Machine Elements Module 1 PDF

BULACAN STATE UNIVERSITY CITY OF MALOLOS, BULACAN COLLEGE OF ENGINEERING MECHANICAL ENGINEERING DEPARTMENT MACHINE ELEMENTS 1 MODULE 1 PREPARED BY: ENGR. ALDRIN C. BERNARDO ...

BULACAN STATE UNIVERSITY CITY OF MALOLOS, BULACAN COLLEGE OF ENGINEERING MECHANICAL ENGINEERING DEPARTMENT MACHINE ELEMENTS 1 MODULE 1 PREPARED BY: ENGR. ALDRIN C. BERNARDO  Machine Elements 1 1 UNIT 1INTRODUCTION TO KINEMATICS OF MACHINES LESSONS COVERED 1.1 Theory of Machines 1.2 Kinematic Link or element 1.3 Structure 1.4 Kinematic Pair 1.5 Inversion of Mechanism 1.6 Kinematic Diagrams DURATION: 5 hours PRETEST Directions: Solve the following problems and encircle the letter that corresponds to your final answer. 1. What is the weight of a mass 10 kg at a location where the acceleration of gravity is 9.77 / 2? a. 77.9 N c. 97.7 N b. 79.7 N d. 977 N 2. Two forces of 20 N and 30 N act at the right angle. What is the magnitude of the resultant force? a. 36 N c. 42 N b. 40 N d. 44 N 3. A simply supported beam is 5 meters in length. It carries a uniformly distributed load including its weight of 300 N/m and a concentrated load of 100 N, 2 meters from the left end. Find the reactions if reaction A is at the left end and  reaction B is at the right end. a. = 700 N; = 800 N c. = 810 N; = 780 N b. = 700 N; = 810 N d. = 810 N; = 700 N 4. A circle has a diameter of 20 cm. Determine the moment of inertia of the circular area relative to the axis perpendicular to the area through the center of the circle in 2. a. 14, 280 c. 17, 279 b. 15, 708 d. 19, 007 5. A rotating wheel has a radius of 2 feet and 6 inches. A point on the rim of the wheel moves 30 feet in 2 seconds. Find the angular velocity of the wheel? a. 2 rad/s c. 5 rad/s b. 4 rad/s d. 6 rad/s Machine Elements 1 2 INTRODUCTION This course deals with the study of mechanisms disregarding the forces and energies that cause the motion. It provides an emphasis on the analytical and graphical study of displacement, velocity, and acceleration. This also includes the study of elements of mechanisms such as gears, trains, rolling bodies, belt and pulleys, cams, and followers. In this module, we will study the different concepts and definitions that are fundamental in understanding different topics on the Kinematics of Machineries. Before the lesson proper, we will have a review of the basics of dynamics which are vital in continuing to the depths of the subject. Each lesson will be provided with corresponding learning activities and assessments that will help you evaluate your performance even in the absence of a face-to-face class. The instructor will still be of minimal supervision through different virtual platforms such as Google Meet and Zoom. Now that we have been introduced to the basics of this course, let us now know what we will acquire at the end of this module. OBJECTIVES/COMPETENCIES At the end of the lesson, the students should be able to: 1. Understand the concepts involved in the study of mechanisms; 2. Familiarize with the terms used in the study of machine elements LESSON 1.1: THEORY OF MACHINES Machines are devices used to alter, transmit, and direct forces to accomplish a specific objective. A chain saw is a familiar machine that directs forces to the chain to cut wood. A mechanism is the mechanical portion of a machine that has the function of transferring motion and forces from a power source to an output. It is the heart of a machine. For the chain saw, the mechanism takes power from a small engine and delivers it to the cutting edge of the chain. A mechanism can be considered rigid parts that are arranged and connected so that they produce the desired motion of the machine. Figure 1.1 Machine Elements 1 3 Synthesis is the process of developing a mechanism to satisfy a set of performance requirements for the machine. Analysis ensures that the mechanism will exhibit motion that will accomplish the set of requirements. 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 a 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 1. Kinematics. It is that branch of Theory of Machines which deals with the relative motion between the various parts of the machines. 2. Dynamics. It is that branch of Theory of Machines which deals with the forces and their effects, while acting upon the machine parts in motion. 3. Kinetics. It is that branch of Theory of Machines which deals with the inertia forces which arise from the combined effect of the mass and motion of the machine parts. 