# Mechanicsof Rigid Bodies and Theory of Machines

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### 1.1.1 **ME 161/2 Basic Mechanics **

*The same course is offered for different groups of students in the first semester and second semesters as ME 161 and ME 162, respectively. The course explores the following topics:*

Units of measurement (SI) and dimensions, Laws of mechanics, Characteristics of a force, force systems and, Moment of a force, Vector representation of forces, Free-body diagrams, Resultant and Equilibrium of system of coplanar and spatial force systems. Centroid: Determination of centroid from first principle, centroid of composite sections. Structural Analysis:** **Two-dimensional trusses using the methods of joints and sections; Simple frames and Machines. Friction:** **Laws of dry friction, angle of friction, problems involving dry friction. Simple Machines:** **Laws of friction, Definitions and calculations of mechanical advantage, velocity ratio and efficiency, self-locking and overhauling in machines, types of simple machine. Kinematics of a Particle: Rectilinear, Rotational and Curvilinear Motions of particles, Dependent and Relative Motion Analysis of Two Particles. Kinetics: Equation of Motion for a system of particles. Work and Energy: Work, Energy, Power, Efficiency, Principle of Conservation of Energy for particles. Impulse and Momentum: Linear impulse and momentum, Conservation of linear momentum for system of particles. Kinetics of a Rigid Body: centre of gravity, mass moment of inertia from first principle, parallel axis theorem, moment of inertia of composite bodies, and radius of gyration. Planar Kinetic Equations of Motion: Translation, rotation about a fixed axis and general planar motion. Impulse and Momentum: Impulse and momentum for rigid bodies. Work and Energy for rigid bodies: Energy equations for rigid bodies, Principle of Conservation of Energy for rigid bodies. Equation of motion of simple harmonic system, calculations involving period, frequency, displacement, velocity and acceleration, equivalent stiffness for springs in series and in parallel, equivalent mass of a spring, energy method.

### 1.1.2 ** ME 164 Statics of Solid Mechanics **

Fundamental Concepts: Basic terminologies in mechanics, laws of mechanics, Units of measurement (SI) and dimensions, Newton's Laws of Motion. Characteristics of a force, System of Forces, Vector representation of planer (2D) and spatial (3D) forces. Resultant and Equilibrium of coplanar forces: Force Systems, Triangle law of forces, resolution and resultant of forces, moment of a force, Varignon’s theorem, free-Body diagrams and Equilibrium Equations. Structural Analysis: Assumptions, Two-dimensional trusses using the methods of joints and sections, Frames and machines. Friction: Frictional force, laws of dry friction, angle of friction, Problems involving dry friction, rope friction, square-and v-threaded screws, rolling resistances. Simple Machines: Definitions, law of machine, mechanical advantage, velocity ratio, and efficiency, self-locking and overhauling in machines, types of simple machines. Method of Virtual Work: Work done by Forces and moments. Centre of gravity and area moment of inertia: centre of gravity and centroid of a body, determination of centroid from first principle, parallel and perpendicular axes theorems, centroid of composite sections, experimental determination of centre of gravity, Resultant of distributed line loads, liquid pressure and flexible cables.

### 1.1.3 **ME 261 Dynamics of Solid Mechanics**

Kinematics of a Particle: Continuous and Erratic Rectilinear Motions, Rotational Motions, Curvilinear Motions including Projectiles, Dependent and Relative Motion Analysis of Two Particles. Kinetics of a Particle: Equation of Motion for a System of Particles. Work and Energy: Work, Energy, Power, Efficiency, principle of Conservation of Energy. Impulse and Momentum: Principle of Linear impulse and momentum, Conservation of linear momentum for system of particles, Impact, Angular momentum, moment of a force and angular moment momentum, principle of angular impulse and momentum. Centre of Gravity and mass moment of inertia: centre of gravity from first principle and composite bodies, mass moment of inertia, radius of gyration, parallel axis theorem, and moment of inertia of composite bodies. Kinetics of a Rigid Body: Planar Kinetic Equations of Motion including Translation, rotation about a fixed axis and general planar motion. Work and Energy for a rigid body: Kinetic energy, work a force and a couple, principle of conservation of energy for rigid bodies. Impulse and Momentum for a rigid body: Linear and angular momentum, principle of impulse and momentum, conservation of momentum, eccentric impact. Rotary balancing: single and multi-planes using graphical and analytical methods.

### 1.1.4 **ME 262 Mechanism Synthesis and Analysis I**

*This course is an introductory course in dynamics of machinery. It covers underlying theories and techniques for analysis and synthesis of mechanical systems which consist of planar linkages, mechanical drives and cams. It places emphasis on the use of graphical techniques and computer simulation tools. The topics covered include*

Fundamentals: Definitions and terminology, degrees of freedom, types of motion, mechanisms and structures, motors and drives. Dynamics of Linkages: Analysis of position, velocity, acceleration and dynamic forces in linkages using both graphical and analytical methods.

Graphical Linkage Synthesis: Introduction to type synthesis, function, path and motion generations, Dimensional synthesis up to three positions including quick-return mechanisms Grashof Condition for four-bar linkage, Inversion, introduction to Coupler and Cognates.

Cam Design and Dynamic Analysis: Cam terminology, single and double dwell cam design, displacement diagrams and polynomial functions, pressure angle and radius of curvature, Practical Design and Manufacturing considerations. Transmission of rotational motion: Gears and gear trains including Epicyclic/Planetary Trains, roller drives, belt drives and Chain drives.

### 1.1.5 ** ME 361 Dynamics of Machinery**

This course is a continuation of ME 262, which is course in dynamics of machinery. It covers: Dynamics of mechanisms and machines in three-dimensions using Cartesian, cylindrical and spherical coordinate systems. Balancing of reciprocating masses including linkages, multi-cylinder in-line, radial and V-engines. Vector treatment of laws of dynamics: Cartesian, cylindrical and spherical systems. Fluctuation of energy and speed in machines: crank-effort and turning moment diagrams, flywheels. Inertia forces and torques in mechanisms. Engine Dynamics. Cam Dynamics. Governors. Gyroscopic motion: simple theory of gyroscopic couple, gyroscopic effects in machinery and vehicles, applications of gyroscopes.

### 1.1.6 **ME 462 Mechanism Synthesis and Analysis II**

Logical synthesis of mechanisms. Freudenstein’s equation. Coordination of Crank velocities. Design of up to six-bar mechanism using algebraic method for a given output function with 4th order approximation. Coupler Curves and Cognates. Motion and Path generation for common link mechanisms. Robert’s theorem. Error estimation in a given synthesis. Optimisation using Chebyscher’s theorem. High speed cam dynamics. Analytical derivation of cam profiles. Introduction to spatial mechanisms.