Theory of Machines

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Chapter One,Kinematics and Kinetics of Mechanisms,Introduction. Theory of Machines may be defined as that branch of. engineering science which deals with the study of relative motion. between the various parts of machine and forces which act on them. The knowledge of this subject is very essential for an engineer in. designing the various parts of a machine,Sub divisions of theory of Machines. They Theory of Machines may be sub divided into the following four. 1 Kinematics is that branch of theory of machines which is. responsible to study the motion of bodies without reference to. the forces which are cause this motion i e it s relate the motion. variables displacement velocity acceleration with the time. 2 Kinetics is that branch of theory of machines which is. responsible to relate the action of forces on bodies to their. resulting motion, 3 Dynamics is that branch of theory of machines which deals. with the forces and their effects while acting upon the machine. parts in motion, 4 Statics is that branch of theory of machines which deals with. the forces and their effects while the machine parts are rest. There are some definitions which are concerned with this subject. must be known, Mechanism is a combination of rigid bodies which are formed and.
connected together by some means so that they are moved to perform. some functions such as the crank connecting rod mechanism of the I C. engines steering mechanisms of automobiles etc, The analysis of mechanisms is a part of machine design which is. concerned with the kinematics and kinetics of mechanisms or the. dynamics of mechanisms, Rigid Body is that body whose changes in shape are negligible. compared with its overall dimensions or with the changes in position of. the body as a whole such as rigid link rigid disc etc. Links are rigid bodies each having hinged holes or slot to be connected. together by some means to constitute a mechanism which able to transmit. motion or forces to some another locations, Absolute motion the motion of body in relative to another body. which is at rest or to a fixed point located on this body. Relative motion the motion of body in relative to another moved. Scalar quantities are those quantities which have magnitude only. e g mass time volume density etc, Vector quantities are those quantities which have magnitude as well. as direction e g velocity acceleration force etc,Disc in motion rigid body.
Hinged hole,Rigid link,Slot used for the purpose of connection. with another link by slider,Hinged hole used for the. purpose the connection with,another link by hinge pin. Connecting rod,Fixed Piston moved on,point horizontal path. Crank Connecting rod mechanisms,Part one Kinematics of Mechanisms.
1 The connection of mechanism parts, The mechanism is a combination of rigid bodies which are connected. together using different methods,1 1 Hinged part, The hinge connection may be used to connect the links together or. connect a link to a fixed point piston disc etc the connection is. achieved using pin which is pass through the hinge holes. Symbled by,1 2 Sliding Parts, The sliding connection may be used to connect two links rotate about. fixed points by means of slot pin and hinge,Slot pin and. hinge Symbled by,Hinge and pin Hinge and pin,1 3 Rolling without slipping parts.
Symbled by,2 Translated bodies, There are some bodies in the mechanism which are constrained to. move in translation manner such as the piston of crank connecting. rod mechanism the body is used to be in translation motion if any. line remain in some configuration during motion then all the points. have the same absolute velocity and acceleration,Velocity diagram. the motion is absolute then select any fixed point such as o be as. a reference point i e point of zero velocity,Draw the path of translation. If vB is known select a scale factor to draw the velocity diagram. denoted by SFv, The draw a line ob vB SFv in direction of vB parallel to the path of. translation,Path of translation of B,Velocity dig, Then all points on the piston have the same velocity such as point.
D i e on the velocity diagram the point d coincide on the point b. Acceleration diagram, the motion is absolute then select any fixed point such as o be as. a reference point i e point of zero acceleration,Draw the path of translation. If aB is known select a scale factor to draw the acceleration. diagram denoted by SFa,In which ob aB SFa, Then all points on the piston have the same acceleration value. Note the base ref point o of vo 0 ao 0,Path of translation of B. Acceleration dig,Dynamic review, Translation motion can by treatment by the dynamics of particles i e body.
B can be treatment as a particle moved on straight or curved path. s displacement v velocity a acceleration,if a uniform. if a uniform,3 Bodies rotate about fixed point, Consider the link shown which is rotate about the fixed point o the. motion of this link can be analyzed using the principle of absolute motion. If angular displacement about fixed rotation centre o. angular velocity about fixed rotation centre, angular acceleration about fixed rotation centre A. but if is uniform,and but if is uniform,Velocity diagram. In order to analyze the velocity of any point we follow with one of. following methods,1 If is given,Draw the link by SFp scale factor for position.
Select SFv then select a reference point of zero velocity such. Draw from o a line of length in direction of, To find the velocity of any point located on the link such as D. specify point d on oa such that od,2 If vA is given. Select SFv specify reference point of zero velocity. Draw oa of length vA SFv in the same direction given O. To find value and direction of D,Value of Position diagram. Acceleration diagram A a,Also we have two method d. velocity diagram o,1 If is given,normal component of acceleration of.
A relative to rotation centre,aAt oA normal component of acceleration of d. A relative to rotation centre o,acceleration diagram. Select a reference point of zero acceleration point o. Select SFa depend on which is greater,aAn or aAt, Start from o to draw o OA directed into the rotation centre by. value of o aAn SFa, From point draw OA in direction of by value aAt SFa. Finally connect oa to represent the absolute value of acceleration. of point A, To find the acceleration of any point located on the link.
such as point D specify d on oa such that, 2 If aA is given as a value and direction absolute acceleration of. Select select refrence point of zero,acceleration point O. Start from O draw two lines,First line directed in to point O. Second line in direction of aA given, Then connect to represent the drawn tangential component of. acceleration of A a,acceleration diagram,4 Bodies under general plane motion.
If a body under general plane motion then it s motion can be. analyzed using the principle of relative motion, The motion of any point can be discretized into translation and. rotation if consider the link shown under general plane motion the. ends B of absolute velocities vA vB and absolute accelerations aA aB. is the relative velocity of B w r t A,is the relative velocity of A w r t B. is the relative acceleration of B w r t A B,is the relative acceleration of A w r t B VB. i e the state of velocity can be replaced by one of the following. vector notation,VAB and VBA,To specify direction of. A Fixed point, VAB mean that B is a fixed rotation a center and A moved a round A.
VBA mean that A is a fixed rotation a center and A moved a round B. And the state of acceleration can be represented by one of the following. vector notation,contain two,in direction of,contain two. in direction of,Velocity diagram, Consider the shown link under general plane motion to specify the. velocity of any point it s required one of following. 1 Absolute velocity of any point value and direction. Absolute velocity of other point value or direction. 2 Absolute velocity of any point value and direction. Angular velocity of the link which is the same for all points. Draw the link position by scale SFp, If VB is known value and direction then select the scale factor of. velocity diagram SFv,Specify the point of zero velocity point O. ob known in mm,Draw ob in direction of VB, To continue we require other direction of absolute velocity of other.
If the direction of absolute velocity of point c is known then. Star from o to draw line direction of Vc, Star from b to draw line link to be bc or Vcb which is. intersected with the line direction of Vc at c,If is known. Draw bc from b link C,Draw line between o and c produce oc. To find VA VD,Specify ba such that,Measure od VD ad SFv. To find value and direction if unknown measure bc,Acceleration diagram.
To dr w the cceler tion di gr m it s required one of following. Absolute acceleration of any point value and direction. Absolute acceleration of other point value or direction. Absolute acceleration of any point value and direction. Theory of Machines 3 Theory of Machine By R S Khurmi and J K Gupta The analysis of mechanisms is a part of machine design which is

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