4. Statics. It is that branch of Theory of Machines which deals with the forces and their effects while the machine parts are at rest. The mass of the parts is assumed to be negligible. LESSON 1.2: KINEMATIC LINK OR ELEMENT Each part of a machine, which moves relative to some other part, is known as a kinematic link (or simply link) or element. A link may consist of several parts, which are rigidly fastened together so that they do not move relative to one another e.g. piston rod.  Figure 1.2 Types of Links 1. Rigid link. A rigid link is one that does not undergo any deformation while transmitting motion. Strictly speaking, rigid links do not exist. However, as the deformation of a connecting rod, crank, etc. of a reciprocating steam engine is not appreciable, they can be considered as rigid links. 2. Flexible link. A flexible link is one that is partly deformed in a manner not to affect the transmission of motion. For example, belts, ropes, chains, and wires are flexible links and transmit tensile forces only. Machine Elements 1 4 3. Fluid link. A fluid link is one that is formed by having a fluid in a receptacle and the motion is transmitted through the fluid by pressure or compression-only, as in the case of hydraulic presses, jacks, and brakes. Parts of a four bar linkage 1. Crank is a link that makes a complete revolution and is provided to ground 2. Rocker is a link that has oscillatory (back and forth) rotation and is pivoted to ground 3. Coupler (connecting rod) is a link that has complex motion and is not pivoted to ground 4. Ground (base, frame) is defined as any link or links that are fixed concerning the reference frame Figure 1.3 A joint is a movable connection between links and allows relative motion between the links. The two primary joints, also called full joints, are the revolute and sliding joints. The revolute joint is also called a pin or hinge joint. It allows pure rotation between the two links that it connects. The sliding joint is also called a piston or prismatic joint. It allows linear sliding between the links that it connects. Figure below illustrates these two primary joints. Figure 1.4 A cam joint is shown in the Figure below. It allows for both rotation and sliding between the two links that it connects. Because of the complex motion permitted, the cam connection is called a higher-order joint, also called half joint. A gear connection also allows rotation and sliding between two gears as their teeth mesh. The gear connection is also a higher-order joint. Machine Elements 1 5 Figure 1.5 A simple link is a rigid body that contains only two joints, which connect it to other links. Figure 1.6a illustrates a simple link. A crank is a simple link that can complete a full rotation about a fixed center. A rocker is a simple link that oscillates through an angle, reversing its direction at certain intervals. A complex link is a rigid body that contains more than two joints. A rocker arm is a complex link, containing three joints, that is pivoted near its center. A bellcrank is similar to a rocker arm, but is bent in the center. The complex link shown in the figure below is a bellcrank. Figure 1.6 A point of interest is a point on a link where the motion is of special interest. The end of the windshield wiper, previously discussed, would be considered a point of interest. Once the kinematic analysis is performed, the displacement, velocity, and accelerations of that point are determined. The last general component of a mechanism is the actuator. An actuator is the component that drives the mechanism. Common actuators include motors (electric and hydraulic), engines, cylinders (hydraulic and pneumatic), ball-screw motors, and Machine Elements 1 6 solenoids. Manually operated machines utilize human motion, such as turning a crank, as the actuator. Linkages can be either open or closed chains. Each link in a closed-loop kinematic chain is connected to two or more other links. An open-loop chain will have at least one link that is connected to only one other link. Common open-loop linkages are robotic arms as shown below and other “reaching” machines such as backhoes and cranes. Figure 1.7 LESSON 1.3: STRUCTURE It is an assemblage of several resistant bodies (known as members) having no relative motion between them and meant for carrying loads having straining action. A railway bridge, a roof truss, machine frames, etc., are the examples of a structure. Figure 1.8 Difference Between a Machine and a Structure The following differences between a machine and a structure are important from the subject point of view : Machine Elements 1 7 1. The parts of a machine move relative to one another, whereas the members of a structure do not move relative to one another. 