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A_Textbook_of_Theory_of_Machines 2

A textbook of theory of machines | CONTENTS CONTENTS 514 l Theory of Machines 15 Features 1. Introduction. 2. Resultant Effect of a System of Forces Acting on a Rigid Body. 3. D-Alembert’s Principle. 4. Velocity and Acceleration of the Reciprocating Parts in Engines. 5. Klien’s Construction. 6. Ritterhaus’s Construction. 7. Bennett’s Construction. 8. Approximate Analytical Method for Velocity and Acceleration of the Piston. 9. Angular Velocity and Acceleration of the Connecting Rod. 10. Forces on the Reciprocating Parts of an Engine Neglecting Weight of the Connecting Rod. 11. Equivalent Dynamical System. 12. Determination of Equivalent Dynamical System of Two Masses by Graphical Method. 13. Correction Couple to be Applied to Make the Two Mass Systems Dynamically Equivalent. 14. Inertia Forces in a Reciprocating Engine Considering the Weight of Connecting Rod. 15. Analytical Method for Inertia Torque. Inertia Forces in Reciprocating Parts 15.1. Introduction The inertia force is an imaginary force, which when acts upon a rigid body, brings it in an equilibrium position. It is numerically equal to the accelerating force in magnitude, but opposite in direction. Mathematically, Inertia force = – Accelerating force = – m.a where m = Mass of the body, and a = Linear acceleration of the centre of gravity of the body. Similarly, the inertia torque is an imaginary torque, which when applied upon the rigid body, brings it in equilibrium position. It is equal to the accelerating couple in magnitude but opposite in direction. 15.2. Resultant Effect of a System of Forces Acting on a Rigid Body Consider a rigid body acted upon by a system of forces. These forces may be reduced to a single resultant force 514 CONTENTS CONTENTS Chapter 15 : Inertia Forces in Reciprocating Parts l 515 F whose line of action is at a distance h from the centre of gravity G. Now let us assume two equal and opposite forces (of magnitude F ) acting through G, and parallel to the resultant force, without influencing the .