This document provides instructions for drawing velocity and acceleration diagrams for a slider-crank mechanism. It includes the following key steps:
1. Calculate angular velocity and linear velocities of points using given dimensions and rotational speed.
2. Draw velocity vectors in the velocity diagram showing velocities of all points relative to fixed references and each other.
3. Derive accelerations of points from the velocity diagram and mechanism dimensions.
4. Draw acceleration vectors in the acceleration diagram showing centripetal, tangential, and coriolis accelerations of all points.
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.
1. The document describes the working of a quick return mechanism, which is used to convert rotary motion to reciprocating motion at different speeds for the forward and backward strokes.
2. It specifically discusses the quick return mechanism used in shaping machines, which uses a sliding block on a slotted bar connected to a ram to rapidly return the cutting tool to its starting position.
3. Applications where a quick return mechanism provides benefits include presses and machines like shaping machines, where reducing the non-cutting return time can improve efficiency.
- Gyroscopes work based on the principle of angular momentum to maintain orientation. A gyroscope is a spinning wheel or disk whose axis remains fixed in space despite external forces.
- Gyroscopic couples occur due to the vector representation of angular motion and cause precessional motion.
- On airplanes and ships, gyroscopic couples from rotating propellers and rotors help provide stability when turning or pitching and rolling in rough seas.
- On vehicles like motorcycles, the gyroscopic couples from the wheels and engine, along with centrifugal forces, help provide stability and prevent the vehicle from falling over when turning.
Relative velocity method, velocity & acceleration analysis of mechanismKESHAV
The document discusses graphical methods for analyzing the velocity and acceleration of mechanisms using relative velocity analysis. It introduces concepts like relative velocity, angular velocity of links, and rubbing velocity at pin joints. Examples are presented to demonstrate how to draw velocity diagrams for different mechanisms. Key steps include drawing the configuration diagram, determining input velocity, marking fixed points, drawing perpendicular lines between links, and measuring velocities using the scale. Numerical examples cover four-bar chains, slider-crank mechanisms, and toggle mechanisms. [/SUMMARY]
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.
Three types of gear trains are described:
1. Simple gear trains involve one gear on each shaft to transmit power.
2. Compound gear trains have more than one gear on a shaft, allowing for larger speed reductions.
3. Epicyclic gear trains have gears mounted on shafts that can move relative to a fixed axis, enabling high velocity ratios with moderate sized gears. Epicyclic trains are used in automotive differentials and machinery.
The document discusses dynamic force analysis of mechanisms. It begins by introducing the concept of dynamic forces that arise due to accelerating masses in machines. It then describes D'Alembert's principle, which states that inertia forces and external forces together produce static equilibrium. The document provides examples of applying dynamic analysis to mechanisms like four-bar linkages and slider-crank mechanisms. It also discusses determining equivalent inertia forces and torques on different components like the piston, connecting rod, and crankshaft. Graphical methods for analyzing inertia forces in reciprocating engines are also presented.
- Today's lecture covers transmission angle, instantaneous center method, and locating instantaneous centers in mechanisms.
- The transmission angle between the output link and coupler is maximum at 90 degrees for maximum torque transmission.
- The instantaneous center method and relative velocity method can be used for velocity or acceleration analysis of mechanisms.
- The instantaneous center method uses the centers of rotation between two links to determine velocities. The number of instantaneous centers equals the number of possible link combinations.
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.
1. The document describes the working of a quick return mechanism, which is used to convert rotary motion to reciprocating motion at different speeds for the forward and backward strokes.
2. It specifically discusses the quick return mechanism used in shaping machines, which uses a sliding block on a slotted bar connected to a ram to rapidly return the cutting tool to its starting position.
3. Applications where a quick return mechanism provides benefits include presses and machines like shaping machines, where reducing the non-cutting return time can improve efficiency.
- Gyroscopes work based on the principle of angular momentum to maintain orientation. A gyroscope is a spinning wheel or disk whose axis remains fixed in space despite external forces.
- Gyroscopic couples occur due to the vector representation of angular motion and cause precessional motion.
- On airplanes and ships, gyroscopic couples from rotating propellers and rotors help provide stability when turning or pitching and rolling in rough seas.
- On vehicles like motorcycles, the gyroscopic couples from the wheels and engine, along with centrifugal forces, help provide stability and prevent the vehicle from falling over when turning.
Relative velocity method, velocity & acceleration analysis of mechanismKESHAV
The document discusses graphical methods for analyzing the velocity and acceleration of mechanisms using relative velocity analysis. It introduces concepts like relative velocity, angular velocity of links, and rubbing velocity at pin joints. Examples are presented to demonstrate how to draw velocity diagrams for different mechanisms. Key steps include drawing the configuration diagram, determining input velocity, marking fixed points, drawing perpendicular lines between links, and measuring velocities using the scale. Numerical examples cover four-bar chains, slider-crank mechanisms, and toggle mechanisms. [/SUMMARY]
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.
Three types of gear trains are described:
1. Simple gear trains involve one gear on each shaft to transmit power.
2. Compound gear trains have more than one gear on a shaft, allowing for larger speed reductions.
3. Epicyclic gear trains have gears mounted on shafts that can move relative to a fixed axis, enabling high velocity ratios with moderate sized gears. Epicyclic trains are used in automotive differentials and machinery.
The document discusses dynamic force analysis of mechanisms. It begins by introducing the concept of dynamic forces that arise due to accelerating masses in machines. It then describes D'Alembert's principle, which states that inertia forces and external forces together produce static equilibrium. The document provides examples of applying dynamic analysis to mechanisms like four-bar linkages and slider-crank mechanisms. It also discusses determining equivalent inertia forces and torques on different components like the piston, connecting rod, and crankshaft. Graphical methods for analyzing inertia forces in reciprocating engines are also presented.
- Today's lecture covers transmission angle, instantaneous center method, and locating instantaneous centers in mechanisms.
- The transmission angle between the output link and coupler is maximum at 90 degrees for maximum torque transmission.
- The instantaneous center method and relative velocity method can be used for velocity or acceleration analysis of mechanisms.
- The instantaneous center method uses the centers of rotation between two links to determine velocities. The number of instantaneous centers equals the number of possible link combinations.
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.
Dynamics of Machines - Unit V-GovernorsDr.S.SURESH
This document discusses different types of governors used to regulate the speed of engines. It describes centrifugal and inertia governors and provides examples of their applications. Centrifugal governors discussed in detail include the Watt, Porter, Proell, and Hartnell governors. Key terms related to governors like equilibrium speed and sleeve lift are defined. The characteristics of governors such as sensitiveness, stability, and isochronism are also explained. Controlling force diagrams are described as a way to examine the stability and sensitiveness of different governor designs.
Relative Velocity Method for Velocity and Acceleration analysis Rohit Singla
This document discusses methods for analyzing velocity and acceleration in mechanisms. It covers the relative velocity method for analyzing velocity using pole vectors. It also discusses constructing velocity and acceleration diagrams for slider crank mechanisms. The key steps for determining acceleration of a point on a link using an acceleration image are outlined. Components of radial and tangential acceleration are defined. Construction of acceleration diagrams and determining angular acceleration of links is also summarized.
This document discusses balancing of machines. It defines static and dynamic balancing and the conditions that must be met for each. Static balancing requires the combined mass center to lie on the axis of rotation, while dynamic balancing requires no resultant centrifugal force or couple. The document also discusses balancing of rotating masses, reciprocating masses, linkages, and multi-cylinder engines. Finally, it briefly introduces different types of balancing machines used to measure static and dynamic unbalance.
1) To analyze accelerations, positions must first be found to calculate velocities by differentiation and accelerations by further differentiation.
2) Acceleration has two components - tangential and centripetal. For uniform motion only centripetal acceleration exists, and for straight-line motion only tangential acceleration exists.
3) The Coriolis component arises for points moving on rotating links and is perpendicular to the link and proportional to the product of linear and angular velocities.
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.
Module 1 introduction to kinematics of machinerytaruian
This document provides information about the Kinematics of Machines course offered by the Department of Mechanical Engineering at JSS Academy of Technical Education in Bangalore, India. It lists the course code, textbooks, reference books, course outcomes, and chapter topics that will be covered. The topics include basic definitions related to kinematic elements, pairs, chains, and mechanisms. It describes types of kinematic pairs and chains, including four-bar chains, single slider-crank chains, and double slider-crank chains. It also covers degrees of freedom, Grubler's criterion, and inversions of mechanisms.
1. The document discusses acceleration analysis in mechanisms. It defines radial and tangential components of acceleration and how to draw acceleration diagrams for links and mechanisms.
2. An example is provided to calculate linear velocity, acceleration, angular velocity and acceleration for a slider crank mechanism with given parameters. Acceleration diagrams are drawn to determine the desired values.
