14
known.
Measure the lengths of vectors and multiply by the scale factor to get the magnitudes
of F14 & F34.
Directions are also fixed.
Since link 3 is acted upon by only two forces, F43 and F23
are collinear, equal in magnitude and opposite in direction
i.e., F43 = -F23 =8.8xl03 N
Also, F23 = - F32 (equal in magnitude and opposite in
direction).
17. 6/19/2015
Hareesha N G, Dept of Aero Engg, DSCE,
Blore
17
Link 2 is acted upon by 2 forces and a torque, for equilibrium
the two forces must be equal, parallel and opposite and their
sense must be opposite to T2.
There fore,
F32 = -F12 =8.8xl03 N
F32 & F12 form a counter clock wise couple of magnitude,
F23 * h = F12 *h
=(8.8xl03)x0.125 = 1100 Nm.
To keep 2 in equilibrium, T: should act clockwise and
magnitude is 1100 Nm.
Note: h is measured perpendicular to F32 &F12
18. 6/19/2015 Hareesha N G, Dept of Aero Engg, DSCE, Blore 18
For the static equilibrium of the quick return mechanism shown in Fig (a), determine the input
torque T2: to be applied on link AB Tor a force of 300N on the slider D. The dimensions of the
various links arc OA=400mm, AB=200mm, OC=800mm. CD=300mm
20. • For the mechanism shown in Fig., determine the torque on the link
AB for the static equilibrium of the mechanism.
6/19/2015 Hareesha N G, Dept of Aero Engg, DSCE, Blore 20
21. • Answers from Composite Graphical Solution
6/19/2015 Hareesha N G, Dept of Aero Engg, DSCE, Blore 21
22. Graphical Solution by Superposition method
6/19/2015 Hareesha N G, Dept of Aero Engg, DSCE, Blore 22
23. Graphical Solution by Superposition method
6/19/2015 Hareesha N G, Dept of Aero Engg, DSCE, Blore 23
24. In a four-link mechanism shown in Fig., torque T3 and T4 have
magnitudes of 30N.m and2 ON. m respectively. The link lengths are AD
= 800 mm, AB = 300 mm, BC = 700 mm and CD = 400 mm. For the static
equilibrium of the mechanism, determine the required input torque T2
6/19/2015 Hareesha N G, Dept of Aero Engg, DSCE, Blore 24
25. In a four-link mechanism shown in Fig., torque T3 and T4 have
magnitudes of 30N.m and2 ON. m respectively. The link lengths are AD
= 800 mm, AB = 300 mm, BC = 700 mm and CD = 400 mm. For the static
equilibrium of the mechanism, determine the required input torque T2
6/19/2015 Hareesha N G, Dept of Aero Engg, DSCE, Blore 25
28. PRINCIPLE OF VIRTUAL WORK
• The principle of virtual (imaginary) work can be stated
as the work done during a virtual displacement from the
equilibrium is equal to zero.
• Virtual displacement may be defined as an imaginary
infinitesimal displacement of the system.
• By applying this principle, an entire mechanism is
examined as a whole and there is no need of dividing it
into free bodies.
6/19/2015 Hareesha N G, Dept of Aero Engg, DSCE, Blore 28
29. • Consider a slider-crank mechanism shown in Fig.
• It is acted upon by the external piston force F, the external
crankshaft torque T and the force at the bearings.
• As the crank rotates through a small angular displacement
δθ, the corresponding displacement of the piston is δx, the
various forces acting on the system are
– Bearing reaction at O (performs no work)
– Force of cylinder on piston, perpendicular to piston
displacement (produces no work)
– Bearing forces at A and B, being equal and opposite (AB is a
two-force member), no work is done
– Work done by torque T= T δθ
– Work done by force F = F δx
• Work done is positive if a force acts in the direction of the
displacement and negative if it acts in the opposite
direction.
6/19/2015 Hareesha N G, Dept of Aero Engg, DSCE, Blore 29
30. The negative sign indicates that for equilibrium, T must be applied in
the opposite direction to the angular displacement.
6/19/2015 Hareesha N G, Dept of Aero Engg, DSCE, Blore 30