This textbook is an introduction to advances in mechanical machinery: Measuring and compensating for off-line to running (OL2R) machinery movement. Actually, all rotating equipments undergo a change in position during start-up (off-line) and while running that affects the alignment of the shafts. The off-line to running movement characteristics of the vast majority of rotating machinery in industries have never been measured. It is very important to know how much movement occurred before concluding that it is insignificant and can be ignored. This book is written out with strongly hoping that some characteristics of both cold and hot misalignment could be displayed for readers. The objective of the research in this book is to find out the characteristics of hot misalignment and to compensate for off-line to running machinery movement. The method for carrying out the research in this book is based on theory and experiments. The experiments are done several times for both cold and hot conditions. The main setup for the research in this book is a pair of generator-electrical motor.