3. Additional diagrams are included for supplementary information but are not analyzed as part of the chapter content.
The document discusses balancing of rotating masses. It defines balancing as restoring a rotor with unbalance to a balanced state by adjusting mass distribution about its axis of rotation. It describes four cases of balancing: a single mass with a single mass in the same plane; a single mass with two masses in different planes; different masses in the same plane; and different masses in different planes. It provides details on balancing a single mass with one or two masses in other planes, including the conditions that must be satisfied. Finally, it mentions analytical and graphical methods can be used to determine the balancing mass magnitude and position.
The aim of this project to design, simulate and analyze the deformations of a slider crank mechanism’s bodies as a rigid body system and with a flexible connecting rod
The document discusses instantaneous centers in mechanisms. It defines an instantaneous center as a point where one member rotates permanently or instantaneously around another, or where the velocities of two members are equal in both direction and magnitude. There are three types of instantaneous centers: fixed, permanent, and neither fixed nor permanent (secondary). Properties are that at the center, two links have no relative velocity and the same linear velocity relative to a third link. Instantaneous centers can be located by determining the number, identifying fixed and permanent centers, and using Kennedy's theorem to find secondary centers which lie on a straight line. An example four-bar mechanism shows the different types of centers.
1. The document discusses gyroscopic couple, which acts on a spinning object that is rotating about another axis.
2. It provides examples of gyroscopic couple in naval ships, where the spinning of propeller shafts affects steering, pitching, and rolling.
3. The document also examines the gyroscopic couple and centrifugal couple in vehicles like cars and motorcycles taking turns, and how this affects their stability.
Kinematic synthesis deals with determining link lengths and orientations of mechanisms to satisfy motion requirements. This document discusses several key concepts in kinematic synthesis of planar mechanisms, including:
1) Movability/mobility synthesis which determines the degrees of freedom using Gruebler's criterion. The simplest mechanism is the four-bar linkage.
2) Transmission angle synthesis which aims to position links for maximum torque transmission, usually near 90°.
3) Limit positions and dead centers which are configurations of four-bar mechanisms where links are collinear.
4) Graphical synthesis methods using the pole and relative pole to determine link lengths and positions based on input/output motion specifications.
This document provides an introduction to kinematics and the analysis of mechanisms using velocity and acceleration diagrams. It discusses:
1. Key concepts in mechanisms including different types of motion transformations and common mechanism components like four-bar linkages.
2. How to determine the displacement, velocity, and acceleration of points within a mechanism using either mathematical equations or graphical methods using velocity and acceleration diagrams.
3. How to construct velocity diagrams by determining the absolute and relative velocities of points and drawing them as vectors. This allows solving for unknown velocities.
4. How to extend the method to acceleration diagrams to determine centripetal and other accelerations which are important for calculating inertia forces.
The document provides examples
This presentation discusses epicyclic gear trains and their applications. It begins by defining an epicyclic gear train as one where the axes of gears can move relative to a fixed axis. Examples of applications include differentials in automobiles and lathes. It then discusses methods to calculate velocity ratios in epicyclic gear trains using tabular and algebraic methods. Compound epicyclic gear trains using sun and planet gears are described. Epicyclic gear trains using bevel gears are also discussed, along with examples of their use in speed reduction gears and differentials. Finally, the presentation covers torques in epicyclic gear trains and how input, output, and holding torques are related.
1. Gyroscopes are devices used to control the orientation and angular velocity of rotating bodies. They use the principle of gyroscopic precession to maintain their orientation.
2. Common applications of gyroscopes include their use in inertial navigation systems, gyrocompasses, and to provide stability in vehicles like ships, airplanes, bicycles, and motorcycles.
3. The reactive gyroscopic couple experienced by rotating objects like the engines of airplanes and ships helps provide stability when turning. For example, when an airplane turns left, the reactive couple presses down on the right wing and lifts the left wing, counteracting the turning moment.
This document provides an introduction to gears and gear trains. It defines common terms used in gears such as pitch circle, pitch diameter, pressure angle, addendum, and dedendum. It also classifies gears based on the position of shaft axes (parallel shaft gears include spur gears, helical gears, herringbone gears, bevel gears; intersecting shaft gears include straight bevel gears and spiral bevel gears). The document discusses advantages of gear drives such as transmitting exact velocity ratios and disadvantages such as requiring specialized manufacturing. It provides examples of different types of gears and their applications.
This presentation provides an overview of worm gears, including their two types (cylindrical and cone), three types of worm gears, common materials used, key terms, how they work to reduce speed and increase torque via a high velocity ratio, common applications, advantages of being self-locking and occupying less space, disadvantages of higher costs and lower efficiency, and areas for further research such as improved lubrication. Worm gears are widely used gear systems for transmitting power between non-intersecting shafts, especially at high velocity ratios.
The document discusses different types of belting used to transmit power between rotating shafts in factories, including flat belts and V-belts. It provides objectives and formulas for calculating the length of open and closed belt drives, as well as the power transmitted by a belt based on the tension in the tight and slack sides and the belt velocity. Worked examples are included to demonstrate calculating belt length and transmitted power.
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.
Dynamics of Machines - Unit V-GovernorsDr.S.SURESH
This document discusses different types of governors used to regulate the speed of engines. It describes centrifugal and inertia governors and provides examples of their applications. Centrifugal governors discussed in detail include the Watt, Porter, Proell, and Hartnell governors. Key terms related to governors like equilibrium speed and sleeve lift are defined. The characteristics of governors such as sensitiveness, stability, and isochronism are also explained. Controlling force diagrams are described as a way to examine the stability and sensitiveness of different governor designs.
Relative Velocity Method for Velocity and Acceleration analysis Rohit Singla
This document discusses methods for analyzing velocity and acceleration in mechanisms. It covers the relative velocity method for analyzing velocity using pole vectors. It also discusses constructing velocity and acceleration diagrams for slider crank mechanisms. The key steps for determining acceleration of a point on a link using an acceleration image are outlined. Components of radial and tangential acceleration are defined. Construction of acceleration diagrams and determining angular acceleration of links is also summarized.
This document discusses balancing of machines. It defines static and dynamic balancing and the conditions that must be met for each. Static balancing requires the combined mass center to lie on the axis of rotation, while dynamic balancing requires no resultant centrifugal force or couple. The document also discusses balancing of rotating masses, reciprocating masses, linkages, and multi-cylinder engines. Finally, it briefly introduces different types of balancing machines used to measure static and dynamic unbalance.
1) To analyze accelerations, positions must first be found to calculate velocities by differentiation and accelerations by further differentiation.
2) Acceleration has two components - tangential and centripetal. For uniform motion only centripetal acceleration exists, and for straight-line motion only tangential acceleration exists.
3) The Coriolis component arises for points moving on rotating links and is perpendicular to the link and proportional to the product of linear and angular velocities.
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.
Module 1 introduction to kinematics of machinerytaruian
This document provides information about the Kinematics of Machines course offered by the Department of Mechanical Engineering at JSS Academy of Technical Education in Bangalore, India. It lists the course code, textbooks, reference books, course outcomes, and chapter topics that will be covered. The topics include basic definitions related to kinematic elements, pairs, chains, and mechanisms. It describes types of kinematic pairs and chains, including four-bar chains, single slider-crank chains, and double slider-crank chains. It also covers degrees of freedom, Grubler's criterion, and inversions of mechanisms.
1. The document discusses acceleration analysis in mechanisms. It defines radial and tangential components of acceleration and how to draw acceleration diagrams for links and mechanisms.
2. An example is provided to calculate linear velocity, acceleration, angular velocity and acceleration for a slider crank mechanism with given parameters. Acceleration diagrams are drawn to determine the desired values.
3. Additional diagrams are included for supplementary information but are not analyzed as part of the chapter content.
The document discusses balancing of rotating masses. It defines balancing as restoring a rotor with unbalance to a balanced state by adjusting mass distribution about its axis of rotation. It describes four cases of balancing: a single mass with a single mass in the same plane; a single mass with two masses in different planes; different masses in the same plane; and different masses in different planes. It provides details on balancing a single mass with one or two masses in other planes, including the conditions that must be satisfied. Finally, it mentions analytical and graphical methods can be used to determine the balancing mass magnitude and position.
The aim of this project to design, simulate and analyze the deformations of a slider crank mechanism’s bodies as a rigid body system and with a flexible connecting rod
The document discusses instantaneous centers in mechanisms. It defines an instantaneous center as a point where one member rotates permanently or instantaneously around another, or where the velocities of two members are equal in both direction and magnitude. There are three types of instantaneous centers: fixed, permanent, and neither fixed nor permanent (secondary). Properties are that at the center, two links have no relative velocity and the same linear velocity relative to a third link. Instantaneous centers can be located by determining the number, identifying fixed and permanent centers, and using Kennedy's theorem to find secondary centers which lie on a straight line. An example four-bar mechanism shows the different types of centers.
