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1 ME 302 DYNAMICS OF MACHINERY INTRODUCTION Dr. Sadettin KAPUCU © 2007 Sadettin Kapucu

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Gaziantep University 2 Introduction to Dynamics of Machinery Engineering Mechanics StaticsDynamics Mechanisms Kinematics Geometry of Motion Dynamics of Machinery Kinetics Force-Motion relationships ME 208 ME 301 ME 302 ME 108 Dynamics of machinery is an applied science which is used to understand the relationship between the motion of a machine and the forces which produce these motions.

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Gaziantep University 3 Introduction to Dynamics of Machinery In this course, we study kinetics, the time-varying forces in machines and the resulting phenomena which must be considered in their design. Design is the process of prescribing the sizes, shapes, material compositions, and arrangements of parts so that the resulting machine will perform the prescribed task. Mechanism: A system of elements arranged to transmit motion in a predetermined fashion. Machine: A system of elements arranged to transmit motion and energy in a predetermined fashion.

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Gaziantep University 4 Introduction to Dynamics of Machinery Mechanism: Assemblage of resistant bodies (rigid) connected by movable joints, to form a closed kinematic chain with one link fixed and having the purpose of transforming motion. Rigid Bodies Joints Kinematic Pair

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Gaziantep University 5 D.O.F of a body in space Dof is defined as the number of independent parameters that is required to define the position of a body in space. P 1 (x 1,y 1,z 1 ) P 2 (x 2,y 2,z 2 ) P 3 (x 3,y 3,z 3 ) l1l1 l2l2 l3l3 9 parameter x 1, y 1, z 1, x 2, y 2, z 2, x 3,y 3,z 3 But ;

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Gaziantep University 6 D.O.F of a body in plane The number of independent parameters that is required to define the position of a body in space. P 1 (x 1,y 1 ) P 2 (x 2,y 2 ) l1l1 4 parameter x 1, y 1, x 2, y 2 But ;

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Gaziantep University 7 Plane motion RotationTranslationRotation+Translation Plane motion

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Gaziantep University 8 Brief Review of Engineering Mechanics l Fundamental principles of dynamics are Newton’s Laws of Motion. They cannot be proved arithmetically. No experimental evidence up till now has been observed to violate them. These are three laws:

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Gaziantep University 9 Brief Review of Engineering Mechanics l Newton’s First Law (Statics): A body at rest tends to stay at rest, and a body in motion tends to stay in uniform motion (direction & magnitude of the velocity not changing) unless a net non-zero force act on it. Newton’s first law is expressed as mathematically;

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Gaziantep University 10 Brief Review of Engineering Mechanics l Newton’s Second Law (Dynamics): When a net, non-zero force acts on a body, the body accelerates in proportion to and in direction of the acting force. N ewton’s Second law is expressed as mathematically; Amount of mater Resistance of a body against motion

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Gaziantep University 11 Brief Review of Engineering Mechanics l Newton’s Third Law (Action- Reaction): Every force has a reaction; equal in magnitude, collinear, and opposite in direction to the original force. Newton’s third law is expressed as mathematically;

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Gaziantep University 12 Brief Review of Engineering Mechanics l Newton’s laws of motion will be the main starting point for the dynamic analysis of machinery. l The basic quantities of dynamics are force, mass and time. l Force can be define in terms of Newton’s first law as an action which tends to change the motion of a body l Mass is the resistance of a body to motion. l Time is a concept for ordering the flow of events.

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Gaziantep University 13 Brief Review of Engineering Mechanics l In this generally SI system of units will be used. QuantitynameSymbol Lenghtmeterm Masskilogramkg ForceNewtonN Timeseconds WorkjouleJ PowerwattW FrequencyhertzHz

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Gaziantep University 14 Subject of ME 302 l Subject of matter of ME 302 is to apply Newton’s laws to multi body, single or multi degree of freedom mechanical systems (mechanism) to understand their mechanical behaviour.

