2Introduction to Dynamics of Machinery ME 108ME 208ME 302ME 301Dynamics 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.
3Introduction 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.
4Introduction to Dynamics of Machinery JointsRigid BodiesMechanism: 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.Kinematic Pair
5D.O.F of a body in spaceDof is defined as the number of independent parameters that is required to define the position of a body in space.P1(x1,y1,z1)l3P3(x3,y3,z3)l1l2P2(x2,y2,z2)9 parameter x1, y1, z1, x2, y2, z2, x3,y3,z39-3=6But ;
64-1=3 D.O.F of a body in plane P1(x1,y1) l1 P2(x2,y2) The number of independent parameters that is required to define the position of a body in space.P1(x1,y1)l1P2(x2,y2)4 parameter x1, y1, x2, y24-1=3But ;
8Brief Review of Engineering Mechanics 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:
9Brief Review of Engineering Mechanics 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;
10Brief Review of Engineering Mechanics 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. Newton’s Second law is expressed as mathematically;Amount of materResistance of a body against motion
11Brief Review of Engineering Mechanics 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;
12Brief Review of Engineering Mechanics Newton’s laws of motion will be the main starting point for the dynamic analysis of machinery.The basic quantities of dynamics are force, mass and time.Force can be define in terms of Newton’s first law as an action which tends to change the motion of a bodyMass is the resistance of a body to motion.Time is a concept for ordering the flow of events.
13Brief Review of Engineering Mechanics In this generally SI system of units will be used.Quantity name SymbolLenght meter mMass kilogram kgForce Newton NTime second sWork joule JPower watt WFrequency hertz Hz
14Subject of ME 302Subject 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.
15Static Force AnalysisWe 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.
16Please remember that for a solution, Freebody DiagramYPlease remember that for a solution,a correct freebody diagram is essential.B34FC2tXA132t4F
17Forces and MomentsForce is a vectorial quantity that has manitude, direction and point of application.
18Forces and MomentsA 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.Moment direction can be found by right hand rule. It is perpendicular to the plane formed by r and F.
19Forces in Machine Systems 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.
20Forces in Machine Systems 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.
21Joint Types and Constraint Forces Revolute JointZXYIt has one degree of freedom, which is in rotation about z-axis.
22Joint Types and Constraint Forces Revolute JointZXYZXYFxFxMxMxFzFyFzFyMyMyIt 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.
23Joint Types and Constraint Forces Prizmatic JointYIt has one degree of freedom, which is a translation along z axis.ZX
24Joint Types and Constraint Forces Prizmatic JointZXYZXYFxFxMxMxFyFyMyMzMyMzIt cannot transmit a force in z axis, but it can transmit forces in x and y directions and moments x, y, and z axis.
25Joint Types and Constraint Forces Cylindrical JointXYZIt has two degree of freedom; a translation along and rotation about the same axis, called the cylindrical axis.
26Joint Types and Constraint Forces Cylindrical JointZXYZXYFxFxMxMxFyFyMyMyNo 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.
27Joint Types and Constraint Forces Screw jointXYZThere 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.
28Joint Types and Constraint Forces Screw JointZXYZXYFxFxMxMxFyFzFyMyFzMyNo 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.
29Joint Types and Constraint Forces Planar jointYIt has three degree of freedom, translation along x and z directions and a rotation about y-axis.ZX
30Joint Types and Constraint Forces Planar JointXXFxFxMxMxMyMzMyYMzYZZThere 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.
31Joint Types and Constraint Forces Spherical jointXYZIt has three rotational degrees of freedom, so it cannot transmit any moments.
32Joint Types and Constraint Forces Spherical JointZXYZXYFxFxFzFyFzFyIt can transmit forces in all directions.