1. The document discusses gyroscopic couple, which acts on a spinning object that is rotating about another axis.
2. It provides examples of gyroscopic couple in naval ships, where the spinning of propeller shafts affects steering, pitching, and rolling.
3. The document also examines the gyroscopic couple and centrifugal couple in vehicles like cars and motorcycles taking turns, and how this affects their stability.
Kinematic synthesis deals with determining link lengths and orientations of mechanisms to satisfy motion requirements. This document discusses several key concepts in kinematic synthesis of planar mechanisms, including:
1) Movability/mobility synthesis which determines the degrees of freedom using Gruebler's criterion. The simplest mechanism is the four-bar linkage.
2) Transmission angle synthesis which aims to position links for maximum torque transmission, usually near 90°.
3) Limit positions and dead centers which are configurations of four-bar mechanisms where links are collinear.
4) Graphical synthesis methods using the pole and relative pole to determine link lengths and positions based on input/output motion specifications.
This document provides an introduction to kinematics and the analysis of mechanisms using velocity and acceleration diagrams. It discusses:
1. Key concepts in mechanisms including different types of motion transformations and common mechanism components like four-bar linkages.
2. How to determine the displacement, velocity, and acceleration of points within a mechanism using either mathematical equations or graphical methods using velocity and acceleration diagrams.
3. How to construct velocity diagrams by determining the absolute and relative velocities of points and drawing them as vectors. This allows solving for unknown velocities.
4. How to extend the method to acceleration diagrams to determine centripetal and other accelerations which are important for calculating inertia forces.
The document provides examples
This presentation discusses epicyclic gear trains and their applications. It begins by defining an epicyclic gear train as one where the axes of gears can move relative to a fixed axis. Examples of applications include differentials in automobiles and lathes. It then discusses methods to calculate velocity ratios in epicyclic gear trains using tabular and algebraic methods. Compound epicyclic gear trains using sun and planet gears are described. Epicyclic gear trains using bevel gears are also discussed, along with examples of their use in speed reduction gears and differentials. Finally, the presentation covers torques in epicyclic gear trains and how input, output, and holding torques are related.
1. Gyroscopes are devices used to control the orientation and angular velocity of rotating bodies. They use the principle of gyroscopic precession to maintain their orientation.
2. Common applications of gyroscopes include their use in inertial navigation systems, gyrocompasses, and to provide stability in vehicles like ships, airplanes, bicycles, and motorcycles.
3. The reactive gyroscopic couple experienced by rotating objects like the engines of airplanes and ships helps provide stability when turning. For example, when an airplane turns left, the reactive couple presses down on the right wing and lifts the left wing, counteracting the turning moment.
This document provides an introduction to gears and gear trains. It defines common terms used in gears such as pitch circle, pitch diameter, pressure angle, addendum, and dedendum. It also classifies gears based on the position of shaft axes (parallel shaft gears include spur gears, helical gears, herringbone gears, bevel gears; intersecting shaft gears include straight bevel gears and spiral bevel gears). The document discusses advantages of gear drives such as transmitting exact velocity ratios and disadvantages such as requiring specialized manufacturing. It provides examples of different types of gears and their applications.
This presentation provides an overview of worm gears, including their two types (cylindrical and cone), three types of worm gears, common materials used, key terms, how they work to reduce speed and increase torque via a high velocity ratio, common applications, advantages of being self-locking and occupying less space, disadvantages of higher costs and lower efficiency, and areas for further research such as improved lubrication. Worm gears are widely used gear systems for transmitting power between non-intersecting shafts, especially at high velocity ratios.
The document discusses different types of belting used to transmit power between rotating shafts in factories, including flat belts and V-belts. It provides objectives and formulas for calculating the length of open and closed belt drives, as well as the power transmitted by a belt based on the tension in the tight and slack sides and the belt velocity. Worked examples are included to demonstrate calculating belt length and transmitted power.
Design of transmission systems question bank - GGGopinath Guru
This document contains questions related to the design of various transmission systems including belt drives, chain drives, gear drives, and rope drives. It provides a question bank with multiple choice and numerical questions on the design, selection and analysis of different types of flexible elements and rigid transmissions used to transmit power between rotating shafts. The questions cover topics such as the selection of V-belts and pulleys, flat belts and pulleys, wire ropes and pulleys, transmission chains and sprockets, as well as the design of gears, including spur gears, helical gears, and gear drives.
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.
This document provides definitions and concepts related to machine elements design. It covers topics such as factor of safety, endurance limit, impact loads, design process phases, types of loads/stresses, factors affecting endurance strength, types of fractures, spring types and properties, joints, keys, couplings, screws, welds and failures. It contains questions and answers on these topics across 4 units - stresses and strains, shafts, fasteners and joints, and springs.
1. The document discusses methods for analyzing the velocity of mechanisms using graphical methods. It provides examples of determining velocities in four-bar and slider crank mechanisms using velocity vector diagrams.
2. Steps include drawing the configuration, choosing scales, locating fixed and rotating links, determining individual link velocities, and using ratios and angular velocities to find velocities of offset points.
3. Velocities include links, sliding surfaces, and rubbing velocities at joints. Solutions are shown for examples involving determining multiple velocities in different mechanisms.
1. The document discusses kinematic pairs which are the contacts between links in a mechanism that constrain their relative motion. It describes the types of kinematic pairs such as lower pairs which have surface contact, and higher pairs which have point or line contact.
2. Key types of kinematic pairs are described based on their relative motion, including revolute pairs which allow rotation, prismatic pairs which allow linear translation, cylindrical pairs which allow both rotation and translation, and spherical pairs which allow three degrees of freedom.
3. The document also compares the differences between mechanisms, machines, and structures. Mechanisms modify and transmit motion between moving parts, machines transform energy and do work, and structures transmit forces without internal motion between
This document discusses kinematic analysis and various methods for velocity analysis of mechanisms. It covers graphical methods, the relative velocity method, instantaneous center method, and the vector loop method. The instantaneous center method is described in detail, including locating instantaneous centers, Kennedy's theorem on three centers in a line, and examples of applying this method to determine velocities and angular velocities in different mechanisms.
The document provides details about the syllabus of a course on Kinematics of Machinery. It is divided into 5 units. Unit I discusses mechanisms, kinematic pairs, degrees of freedom and inversions. Unit II covers velocity and acceleration analysis using graphical and relative velocity methods. Unit III focuses on straight line motion mechanisms. Unit IV discusses cams and cam mechanisms. Unit V is about higher pairs like gears, gear trains, epicyclic gears and their analysis. The document also provides the session planner and question bank for the course.
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise boosts blood flow, releases endorphins, and promotes changes in the brain which help regulate emotions and stress levels.
This document discusses different types of gears used in mechanical systems to transmit rotational motion between parallel or intersecting shafts. It describes spur gears, helical gears, bevel gears, and worm gears. Key terminology for gears like pitch circle, diametral pitch, module, addendum, dedendum, and contact ratio are defined. The fundamental law of gearing relating the rotational speeds of meshing gears is explained. Involute tooth profiles and pressure angles are also covered.
Theory of machines by rs. khurmi_ solution manual _ chapter 11Darawan Wahid
This document provides solutions to problems involving belt drives, including calculations of speed ratios, tensions, power transmission, and efficiency. It solves for:
1) The speeds of driven pulleys using no-slip and slip equations, with sample speeds of 239.4 r.p.m and 232.22 r.p.m.
2) Transmitted power of 3.983 kW for a pulley drive system with given parameters.
3) A belt width of 67.4 mm needed to transmit 7.5 kW between pulleys without exceeding tension limits.
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.
Solutions for machine design by KHURMI and GUPTAAzlan
This document appears to be notes from a machine design textbook created by Eng. Younis Fakher of Thi-Qar University's College of Engineering. It contains solutions to problems from chapters 4-6 of a machine design textbook by Khurmi and Gupta for 4th year mechanical engineering students from the 2010-2011 academic year. The notes are broken down by chapter and contain problem solutions.
Mechanical Engineering : Engineering mechanics, THE GATE ACADEMYklirantga
THE GATE ACADEMY's GATE Correspondence Materials consist of complete GATE syllabus in the form of booklets with theory, solved examples, model tests, formulae and questions in various levels of difficulty in all the topics of the syllabus. The material is designed in such a way that it has proven to be an ideal material in-terms of an accurate and efficient preparation for GATE.