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Gaziantep University 15 Static Force Analysis l We start with simple problem where the bodies accelerations are zero. Then all the forces and moments will add to zero. This is the static condition. Every sub component of a static system is also static. If a mechanism is static each of its link are also static. Big problem of the whole mechanism is now broken into several simpler problems. Each body with all the acting forces is called a free body. Pictorial representation of a body is called the free body diagram.

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Gaziantep University 16 Freebody Diagram X Y A B C F F

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Gaziantep University 17 Forces and Moments l Force is a vectorial quantity that has manitude, direction and point of application.

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Gaziantep University 18 Forces and Moments l A force generates a moment (or torque) about a point which is not in its line of action moment is the turning effect of a force. l Moment direction can be found by right hand rule. It is perpendicular to the plane formed by r and F.

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Gaziantep University 19 Forces in Machine Systems l External forces are generated by effects external to the mechanism, like actuation forces from a motor or actuator. Reactions of the external forces are outside our system boundary.

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Gaziantep University 20 Forces in Machine Systems l Constraint forces “constraint” means “limitation of freedom”, in our case, limitation of free motion. These forces are applied onto each link to prevent their free motion. Reactions of constraint forces are inside the system boundary.

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Gaziantep University 21 Joint Types and Constraint Forces Revolute Joint It has one degree of freedom, which is in rotation about z-axis. Z X Y

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Gaziantep University 22 Joint Types and Constraint Forces Revolute Joint It cannot transfer force or torque or angular motion about z-axis, but it transmits forces and torques and related motions in all the other remaining directions. These are; Forces in x, y and z directions, Torques about x and y-axis. Z X Y Z X Y FxFx FyFy FzFz MxMx MyMy FxFx FyFy FzFz MxMx MyMy

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Gaziantep University 23 Joint Types and Constraint Forces Prizmatic Joint X Y Z It has one degree of freedom, which is a translation along z axis.

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Gaziantep University 24 Joint Types and Constraint Forces Prizmatic Joint It cannot transmit a force in z axis, but it can transmit forces in x and y directions and moments x, y, and z axis. Z X Y Z X Y FxFx FxFx FyFy FyFy MxMx MxMx MyMy MyMy MzMz MzMz

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Gaziantep University 25 Joint Types and Constraint Forces Cylindrical Joint It has two degree of freedom; a translation along and rotation about the same axis, called the cylindrical axis. X Y Z

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Gaziantep University 26 Joint Types and Constraint Forces Cylindrical Joint No torque transmission about z-axis, no force transmission along z-axis is possible. In all other directions, there can be forces and moments transmitted, which are forces in x and y-axis and moments about y and z- axis. Z X Y Z X Y FxFx FxFx FyFy FyFy MxMx MxMx MyMy MyMy

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Gaziantep University 27 Joint Types and Constraint Forces Screw joint There are two apparent motions, which are translation along and rotation about z-axis, are not independent from each other. Therefore degree of freedom is only one. This is a rotation about z-axis. X Y Z

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Gaziantep University 28 Joint Types and Constraint Forces Screw Joint No torque transmission about z-axis, no force transmission along z-axis is possible. In all other directions, there can be forces and moments transmitted, which are forces in x and y-axis and moments about y and z- axis. Z X Y Z X Y FxFx FxFx FyFy FyFy MxMx MxMx MyMy MyMy FzFz FzFz

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Gaziantep University 29 Joint Types and Constraint Forces Planar joint It has three degree of freedom, translation along x and z directions and a rotation about y-axis. X Y Z

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Gaziantep University 30 Joint Types and Constraint Forces Planar Joint There are no forces and a torque transmission in these directions. In all other directions there can be force and moment transmitted, which are force in y-axis and moments x and z-axis. Z X Y Z X Y FxFx FxFx MxMx MxMx MyMy MyMy MzMz MzMz

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Gaziantep University 31 Joint Types and Constraint Forces Spherical joint It has three rotational degrees of freedom, so it cannot transmit any moments. X Y Z

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Gaziantep University 32 Joint Types and Constraint Forces Spherical Joint It can transmit forces in all directions. Z X Y Z X Y FxFx FyFy FzFz FxFx FyFy FzFz

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