2. A machine transforms the available energy into some useful work, whereas in a structure no energy is transformed into useful work. 3. The links of a machine may transmit both power and motion, while the members of a structure transmit forces only. LESSON 1.4: KINEMATIC PAIR The two links or elements of a machine, when in contact with each other, are said to form a pair. If the relative motion between them is completely or successfully constrained (i.e. in a definite direction), the pair is known as kinematic pair. Types of Constrained Motions Following are the three types of constrained motions: 1. Completely constrained motion. When the motion between a pair is limited to a definite direction irrespective of the direction of force applied, then the  motion is said to be a completely constrained motion. For example, the piston and cylinder (in a steam engine) form a pair and the motion of the piston is limited to a definite direction (i.e. it will only reciprocate) relative to the cylinder irrespective of the direction of motion of the crank, as shown in Fig. The motion of a square bar in a square hole, as shown in Fig., and the motion of a shaft with collars at each end in a circular hole, as shown in Fig., are also examples of completely constrained motion. Figure 1.9 2. Incompletely constrained motion. When the motion between a pair can take place in more than one direction, then the motion is called an incompletely constrained motion. The change in the direction of the impressed force may alter the direction of relative motion between the pair. A circular bar or shaft in a circular hole, as shown in figure, is an example of an incompletely constrained motion as it may either rotate or slide in a hole. Both motions have no relationship with the other. Machine Elements 1 8 Figure 1.10 3. Successfully constrained motion. When the motion between the elements, forming a pair, is such that the constrained motion is not completed by itself, but by some other means, then the motion is said to be successfully constrained motion. Consider a shaft in a foot-step bearing as shown in Fig. The shaft may rotate in a bearing or it may move upwards. This is a case of incompletely constrained motion. But if the load is placed on the shaft to prevent axial upward movement of the shaft, then the motion of the pair is said to be successfully constrained motion. The motion of an I.C. engine valve (these are kept on their seat by a spring) and the piston reciprocating inside an engine cylinder are also examples of successfully constrained motion. Classification of Kinematic Pairs The kinematic pairs may be classified according to the following considerations: 1. According to the type of relative motion between the elements. The kinematic pairs according to the type of relative motion between the elements may be classified as discussed below: (a) Sliding pair. When the two elements of a pair are connected in such a way that one can only slide relative to the other, the pair is known as a sliding pair. The piston and cylinder, cross-head, and guides of a reciprocating steam engine, ram and its guides in shaper, tailstock on the lathe bed, etc. are the examples of a sliding pair. A little consideration will show that a sliding pair has a completely constrained motion. Figure 1.11 (b) Turning pair. When the two elements of a pair are connected in such a way that one can only turn or revolve about a fixed axis of another link, the pair is Machine Elements 1 9 known as a turning pair. A shaft with collars at both ends fitted into a circular hole, the crankshaft in a journal bearing in an engine, lathe spindle supported in the headstock, cycle wheels turning over their axles, etc. are the examples of a turning pair. A turning pair also has a completely constrained motion. Figure 1.12 (c) Rolling pair. When the two elements of a pair are connected in such a way that one rolls over another fixed link, the pair is known as rolling pair. Ball and roller bearings are examples of rolling pair.  