Quick Refresher Guide : is especially developed for the students, for their quick revision of concepts preparing for GATE examination. Also get 1 All India Mock Tests with results including Rank,Percentile,detailed performance analysis and with video solutions
GATE QUESTION BANK : is a topic-wise and subject wise collection of previous year GATE questions ( 2001 – 2013). Also get 1 All India Mock Tests with results including Rank,Percentile,detailed performance analysis and with video solutions
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The document discusses the history and development of chocolate over centuries. It details how cocoa beans were first used by Mesoamerican cultures before being introduced to Europe, where it became popular in drinks and confections. The document also notes that modern chocolate production methods were established in the 19th century to allow chocolate to be consumed on a larger scale.
This document discusses types of mechanisms obtained through inversion of a single kinematic chain. It describes four bar chain mechanisms that have all four turning pairs, single slider crank chains that have three turning pairs and one sliding pair, and double slider mechanisms that have two turning pairs and two sliding pairs. Examples are given for each type of mechanism along with their purposes.
Velo & accel dia by relative velo & accl methodUmesh Ravate
1) The document discusses key concepts in kinematics including displacement, velocity, acceleration, absolute velocity, and relative velocity. It provides equations to calculate linear and angular velocity and acceleration.
2) Graphical and analytical methods for analyzing velocity in mechanisms are described. The graphical method involves constructing configuration and velocity vector diagrams.
3) An example problem is presented and solved step-by-step using the graphical method to determine velocities at various points in a four-bar linkage mechanism.
1. This document describes methods for analyzing the velocity of mechanisms using graphical and relative velocity methods.
2. The graphical method involves constructing configuration and velocity vector diagrams to determine velocities and angular velocities at various points.
3. An example problem is provided to illustrate the graphical method for a four-bar mechanism.
1. This document describes methods for analyzing the velocity of mechanisms using graphical and relative velocity methods.
2. The graphical method involves constructing configuration and velocity vector diagrams to determine velocities and angular velocities at various points.
3. An example problem is provided to illustrate the graphical method for a four-bar mechanism.
The document provides information to solve a mechanics problem involving the velocity and acceleration of links in a toggle mechanism. It includes:
1) Dimensions and rotational speed of the crank.
2) Equations to calculate velocities and accelerations of points A, B, and D using velocity and acceleration diagrams.
3) The solutions for the velocity of slider D (2.05 m/s), angular velocity of BD (4.5 rad/s), acceleration of slider D (13.3 m/s^2), and angular acceleration of BD (71.3 rad/s^2 clockwise).
lec09_part1.pptx PLANAR KINEMATICS OF RIGID BODIESShyamal25
The document discusses planar kinematics of rigid bodies and mechanisms. It introduces concepts such as translation, rotation, angular and linear velocity, and angular and linear acceleration. Examples are provided to demonstrate how to analyze the velocity and acceleration of points on rigid bodies undergoing various motions like rotation, translation, and general plane motion using concepts like velocity diagrams, acceleration diagrams, and instantaneous centers of rotation. Sample problems are worked through applying these concepts to determine velocities and accelerations of parts in mechanisms like slider-crank and four-bar linkages.
This document provides instruction on determining velocities and angular velocities in mechanisms using the relative velocity method. It contains 5 problems:
1) Finding the angular velocity of a link in a 4-bar chain mechanism.
2) Determining velocities in a steam engine mechanism including the piston, connecting rod, and points on the connecting rod.
3) Finding the linear velocity of a slider and angular velocity of a link in a mechanism when the crank is at a specified angle.
4) Drawing a velocity diagram for an engine mechanism and determining the slider and link accelerations.
5) Determining velocities and angular velocities, and then accelerations, in a toggle mechanism where the crank speed is increasing.
The document discusses kinematics of rigid bodies, including definitions of translation, rotation about a fixed axis, and general plane motion. It provides equations relating position, velocity, and acceleration for particles undergoing translation and rotation. Examples are presented of determining velocities and accelerations of points on rigid bodies in translation, rotation, and rolling contact motion. Key concepts covered include absolute and relative velocity diagrams.
Surveying Engineering
Traversing Practical part 1
Plane and Applied surveying 2
Report number(2)
• Report name :Gales Traverse Table(Horizontal angle
measurement (FL)of closed traversing
• Apparatus
• Theodolite Instrument
• Tripod
• Compass
• Pin
• Tape
• Range pole
Object
• To conducted survey work in a closed traversing and calculate
in depend coordinates and area calculation by coordinate rule.
Procedure Traverse;
Calculations Traverse .Dada Sheet and Table method work clock wise surveying
-Gales Traverse Table.
*Traverse Calculations
-Traverse Calculation.
-Coordinate conversions.
-Signs of Departures and Latitudes.
*Balancing latitude and departure
-Correction for ∆E& ∆N:
Bowditch adjustment or compass method
-The example…
-Vector components (pre-adjustment)
*The adjustment components
Prepared by:
Asst. Prof. Salar K.Hussein
Mr. Kamal Y.Abdullah
Asst.Lecturer. Dilveen H. Omar
Erbil Polytechnic University
Technical Engineering College
Civil Engineering Department
A traverse is a series of connected lines whose lengths and directions are to be measured and the process of surveying to find such measurements is known as traversing. In general, chains are used to measure length and compass or theodolite are used to measure the direction of traverse lines.
1) Fore and back bearings are the bearings of a line observed from each end, with the fore bearing indicating the direction of progress and the back bearing being 180° different.
2) To find the back bearing from the fore bearing, add or subtract 180° depending on whether the fore bearing is less than or greater than 180°.
3) Local attraction refers to deviations of the magnetic needle from its normal position due to external magnetic forces, while dip is the inclination of the needle from the horizontal plane.
- The document discusses kinematics of rigid body motions, including translation, rotation about a fixed axis, and general plane motion.
- Rigid body translation involves all particles moving with the same velocity and acceleration. For rotation about a fixed axis, particle velocity is tangential to the path and depends on angular velocity and distance from the axis. Particle acceleration has both tangential and radial components.
- General plane motion can be analyzed as a combination of translation and rotation, with the motion of each particle equal to the translation plus rotation about a reference point. Relative velocities depend on choice of reference point.
The document provides information about geometry and trigonometry concepts. It discusses segments of a line, harmonic division of segments, the golden section, relationships between points on a line, and exercises related to finding lengths and distances given information about points. It also covers trigonometric angles and systems for measuring angles, including the sexagesimal, centesimal, and radial systems. Conversions between these systems are discussed along with example exercises calculating angle measures in different systems.
This document provides information on theodolite surveying. It discusses how to measure the magnetic bearing of a line, prolong and range a line, measure deflection angles, vertical angles, and includes steps for closed and open traverse surveys using the included angle and deflection angle methods. It also covers topics like observation tables, consecutive and independent coordinates, and balancing a traverse using Bowditch's rule and the transit rule.
This document defines and describes properties of various quadrilaterals:
- Rectangles have four right angles and opposite sides of equal length. The area formula is length x width.
- Parallelograms have two pairs of parallel sides. The opposite angles are equal and adjacent angles sum to 180 degrees. Diagonals bisect each other.
- Trapezoids have one pair of parallel sides. Isosceles trapezoids have two pairs of equal angles and equal or equal length diagonals. Right trapezoids contain one right angle. The area of any trapezoid is half the product of the height and sum of the parallel sides.
This document contains multiple choice practice questions and explanations about geometric constructions using only a ruler and compass. It includes questions about constructing angles and lines, finding loci of points, and measuring lengths and angles related to triangles, circles, and lines constructed with a ruler and compass. The document provides explanations for the answers.
1) The document provides information about various types of quadrilaterals including their properties and theorems related to rectangles and parallelograms.
2) Key quadrilaterals discussed include trapezoids, parallelograms, rectangles, squares, rhombus, and kites. Theorems are presented regarding the properties of diagonals and angles of rectangles.
3) Exercises with solutions are provided applying the theorems to problems involving finding angles of quadrilaterals, properties of rectangles and parallelograms, and relationships between sides and angles of figures.
This document discusses planar kinematics of rigid bodies. It describes three types of planar rigid body motion: translation, rotation about a fixed axis, and general plane motion which is a combination of translation and rotation. Translation and rotation about a fixed axis are analyzed in detail. Translation results in all points of the rigid body having equal velocities and accelerations. During rotation about a fixed axis, a point's velocity is equal to the product of the angular velocity and distance from the axis of rotation, and its acceleration has both tangential and normal components. Relative motion analysis using two coordinate systems is introduced to analyze general plane rigid body motion.
This document discusses the analysis of accelerations in mechanisms. It defines linear and angular acceleration and describes how to calculate the accelerations of links in pure rotation and the general case. Graphical and algebraic methods are presented for solving acceleration problems in four-bar linkages. The document also covers Coriolis acceleration, rolling acceleration with both normal and inverse curvature, and how to account for nonzero angular acceleration.
