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Mechanical Engineering · 400 Level
This is the complete lecture note for MEE 402 Theory (Mechanics) of Machines II, prepared for Mechanical Engineering students at 400 Level. You can read it online below, open it in the full viewer, or download the PDF for offline study. It pairs with the course's video lectures, so you can read and watch together.
Course code: MEE 402 Course title: Theory (Mechanics) of Machines II Course credit load: 2 Units Series 1: Force Analysis of Mechanisms and Dynamic Analysis • Part 1.1: Types of Motion in Mechanisms o Sub Part 1.1.1: Kinematics and Dynamics Defined o Sub Part 1.1.2: Types of Motion: Translation, Rotation, and General Plane Motion o Sub Part 1.1.3: Degrees of Freedom and Mechanism Mobility • Part 1.2: Force Analysis of Mechanisms o Sub Part 1.2.1: Static Force Analysis o Sub Part 1.2.2: Dynamic Force Analysis and D'Alembert's Principle o Sub Part 1.2.3: Resolution of Forces in a Mechanism • Part 1.3: Fluctuation of Kinetic Energy and Inertial Effects o Sub Part 1.3.1: Kinetic Energy Fluctuation in a Machine Cycle o Sub Part 1.3.2: Inertial Effects of Reciprocating and Rotating Masses o Sub Part 1.3.3: Complete Static and Dynamic Analysis of a Mechanism • Part 1.4: Professional Practice in Mechanism Analysis and Design o Sub Part 1.4.1: Presenting Analysis and Design Results Professionally o Sub Part 1.4.2: Conceptual Design Using Engineering Drawings o Sub Part 1.4.3: Conceptual Design Using Computer-Aided Design Introduction Every machine, however complex, is ultimately built from mechanisms whose links move, accelerate, and carry force in ways that can be precisely analysed. This Series opens the course by establishing how a mechanism's motion is classified and analysed kinematically, how the
forces acting on it are resolved and analysed both statically and dynamically, and how the resulting analysis is communicated professionally through drawings, models, and clear presentation. The aim of this Series is to equip you with the ability to identify the forces acting on a mechanism, understand the kinematics and dynamics of machine elements, and translate a conceptual design into professional engineering drawings and computer-aided design. We shall commence this Series with the types of motion in mechanisms, before turning to force analysis of mechanisms. We will then examine the fluctuation of kinetic energy and inertial effects, and conclude this Series by considering professional practice in mechanism analysis and design. Series Learning Outcomes Upon completing this Series, you should be able to: • SLO 1.1: distinguish between kinematics and dynamics in the analysis of mechanisms, • SLO 1.2: identify the types of motion exhibited by machine elements and their applications, • SLO 1.3: carry out static and dynamic force analysis of a simple mechanism, • SLO 1.4: apply the resolution of forces to a mechanism, • SLO 1.5: explain the fluctuation of kinetic energy within a machine cycle, • SLO 1.6: describe the inertial effects of reciprocating and rotating masses, • SLO 1.7: prepare a professional presentation of analysis and design results, • SLO 1.8: translate a conceptual design into engineering drawings and computer-aided design, 1.1 Types of Motion in Mechanisms 1.1.1 Kinematics and Dynamics Defined Kinematics is the branch of mechanics concerned purely with describing a mechanism's motion, its displacement, velocity, and acceleration, without reference to the forces or masses that actually cause that motion. Dynamics, by contrast, is concerned with the relationship between
motion and the forces and masses producing it, and together kinematics and dynamics form the theory of machines examined throughout this course. A mechanism's kinematic behaviour must generally be understood before its dynamic behaviour can be analysed, since the velocities and accelerations a kinematic analysis produces are themselves required inputs to the force and inertia calculations dynamic analysis depends on. This sequence, kinematics first and dynamics second, is followed consistently throughout this Series and the remainder of this course. Worked example: A mechanism's kinematic analysis produces the velocity and acceleration of each link, values that a subsequent dynamic analysis then requires as direct input to calculate the resulting inertia forces. Application: This kinematics-first sequence, introduced here, is followed consistently throughout this Series and the remainder of this course. Fill in the blank: The branch of mechanics concerned purely with describing motion, without reference to the forces causing it, is called ________. 