Figure 1.13 (d) Screw pair. When the two elements of a pair are connected in such a way that one element can turn about the other by screw threads, the pair is known as screw pair. The lead screw of a lathe with nut and bolt with a nut are examples of a screw pair. Figure 1.14 (e) Spherical pair. When the two elements of a pair are connected in such a way that one element (with the spherical shape) turns or swivels about the other fixed element, the pair formed is called a spherical pair. The ball and socket joint, attachment of a car mirror, pen stand, etc., are the examples of a spherical pair. Machine Elements 1 10 Figure 1.15 2. According to the type of contact between the elements. The kinematic pairs according to the type of contact between the elements may be classified as discussed below: (a) Lower pair. When the two elements of a pair have a surface contact when relative motion takes place and the surface of one element slides over the surface of the other, the pair formed is known as lower pair. It will be seen that sliding pairs, turning pairs and screw pairs form lower pairs. (b) Higher pair. When the two elements of a pair have a line or point contact when relative motion takes place and the motion between the two elements is partly turning and partly sliding, then the pair is known as higher pair. A pair of friction discs, toothed gearing, belt and rope drives, ball and roller bearings and cam and follower are the examples of higher pairs. Figure 1.16 3. According to the type of closure. The kinematic pairs according to the type of closure between the elements may be classified as discussed below : (a) Self closed pair. When the two elements of a pair are connected mechanically in such a way that only required kind of relative motion occurs, it is then known as self closed pair. The lower pairs are self closed pair. (b) Force - closed pair. When the two elements of a pair are not connected mechanically but are kept in contact by the action of external forces, the pair is said Machine Elements 1 11 to be a force-closed pair. The cam and follower is an example of force closed pair, as it is kept in contact by the forces exerted by spring and gravity. Figure 1.17 LESSON 1.5: INVERSION OF MECHANISM We have already discussed that when one of the links is fixed in a kinematic chain, it is called a mechanism. So we can obtain as many mechanisms as the number of links in a kinematic chain by fixing, in turn, different links in a kinematic chain. This method of obtaining different mechanisms by fixing different links in a kinematic chain, is known as inversion of the mechanism Types of Kinematic Chains The most important kinematic chains are those which consist of four lower pairs, each pair being a sliding pair or a turning pair. The following three types of kinematic chains with four lower pairs are important from the subject point of view: 1. Four bar chain or quadric cyclic chain, 2. Single slider crank chain, and 3. Double slider crank chain. LESSON 1.6: KINEMATIC DIAGRAMS DIAGRAMS In analyzing the motion of a machine, it is often difficult to visualize the movement of the components in a full assembly drawing. A motor produces rotational power, which drives a mechanism that moves the arms back and forth in a synchronous fashion. It is easier to represent the parts in skeleton form so that only the dimensions that influence the motion of the mechanism are shown. These “stripped-down” sketches of mechanisms are often referred to as kinematic diagrams. The purpose of these diagrams is similar to the electrical circuit schematic or piping diagrams in that they represent variables that affect the primary function of the mechanism. Table 1.1 shows typical conventions used in creating kinematic diagrams. A kinematic diagram should be drawn to a scale proportional to the actual mechanism. For convenient reference, the links are numbered, starting with the frame as link number 1. To avoid confusion, the joints should be lettered. Machine Elements 1 12 Machine Elements 1 13 POST-TEST Answer the following questions: 1. Differentiate machines from mechanisms. ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ 2. What are the divisions of Theory of Machines? Create a simple example, with drawing, showing these divisions. ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ 3. What are the types of link? ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ 4. What is the difference of machine and a structure? ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ 5. Explain the types of kinematic pairs and its application. Include figures or drawings for the application. ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ 6. Explain the necessity of diagram in kinematics. ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ ______________________________________________________________  Machine Elements 1 14 REFERENCES Myszka, David H. Machines and Mechanisms: Applied Kinematic Analysis James, V. D. (1954). Elements of Mechanism. New York and London: Wiley & Sons, Inc. Norton, R. L. (1999). Design of Machinery: An Introduction to the Synthesis and Analysis of Mechanisms and Machines, Second Edition. McGraw-Hill Inc. Reinholtz, H. M. (1987). Mechanism and Dynamics of Machinery. New York: Wiley & Sons, Inc. Machine Elements 1 15