Redefining brain tumor segmentation: a cutting-edge convolutional neural netw...IJECEIAES
Medical image analysis has witnessed significant advancements with deep learning techniques. In the domain of brain tumor segmentation, the ability to
precisely delineate tumor boundaries from magnetic resonance imaging (MRI)
scans holds profound implications for diagnosis. This study presents an ensemble convolutional neural network (CNN) with transfer learning, integrating
the state-of-the-art Deeplabv3+ architecture with the ResNet18 backbone. The
model is rigorously trained and evaluated, exhibiting remarkable performance
metrics, including an impressive global accuracy of 99.286%, a high-class accuracy of 82.191%, a mean intersection over union (IoU) of 79.900%, a weighted
IoU of 98.620%, and a Boundary F1 (BF) score of 83.303%. Notably, a detailed comparative analysis with existing methods showcases the superiority of
our proposed model. These findings underscore the model’s competence in precise brain tumor localization, underscoring its potential to revolutionize medical
image analysis and enhance healthcare outcomes. This research paves the way
for future exploration and optimization of advanced CNN models in medical
imaging, emphasizing addressing false positives and resource efficiency.
artificial intelligence and data science contents.pptxGauravCar
What is artificial intelligence? Artificial intelligence is the ability of a computer or computer-controlled robot to perform tasks that are commonly associated with the intellectual processes characteristic of humans, such as the ability to reason.
› ...
Artificial intelligence (AI) | Definitio
Use PyCharm for remote debugging of WSL on a Windo cf5c162d672e4e58b4dde5d797...shadow0702a
This document serves as a comprehensive step-by-step guide on how to effectively use PyCharm for remote debugging of the Windows Subsystem for Linux (WSL) on a local Windows machine. It meticulously outlines several critical steps in the process, starting with the crucial task of enabling permissions, followed by the installation and configuration of WSL.
The guide then proceeds to explain how to set up the SSH service within the WSL environment, an integral part of the process. Alongside this, it also provides detailed instructions on how to modify the inbound rules of the Windows firewall to facilitate the process, ensuring that there are no connectivity issues that could potentially hinder the debugging process.
The document further emphasizes on the importance of checking the connection between the Windows and WSL environments, providing instructions on how to ensure that the connection is optimal and ready for remote debugging.
It also offers an in-depth guide on how to configure the WSL interpreter and files within the PyCharm environment. This is essential for ensuring that the debugging process is set up correctly and that the program can be run effectively within the WSL terminal.
Additionally, the document provides guidance on how to set up breakpoints for debugging, a fundamental aspect of the debugging process which allows the developer to stop the execution of their code at certain points and inspect their program at those stages.
Finally, the document concludes by providing a link to a reference blog. This blog offers additional information and guidance on configuring the remote Python interpreter in PyCharm, providing the reader with a well-rounded understanding of the process.
Electric vehicle and photovoltaic advanced roles in enhancing the financial p...IJECEIAES
Climate change's impact on the planet forced the United Nations and governments to promote green energies and electric transportation. The deployments of photovoltaic (PV) and electric vehicle (EV) systems gained stronger momentum due to their numerous advantages over fossil fuel types. The advantages go beyond sustainability to reach financial support and stability. The work in this paper introduces the hybrid system between PV and EV to support industrial and commercial plants. This paper covers the theoretical framework of the proposed hybrid system including the required equation to complete the cost analysis when PV and EV are present. In addition, the proposed design diagram which sets the priorities and requirements of the system is presented. The proposed approach allows setup to advance their power stability, especially during power outages. The presented information supports researchers and plant owners to complete the necessary analysis while promoting the deployment of clean energy. The result of a case study that represents a dairy milk farmer supports the theoretical works and highlights its advanced benefits to existing plants. The short return on investment of the proposed approach supports the paper's novelty approach for the sustainable electrical system. In addition, the proposed system allows for an isolated power setup without the need for a transmission line which enhances the safety of the electrical network
Software Engineering and Project Management - Introduction, Modeling Concepts...Prakhyath Rai
Introduction, Modeling Concepts and Class Modeling: What is Object orientation? What is OO development? OO Themes; Evidence for usefulness of OO development; OO modeling history. Modeling
as Design technique: Modeling, abstraction, The Three models. Class Modeling: Object and Class Concept, Link and associations concepts, Generalization and Inheritance, A sample class model, Navigation of class models, and UML diagrams
Building the Analysis Models: Requirement Analysis, Analysis Model Approaches, Data modeling Concepts, Object Oriented Analysis, Scenario-Based Modeling, Flow-Oriented Modeling, class Based Modeling, Creating a Behavioral Model.
Rainfall intensity duration frequency curve statistical analysis and modeling...bijceesjournal
Using data from 41 years in Patna’ India’ the study’s goal is to analyze the trends of how often it rains on a weekly, seasonal, and annual basis (1981−2020). First, utilizing the intensity-duration-frequency (IDF) curve and the relationship by statistically analyzing rainfall’ the historical rainfall data set for Patna’ India’ during a 41 year period (1981−2020), was evaluated for its quality. Changes in the hydrologic cycle as a result of increased greenhouse gas emissions are expected to induce variations in the intensity, length, and frequency of precipitation events. One strategy to lessen vulnerability is to quantify probable changes and adapt to them. Techniques such as log-normal, normal, and Gumbel are used (EV-I). Distributions were created with durations of 1, 2, 3, 6, and 24 h and return times of 2, 5, 10, 25, and 100 years. There were also mathematical correlations discovered between rainfall and recurrence interval.
Findings: Based on findings, the Gumbel approach produced the highest intensity values, whereas the other approaches produced values that were close to each other. The data indicates that 461.9 mm of rain fell during the monsoon season’s 301st week. However, it was found that the 29th week had the greatest average rainfall, 92.6 mm. With 952.6 mm on average, the monsoon season saw the highest rainfall. Calculations revealed that the yearly rainfall averaged 1171.1 mm. Using Weibull’s method, the study was subsequently expanded to examine rainfall distribution at different recurrence intervals of 2, 5, 10, and 25 years. Rainfall and recurrence interval mathematical correlations were also developed. Further regression analysis revealed that short wave irrigation, wind direction, wind speed, pressure, relative humidity, and temperature all had a substantial influence on rainfall.
Originality and value: The results of the rainfall IDF curves can provide useful information to policymakers in making appropriate decisions in managing and minimizing floods in the study area.
Applications of artificial Intelligence in Mechanical Engineering.pdfAtif Razi
Historically, mechanical engineering has relied heavily on human expertise and empirical methods to solve complex problems. With the introduction of computer-aided design (CAD) and finite element analysis (FEA), the field took its first steps towards digitization. These tools allowed engineers to simulate and analyze mechanical systems with greater accuracy and efficiency. However, the sheer volume of data generated by modern engineering systems and the increasing complexity of these systems have necessitated more advanced analytical tools, paving the way for AI.
AI offers the capability to process vast amounts of data, identify patterns, and make predictions with a level of speed and accuracy unattainable by traditional methods. This has profound implications for mechanical engineering, enabling more efficient design processes, predictive maintenance strategies, and optimized manufacturing operations. AI-driven tools can learn from historical data, adapt to new information, and continuously improve their performance, making them invaluable in tackling the multifaceted challenges of modern mechanical engineering.
Null Bangalore | Pentesters Approach to AWS IAMDivyanshu
#Abstract:
- Learn more about the real-world methods for auditing AWS IAM (Identity and Access Management) as a pentester. So let us proceed with a brief discussion of IAM as well as some typical misconfigurations and their potential exploits in order to reinforce the understanding of IAM security best practices.
- Gain actionable insights into AWS IAM policies and roles, using hands on approach.
#Prerequisites:
- Basic understanding of AWS services and architecture
- Familiarity with cloud security concepts
- Experience using the AWS Management Console or AWS CLI.
- For hands on lab create account on [killercoda.com](https://killercoda.com/cloudsecurity-scenario/)
# Scenario Covered:
- Basics of IAM in AWS
- Implementing IAM Policies with Least Privilege to Manage S3 Bucket
- Objective: Create an S3 bucket with least privilege IAM policy and validate access.
- Steps:
- Create S3 bucket.
- Attach least privilege policy to IAM user.
- Validate access.
- Exploiting IAM PassRole Misconfiguration
-Allows a user to pass a specific IAM role to an AWS service (ec2), typically used for service access delegation. Then exploit PassRole Misconfiguration granting unauthorized access to sensitive resources.
- Objective: Demonstrate how a PassRole misconfiguration can grant unauthorized access.
- Steps:
- Allow user to pass IAM role to EC2.
- Exploit misconfiguration for unauthorized access.
- Access sensitive resources.
- Exploiting IAM AssumeRole Misconfiguration with Overly Permissive Role
- An overly permissive IAM role configuration can lead to privilege escalation by creating a role with administrative privileges and allow a user to assume this role.
- Objective: Show how overly permissive IAM roles can lead to privilege escalation.
- Steps:
- Create role with administrative privileges.