1.1.2 Types of Motion: Translation, Rotation, and General Plane Motion A machine element can exhibit translation, in which every point of the element moves the same distance in the same direction, rotation, in which every point moves in a circular path about a fixed axis, or general plane motion, a combination of both translation and rotation occurring simultaneously within a single plane. Each of these motion types finds direct application within real machine elements: a piston within a cylinder exhibits pure translation, a flywheel about its shaft exhibits pure rotation, and a connecting rod linking a piston to a crankshaft exhibits general plane motion, simultaneously translating and rotating as the mechanism cycles. Correctly identifying which type of motion a specific element exhibits is the essential first step before its kinematics can be analysed. Worked example: A connecting rod linking a piston to a crankshaft exhibits general plane motion, simultaneously translating and rotating as the mechanism cycles through a complete revolution. Application: Correctly identifying which type of motion a specific element exhibits, introduced here, is the essential first step before its kinematics can be analysed. Fill in the blank: Motion combining both translation and rotation occurring simultaneously within a single plane is called ________ plane motion. 1.1.3 Degrees of Freedom and Mechanism Mobility The degrees of freedom of a mechanism describe the number of independent parameters needed to completely specify its configuration at any instant, with a mechanism's overall mobility
calculated from the number of links and the number and type of joints connecting them, commonly using the Kutzbach criterion. A mechanism with exactly one degree of freedom, the most common case in practical machine design, can be fully controlled by a single input motion, such as a single rotating crank, with every other link's position then determined uniquely by that one input. Correctly calculating a mechanism's degrees of freedom before attempting a detailed kinematic analysis avoids wasted effort on a mechanism that is either under-constrained or over-constrained for its intended purpose. Worked example: A simple slider-crank mechanism with exactly one degree of freedom can be fully controlled by a single rotating crank, with the piston's position determined uniquely by that one input at every instant. Application: Correctly calculating a mechanism's degrees of freedom, introduced here, avoids wasted effort on a mechanism that is under-constrained or over-constrained for its intended purpose. Fill in the blank: The number of independent parameters needed to completely specify a mechanism's configuration is called its degrees of ________. Figure 1.1: Translation, rotation, and general plane motion compared. Pilot questions 1.1 1. Distinguish between kinematics and dynamics. (Linked to SLO 1.1)
2. Explain why kinematic analysis generally precedes dynamic analysis. (Linked to SLO 1.1) 3. Describe the three types of motion a machine element can exhibit. (Linked to SLO 1.2) 4. Describe one machine element example for each type of motion. (Linked to SLO 1.2) 5. Explain the concept of degrees of freedom in a mechanism. (Linked to SLO 1.2) 1.2 Force Analysis of Mechanisms 1.2.1 Static Force Analysis Static force analysis determines the forces acting on and within a mechanism's links under conditions of equilibrium, assuming the mechanism's inertia effects are negligible, typically because the mechanism moves slowly or the analysis is concerned only with a specific static loading condition rather than the machine's full operating cycle. This analysis applies the equilibrium equations already introduced earlier in this course, requiring the sum of forces and the sum of moments acting on each individual link to equal zero, solved systematically link by link throughout the mechanism to determine the internal forces transmitted at each joint. Static force analysis, while an approximation once genuine dynamic effects become significant, remains a useful and considerably simpler first step before a full dynamic analysis is undertaken. Worked example: A slowly moving mechanism, such as a hand-operated lever mechanism, is analysed using static force analysis alone, since its inertia effects remain genuinely negligible at such a low operating speed. Application: This simpler static analysis, introduced here, remains a useful first step before a full dynamic analysis is undertaken for a faster-moving mechanism. Fill in the blank: Force analysis that determines the forces acting on a mechanism under equilibrium, assuming negligible inertia effects, is called ________ force analysis. 1.2.2 Dynamic Force Analysis and D'Alembert's Principle Dynamic force analysis accounts for the inertia forces generated by a mechanism's accelerating masses, forces that static analysis alone ignores but that can become substantial, or even dominant, once a mechanism operates at genuinely high speed. D'Alembert's principle allows a dynamic problem to be solved using the familiar methods of static equilibrium by introducing a fictitious inertia force, equal and opposite to the product of a mass and its acceleration, applied at that mass's centre of gravity, effectively converting a dynamics problem into an equivalent statics problem the analyst already knows how to solve.
This principle is applied throughout the remainder of this Series whenever a mechanism's accelerating masses must be accounted for. Worked example: Introducing a fictitious inertia force at a connecting rod's centre of gravity, equal and opposite to the product of its mass and acceleration, allows the
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