Introduction to Machine Dynamics

This book introduces machine dynamics, an essential competency important for many applications such as designing robots for manufacturing/materials handling or the landing gear of an airplane, analyzing the motion of a piston in an internal combustion engine or a compressor, and designing a Mars Rover. Wherever a machine is used for force or power transmission, or a mechanism creates a desired motion, the methods studied in this book provide the fundamental knowledge needed for optimal design. Specific sections are provided on different types of mechanisms and conditions that should be met for obtaining a desired performance, including kinematic analysis of mechanisms using direct differentiation, relative motion, kinematic coefficients, and instantaneous centers. The Newton-Raphson method for solving complex nonlinear position analysis problems is discussed and the determination of dead and limit positions in mechanisms is presented. The relation between the angular velocity ratio theorem and the fundamental law of gearing is shown to provide a bridge between the concept of instantaneous centers and analyzing gears. Gears and gear trains are covered in detail and calculation of gear ratios in fixed-axis and planetary gear trains using the rolling contact equations is illustrated. Finally, power and force transmission in machines is covered. Static and dynamic cases are analyzed, and the author shows how the static solutions can provide approximations for the dynamic problems where inertia effects are not significant (low inertia and low accelerations). Application of matrix algebra for solving the system of equations of equilibrium (in statics) or equations of motion (in dynamics) is also illustrated. Because of the importance of balancing in any application involving rotating machinery, static and dynamic balancing are analyzed. The book concludes with a brief coverage of three-dimensional dynamics including Euler’s equations and gyroscopic effect. Aimed at engineering students interested in machine dynamics across a range of disciplines, the book is also ideal as a reference for practicing engineers with a good understanding of statics, dynamics, and matrix algebra.