- Allow user to assume the role.
- Perform administrative actions.
- Differentiation between PassRole vs AssumeRole
Try at [killercoda.com](https://killercoda.com/cloudsecurity-scenario/)
1. P
r
O
C
Slider - B
A on CD
DR
Draw crank and slotted mechanism as per given configuration.
OA = 60 mm, NOA = 200 RPM clockwise, CD = 300 mm, DR = 400 mm, Angle BOC =
120°, OC = 160 mm, distance between horizontal line from R & point O = 120 mm. Find
out velocity & acceleration of ram R, acceleration of block A along slotted bar CD.
1
2. P
r
O
C
Slider - B
A on CD
DR
o , c
b
• Find ω = (2πN) / 60, substituting value of N=200 rpm, ω = 20.952 rad/s.
• Now velocity of slider b with respect to o,
Vbo = ω × OB = 20.952 × 0.06 = 1.257 m/s.
• Take two fixed reference points, o & c.
• Draw vector Vbo from o perpendicular to crank OB.
2
3. P
r
O
C
Slider - B
A on CD
DR
o , c
b
• Velocity of point A on CD w. r. t. slider B will be parallel to link CD.
• Hence from b draw a vector parallel to link CD. Value is unknown so draw
vector taking any arbitrary length.
3
4. P
r
O
C
Slider - B
A on CD
DR
o , c
b
a
• Velocity of point A (on link CD) with respect to point C is perpendicular to
link CD.
• Hence from c draw a vector perpendicular to CD.
• Intersection of two vectors will give ‘point a’ in velocity diagram.
4
5. P
r
O
C
Slider - B
A on CD
DR
o , c
b
a
• Now, points C, A and D are on a single link.
• So in velocity diagram points c, a and d will be co-linear.
• To draw velocity of point d, extend the vector ca taking ratio ca/cd = CA/CD
• Take dimension from velocity diagram in case of small letters.
• Take dimension from mechanism in case of capital letters.
• Values of ca from velocity diagram & CA, CD from mechanism can be found.
• The value of cd for velocity diagram can be found.
• Draw vector as per the derived length.
d
5
6. P
r
O
C
Slider - B
A on CD
DR
o , c
b
a
d
• From d draw velocity of r with respect to point d (Vrd), perpendicular to RD.
6
7. P
r
O
C
Slider - B
A on CD
DR
o , c
b
a
d
r
• Now, velocity of slider r with respect to fixed point o or c will be in horizontal
line. So, from o or c draw horizontal line.
• Intersection of two vectors will be point r.
7
8. P
r
O
C
Slider - B
A on CD
DR
o , c
b
a
d
r
1 f c
OB = Vob
2 / OB = 1.2572 / 0.06 = 26.33 m/s Parallel to OB → O
2 f c
AC = Vac
2 / AC = 0.89342 / 0.19698 = 4.052 m/s Parallel to AC → C
3 f t
AC = unknown ┴ to AC -
4 f c
AB = unknown Parallel to AB -
5 f cr
AB = 2Vab ωCD = 2 x 0.8842 x 4.54 = 8.021 m/s ┴ to CD -
6 f c
RD = Vrd
2 / RD = 0.3592 / 0.4 = 0.322 m/s Parallel to DR → D
7 f t
RD = unknown ┴ to DR -
8 f t
R = unknown Parallel to Vro -
• Derive all components for acceleration analysis.
8
9. P
r
O
C
Slider - B
A on CD
DR
o , c
b
a
d
r
o1 , c1
b1
• From acceleration table draw 1st acceleration vector.
• Centripetal acceleration of slider B with respect of O, will be parallel to OB &
it will be toward centre of rotation of link OB, i.e. O.
• So from O1 draw vector parallel to OB & head of vector towards O.
• Magnitude of vector will be same as the value which we have found.
1 f c
OB = Vob
2 / OB = 1.2572 / 0.06 = 26.33 m/s Parallel to OB → O
9
10. P
r
O
C
Slider - B
A on CD
DR
o , c
b
a
d
r
o1 , c1
b1
oa
22 f c
AC = Vac
2 / AC = 0.89342 / 0.19698 = 4.052 m/s Parallel to AC → C
• Now centripetal acceleration of A with respect to C, it will be parallel to AC
& towards the centre of rotation of link AC, i.e. towards C.
• So from C1 draw vector parallel to CD & magnitude of vector will be as per
the value derived.
10
11. P
r
O
C
Slider - B
A on CD
DR
o , c
b
a
d
r
o1 , c1
b1
oa
3 f t
AC = unknown ┴ to AC -
• Now tangential acceleration of A with respect to C, it will be perpendicular
to AC.
• So from Oa draw vector perpendicular to CD & magnitude of vector is
unknown.
11
12. P
r
O
C
Slider - B
A on CD
DR
o , c
b
a
d
r
o1 , c1
b1
ba
oa
5 f cr
AB = 2Vab ωCD = 2 x 0.8842 x 4.54 = 8.021 m/s ┴ to CD -
• Here we are interested in finding out acceleration of slider B with respect to
C. It is addition of acceleration of B with respect to A & acceleration of A
with respect to C.
• Here coriolis component will come into picture.
• It can be found our by the method shown in red figure. Blue vector is coriolis
component of acceleration.
• Pick coriolis component & put its head at b1. 12
13. P
r
O
C
Slider - B
A on CD
DR
o , c
b
a
d
r
o1 , c1
b1
ba
oa
a1
4 f c
AB = unknown Parallel to AB -
• From ba draw centripetal acceleration of B with respect to A.
• Draw a line parallel to CD from ba.
• Intersection of two vectors will be point a1.
13
14. P
r
O
C
Slider - B
A on CD
DR
o , c
b
a
d
r
o1 , c1
b1
ba
oa
a1
d1
• a1b1 = Total acceleration of B with respect to A.
• c1a1 = Total acceleration of A with respect to C.
• Now links C, A & D are co-linear.
• Hence in acceleration diagram these three points must be co-linear.
• So taking ratio, c1a1/c1d1 = CA / CD.
• Capital letter indicates measurements from mechanism drawn.
• Small letter indicates measurements from acceleration diagram. 14
16. P
r
O
C
Slider - B
A on CD
DR
o , c
b
a
d
r
o1 , c1
b1
ba
oa
a1
d1 rd
6 f c
RD = Vrd
2 / RD = 0.3592 / 0.4 = 0.322 m/s Parallel to DR → D
• Now draw centripetal component of point R with respect to D. It is parallel to
DR & it is towards centre of rotation of link DR, i.e. towards D.
• Do from rd draw a line parallel to DR.
• Magnitude is same as the derived one.
d1 rd
16
17. P
r
O
C
Slider - B
A on CD
DR
o , c
b
a
d
r
o1 , c1
b1
ba
oa
a1
d1 rd
7 f t
RD = unknown ┴ to DR -
• Now tangential acceleration of point R with respect to D.
• Value is unknown.
• So from rd draw a line perpendicular to DR.
17
18. P
r
O
C
Slider - B
A on CD
DR
o , c
b
a
d
r
o1 , c1
b1
ba
oa
a1
d1
r1
rd
8 f t
R = unknown Parallel to Vro -
• Now draw tangential acceleration of slider R.
• Value is unknown.
• From c1 draw a horizontal line.
• Intersection of two points will be point r1.
18
19. P
r
O
C
Slider - B
A on CD
DR
o , c
b
a
d
r
o1 , c1
b1
ba
oa
a1
d1
r1
rd
Configuration Diagram
Velocity
Diagram
Acceleration
Diagram
19
20. P
r
D
A
C
B E
Q on EFO
F
S
a, d, o
b
• Draw configuration diagram as per given dimensions.
• Speed of crank AB in rpm is given.
• So find out angular velocity of link AB, ω = (2πN) / 60.
• Now find velocity of B with respect to A, Vba = ω x AB.
• Now Vba is perpendicular to AB.
• So, from the fixed points a, d, o draw vector perpendicular to AB &
magnitude = Vba.
400
400
300
AD = 650 mm, AB = 100 mm, BC = 800 mm, DC = 250 mm, BE=CE, EF = 400 mm,
FO = 240 mm, FS = 400 mm, Angle BAD = 135°. NAB = 300 RPM Clockwise. Find
acceleration of sliding of link EF in trunion.
20
21. P
r
D
A
C
B E
Q on EFO
F
S
a, d, o
b
• Now velocity of C with respect to B will be perpendicular to BC.
• So from B draw a line perpendicular to BC.
21
22. P
r
D
A
C
B E
Q on EFO
F
S
a, d, o
c
b
• Now velocity of C with respect to D will be perpendicular to CD.
• So from d draw a line perpendicular to CD.
• Intersection of two velocity vector (1) velocity of C with respect to B & (2)
velocity if C with respect to D will be point c in velocity diagram.
22
23. P
r
D
A
C
B E
Q on EFO
F
S
a, d, o
c
e
b
• Now B, E & C are on single link. So in velocity diagram these three points
must be on one line.
• So take ratio, BE / BC = be / bc.
• BE & BC = dimensions from mechanism, which can be easily measured.
• bc = dimension from velocity diagram, which can be measured.
• So, the value of be can be found out.
• Based on derived value show point e on vector bc in velocity diagram.
23
24. P
r
D
A
C
B E
Q on EFO
F
S
a, d, o
c
e
b
• Now velocity of q with respect to E will be perpendicular to EQ.
• So from e draw vector perpendicular to EQ.
24
25. P
r
D
A
C
B E
Q on EFO
F
S
a, d, o
c
q
e
b
• Now velocity of Q with respect to O, is parallel to EQ.
• So from o draw a line parallel to EQ.
• Intersection of two vectors (1) velocity of Q with respect to E, (2) velocity of
Q with respect to O, will be point q in velocity diagram.
25
26. P
r
D
A
C
B E
Q on EFO
F
S
a, d, o
f
c
q
e
b
• Now, E, Q & F are on one link.
• So in velocity diagram they must be co-linear.
• So extend line eq & find out point f by ratio as follows:
• eq / ef = EQ / EF.
• EQ & EF can be found out by measurement from configuration diagram.
• eq can be measured from velocity diagram.
• Hence unknown ef can be found out & based on it vector eq can be extended.
26
27. P
r
D
A
C
B E
Q on EFO
F
S
a, d, o
f
c
q
e
b
• Now velocity of S with respect to F will be perpendicular to SF.
• So from f draw a line perpendicular to SF.
27
28. P
r
D
A
C
B E
Q on EFO
F
S
a, d, os
f
c
q
e
b
• Now velocity of S with respect to fixed point is parallel to velocity of S.
• So from fixed point draw line parallel to velocity of S.
• Intersection of two vectors (1) velocity of S with respect to F & (2) velocity of
S with respect to fixed point will give the point s in velocity diagram.
28
29. P
r
D
A
C
B E
Q on EFO
F
S
a, d, os
f
c
q
e
b
1 fc
AB = Vab
2 / AB = 3.142 / 0.1 = 98.6 m/s2 Parallel to AB → A
2 fc
BC = Vbc
2 / BC = 32 / 0.8 = 11.25 m/s2 Parallel to BC → B
3 ft
BC = Unknown ┴ to BC
4 fc
CD = Vcd
2 / CD = 2.92 / 0.25 = 33.64 m/s2 Parallel to CD → D
5 ft
CD = Unknown ┴ to CD
6 fc
QE = Vqe
2 / QE = 1.832 / 0.16 = 20.93 m/s2 Parallel to QE → E
7 ft
QE = Unknown ┴ to QE
8 fcr
QO = 2Vqo ωEF = 2 x 1.95 x 11.44 = 44.6 m/s2
┴ to QE
9 fc
QO = Unknown Parallel to QO
10 fc
FS = Vfs
2 / FS = 3.172 / 0.4 = 25.12 m/s2 Parallel to FS → F
11 ft
FS = Unknown ┴ to FS
12 ft
S = Unknown Parallel to VS
Draw acceleration vector
table as follows:
29
30. P
r
D
A
C
B E
Q on EFO
F
S
a, d, os
f
c
q
e
b
a1, d1, o1
b1
1 fc
AB = Vab
2 / AB = 3.142 / 0.1 = 98.6 m/s2 Parallel to AB → A
• Centripetal acceleration of B with respect to A, is parallel AB & towards
center of rotation of link AB, i.e. towards A.
• So from fixed points a1, d1, o1 draw vector parallel to AB.
• Magnitude of vector will be the value which we have derived as above.
30
31. P
r
D
A
C
B E
Q on EFO
F
S
a, d, os
f
c
q
e
b
a1, d1, o1
b1
bc
2 fc
BC = Vbc
2 / BC = 32 / 0.8 = 11.25 m/s2 Parallel to BC → B
• Now centripetal acceleration of C with respect to B, is parallel to BC &
towards direction of rotation of link BC, i.e. towards B.
• So from b1 draw vector parallel to BC.
• Magnitude of vector will be same as derived value from the table.
31
32. P
r
D
A
C
B E
Q on EFO
F
S
a, d, os
f
c
q
e
b
a1, d1, o1
b1
bc
3 ft
BC = Unknown ┴ to BC
• Now tangential acceleration of C with respect to B, is perpendicular to BC.
• So, from bc draw a vector perpendicular to BC.
• Magnitude is unknown so draw line with arbitrary length.
32
33. P
r
D
A
C
B E
Q on EFO
F
S
a, d, os
f
c
q
e
b
a1, d1, o1
b1
dc
bc
4 fc
CD = Vcd
2 / CD = 2.92 / 0.25 = 33.64 m/s2 Parallel to CD → D
• Now centripetal acceleration of C with respect to D, is parallel to CD &
towards center of rotation of link CD, i.e. towards D.
• So from fixed point a1, d1, o1 draw vector in direction parallel to CD.
• The magnitude is same as the derived in above table.
33
34. P
r
D
A
C
B E
Q on EFO
F
S
a, d, os
f
c
q
e
b
a1, d1, o1
b1
c1
dc
bc
5 ft
CD = Unknown ┴ to CD
• Now tangential acceleration of C with respect to D, is perpendicular to CD.
• So from dc draw a vector perpendicular to CD.
• Intersection of two vectors (1) tangential acceleration of C with respect to B
(2) tangential acceleration of C with respect to D, will be point c1.
34
35. P
r
D
A
C
B E
Q on EFO
F
S
a, d, os
f
c
q
e
b
a1, d1, o1
b1
c1
e1
dc
bc
• Join c1a1 & c1b1.
• c1a1 = acceleration of C with respect to A.
• c1b1 = acceleration of C with respect to B.
35
36. P
r
D
A
C
B E
Q on EFO
F
S
a, d, os
f
c
q
e
b
a1, d1, o1
b1
c1
e1
dc
bc
qe
6 fc
QE = Vqe
2 / QE = 1.832 / 0.16 = 20.93 m/s2 Parallel to QE → E
• Now centripetal acceleration of Q with respect to E, is parallel to QE &
towards center of rotation of link QE, i.e. towards e.
• So from e1 draw vector parallel to QE.
• Magnitude will be same as the derived value in above table.
36
37. P
r
D
A
C
B E
Q on EFO
F
S
a, d, os
f
c
q
e
b
a1, d1, o1
b1
c1
e1
dc
bc
qe
7 ft
QE = Unknown ┴ to QE
• Now tangential acceleration of Q with respect to E, will be perpendicular to
link QE.
• So from qe draw vector perpendicular to link QE.
• Magnitude is unknown. So draw a line with arbitrary length.
37
38. P
r
D
A
C
B E
Q on EFO
F
S
a, d, os
f
c
q
e
b
a1, d1, o1
b1
c1
e1
qo
dc
bc
qe
8 fcr
QO = 2Vqo ωEF = 2 x 1.95 x 11.44 = 44.6 m/s2
┴ to QE
• Now acceleration of Q with respect to O will be having two components. (1)
Coriolis component (2) centripetal acceleration of Q with respect to O.
• So find out Coriolis component value as per the above table.
• The direction can be found out as per the figure as shown with red lines.
• So from fixed points a1, d1, o1, draw vector same as we found in the red lines
figure & magnitude same as derived in above table.
38
39. P
r
D
A
C
B E
Q on EFO
F
S
a, d, os
f
c
q
e
b
a1, d1, o1
b1
c1
e1
q1
qo
dc
bc
qe
9 fc
QO = Unknown Parallel to QO
• Now centripetal acceleration of Q with respect to O will be parallel to EF.
• So from qo draw a line parallel to EF.
• Intersection of two vectors (1) tangential acceleration of Q with respect to E
& (2) centripetal acceleration of Q with respect to O will be point q1.
39
40. P
r
D
A
C
B E
Q on EFO
F
S
a, d, os
f
c
q
e
b
a1, d1, o1
b1
c1
e1
q1
qo
dc
bc
qe
• Join vector q1e1 & q1o1.
• q1e1 = Acceleration of Q with respect to point E.
• q1o1 = Acceleration of Q with respect to tunion O.
Configuration Diagram Velocity
Diagram Acceleration
Diagram
40
41. O
A
F on CD
nearer to A
Slider B
E on CD
nearer to
slider B
C
D
Oscillating Cylinder - CD Piston rod - AB
Draw the configuration diagram as per the dimensions given.
41
42. O
A
F on CD
Slider B
E on CD
C
D o
a
• Now to start velocity diagram, start with angular speed of crank OA.
• From speed N, use equation, ω = 2πN / 60.
• Now velocity of point A with respect to O, will be perpendicular to OA.
• So fixing point o draw vector perpendicular to OA, in the direction of rotation of the
crank OA.
• The magnitude of vector Vao = ω x OA.
42
43. O
A
F on CD
Slider B
E on CD
C
D o
a
• Now point F is the point nearer to A but on the oscillating cylinder CD.
• Observer standing at A will find that point F is sliding inside the oscillating cylinder.
• So velocity of point F with respect to point A will be parallel to AB (because F is
sliding inside oscillating cylinder).
• So from a draw a vector parallel to AB.
• The magnitude is unknown so draw a vector of arbitrary length.
43
44. O
A
F on CD
Slider B
E on CD
C
D o, c
f
a
• Now point F is on oscillating cylinder CD.
• So velocity of point F with respect to C will be perpendicular to CD.
• So from fixed point c draw a vector perpendicular to CD.
• Intersection of two vectors (1) velocity of F with respect to A & (2) velocity of F
with respect to C will give point F.
44
45. O
A
F on CD
Slider B
E on CD
C
D o, c
e
f
a
• Now point E is on CD.
• So in velocity diagram these three points must be co linear.
• So taking ratio as follows find point e on vector ‘cf’ in velocity diagram.
• CE / CF = ce / cf.
• CE & CF can be measured from the mechanism drawn.
• cf can be measured from the velocity diagram.
45
46. O
A
F on CD
Slider B
E on CD
C
D o, c
e
f
a
• Now velocity of point B on piston rod with respect to point E on cylinder CD is
parallel to AB. (Because point B is sliding inside the cylinder CD).
• So from e draw a vector parallel to AB.
• Magnitude is unknown, so take the length of vector arbitrary.
46
47. O
A
F on CD
Slider B
E on CD
C
D o, c
e
f
b
a
• Now velocity of point B with respect to A on piston rod AB, is perpendicular to AB.
• So from a draw a vector perpendicular to AB.
• Intersection of two vectors (1) velocity of B with respect to E & (2) velocity of B
with respect to A, will be point b.
47
48. O
A
F on CD
Slider B
E on CD
C
D o, c
e
f
b
a
Find out all the acceleration
components as per the table.
1 fc
OA = Voa
2 / OA = 1.572 / 0.05 = 49.3 m/s2 Parallel to OA → O
2 fc
FC = Vfc
2 / FC = 0.5142 / 0.22913 = 1.153 m/s2 Parallel to FC → C
3 ft
FC = Unknown ┴ to FC
4 fcr
AF = 2x VafxωCF = 2 x 1.48 x 2.24 = 33.64 m/s2
┴ to CF
5 fc
AF = Unknown Parallel to CF
48
49. O
A
F on CD
Slider B
E on CD
C
D o, c
e
f
b
a
1 fc
OA = Voa
2 / OA = 1.572 / 0.05 = 49.3 m/s2 Parallel to OA → O
• Centripetal acceleration of A with respect to O can be found as per step 1 as above.
• It is parallel to OA as well as towards center of rotation of link OA, i.e. towards O.
• So from fixed points o1 & c1 draw a line parallel to OA towards O.
• Length is decided from the magnitude of acceleration which we found in step-1.
o1
a1
,c1
49
50. O
A
F on CD
Slider B
E on CD
C
D o, c
e
f
b
a
2 fc
FC = Vfc
2 / FC = 0.5142 / 0.22913 = 1.153 m/s2 Parallel to FC → C
• Centripetal acceleration of F with respect to C can be found as per step-2 as above.
• It is parallel to CF as well as towards center of rotation of link CF, i.e. towards C.
• So from fixed points o1 & c1 draw a line parallel to CF towards C.
• Length is decided from the magnitude of acceleration which we found in step-2.
o1
a1
,c1
cf
50
51. O
A
F on CD
Slider B
E on CD
C
D o, c
e
f
b
a
3 ft
FC = Unknown ┴ to FC
• Tangential acceleration of F with respect to C will be perpendicular to CF.
• So from point cf draw a vector perpendicular to CF.
• Magnitude of acceleration is unknown so the vector will be of arbitrary length.
o1
a1
,c1
cf
51
52. O
A
F on CD
Slider B
E on CD
C
D o, c
e
f
b
a
4 fcr
AF = 2x VafxωCF = 2 x 1.48 x 2.24 = 33.64 m/s2
┴ t CF -
• Now acceleration of A with respect to F will have two component (1) Coriolis
component & (2) Sliding component (Centripetal).
• Direction of Coriolis component can be found as per the red figure drawn.
• So pick head of Coriolis component vector & place at point a1.
o1
a1
,c1
f1
af
cf
52
53. O
A
F on CD
Slider B
E on CD
C
D o, c
e
f
b
a
5 fc
AF = Unknown Parallel to CF
• Centripetal acceleration of A with respect to F or sliding acceleration of F with
respect to A will be parallel to CF.
• So from af draw a vector parallel to CF.
• Intersection of two vector (1) Sliding acceleration of F with respect to A (2)
Tangential acceleration of F with respect to C, will be point f1.
o1
a1
,c1
f1
af
cf
53
54. O
A
F on CD
Slider B
E on CD
C
D o, c
e
f
b
a
• o1f1 = Acceleration of F with respect to C.
• a1f1 = Acceleration of point A with respect to cylinder walls F.
o1
a1
,c1
f1
af
cf
54
55. O
A
F on CD
Slider B
E on CD
C
D o, c
e
f
b
a
• From velocity diagram, it can be found that vector ‘af’ & ‘be’ are equal in length.
• In other words, velocity of point F with respect to A & velocity of point B with
respect to E are same.
• Similarly acceleration of slider B with respect to cylinder wall i.e. point E will be
same as acceleration of A with respect to F, i.e. vector a1f1.
• This can be proved by considering acceleration of B with respect to E & acceleration
of B with respect to A. (Refer next 4 slides)
o1
a1
,c1
f1
af
cf
55
56. O
A
F on CD
Slider B
E on CD
C
D o, c
e
f
b
a
• Point E is on link CF.
• So in acceleration diagram points c1, e1 & f1 must be co-linear. Point e1 on c1f1 can
be found by the ratio as follows:
• CE / CF = c1e1 / c1f1
• CE & CF can be measured from the mechanism drawn.
• c1f1 can be measured from acceleration diagram.
o1
a1
,c1
f1
af
e1
cf
56
57. O
A
F on CD
Slider B
E on CD
C
D o, c
e
f
b
a
1 fcr
BE = 2 x Vbe x ωCF = 2x1.48x 2.24 = 6.66 m/s2 Perpendicular to CF -
• Now acceleration of B with respect to E will have two component (1) Coriolis
component & (2) Sliding component (Centripetal).
• Direction of Coriolis component can be found as per the red figure drawn.
• So pick head of Coriolis component vector & place at point e1.
o1
a1
,c1
f1
af
e1
be
cf
57
58. O
A
F on CD
Slider B
E on CD
C
D o, c
e
f
b
a
2 fs
BE = Unknown Parallel to CF -
• Now sliding acceleration of point B with respect to E on CD will be parallel to CF.
• So from be draw a vector parallel to CF.
• Magnitude is unknown. So draw a vector of arbitrary length.
o1
a1
,c1
f1
af
e1
be
cf
58
59. O
A
F on CD
Slider B
E on CD
C
D o, c
e
f
b
a
3 fc
AB = Vab
2 / AB = 0.33642 / 0.15 = 0.7544 m/s2 Parallel to AB → A
• Now centripetal acceleration of point B on piston rod AB with respect to A, will be
parallel to AB & towards center of rotation of link AB, i.e. towards A.
• So from a1 draw a vector parallel to AB towards A.
• Magnitude of acceleration can be found as per the calculation shown above.
• So fix length of vector taking value of above acceleration in to consideration.
o1
a1
,c1
f1
af
ab
e1
be
cf
59
60. O
A
F on CD
Slider B
E on CD
C
D o, c
e
f
b
a
4 ft
AB = Unknown Perpendicular to AB -
• Now tangential acceleration of point B with respect to point A on piston rod AB will
be perpendicular to AB.
• So from ab draw a line perpendicular to AB.
• Intersection of two vectors (1) tangential acceleration of B with respect to A (2)
Sliding acceleration of B with respect to E, will be point b1.
o1
a1
,c1
f1
af
b1
ab
e1
be
cf
60
61. O
A
F on CD
Slider B
E on CD
C
D o, c
e
f
b
a
o1
a1
,c1
f1
cf
af
b1
ab
e1
be
• From acceleration diagram, a1f1 & b1e1 , both vectors can be measured same.
• In other words,
Acceleration of A with
respect to cylinder wall F
is equal to
Acceleration of slider B
with respect to cylinder
wall F.
=
61