## Archive for March, 2017

### The Difference Between Driven and Driving Pulleys

Friday, March 31st, 2017
 Last time we introduced two historical legends in the field of engineering who pioneered the science of mechanical power transmission using belts and pulleys, Leonhard Euler and Johann Albert Eytelwein.   Today we’ll build a foundation for understanding their famous Euler-Eytelwein Formula through our example of a simple mechanical power transmission system consisting of two pulleys and a belt, and in so doing demonstrate the difference between driven and driving pulleys.     Our example of a basic mechanical power transmission system consists of two pulleys connected by a drive belt.   The driving pulley is attached to a source of mechanical power, for example, the shaft of an electric motor.   The driven pulley, which is attached to the shaft of a piece of rotating machinery, receives the mechanical power from the electric motor so the machinery can perform its function. The Difference Between Driven and Driving Pulleys          Next time we’ll see how driven pulleys can be made to spin at different speeds from the driving pulley, enabling different modes of operation in mechanical devices. Copyright 2017 – Philip J. O’Keefe, PE Engineering Expert Witness Blog ____________________________________

### Johann Albert Eytelwein, Engineering Trailblazer

Monday, March 20th, 2017
 They say necessity is the mother of invention, and today’s look at an influential historical figure in engineering bears that out.   Last week we introduced Leonhard Euler and touched on his influence to the science of pulleys.   Today we’ll introduce his contemporary and partner in science, Johann Albert Eytelwein, a German mathematician and visionary, a true engineering trailblazer whose contributions to the blossoming discipline of engineering led to later studies with pulleys.   Johann Albert Eytelwein, Engineering Trailblazer         Johann Albert Eytelwein’s experience as a civil engineer in charge of the dikes of former Prussia led him to develop a series of practical mathematical problems that would enable his subordinates to operate more effectively within their government positions.   He was a trailblazer in the field of applied mechanics and their application to physical structures, such as the dikes he oversaw, and later to machinery.   He was instrumental in the founding of Germany’s first university level engineering school in 1799, the Berlin Bauakademie, and served as director there while lecturing on many developing engineering disciplines of the time, including machine design and hydraulics.   He went on to publish in 1801 one of the most influential engineering books of his time, entitled Handbuch der Mechanik (Handbook of the Mechanic), a seminal work which combined what had previously been mere engineering theory into a means of practical application.     Later, in 1808, Eytelwein expanded upon this work with his Handbuch der Statik fester Koerper (Handbook of Statics of Fixed Bodies), which expanded upon the work of Euler.   In it he discusses friction and the use of pulleys in mechanical design.  It’s within this book that the famous Euler-Eytelwein Formula first appears, a formula Eytelwein derived in conjunction with Euler.   The formula delves into the usage of belts with pulleys and examines the tension interplay between them.     More on this fundamental foundation to the discipline of engineering next time, with a specific focus on pulleys. Copyright 2017 – Philip J. O’Keefe, PE Engineering Expert Witness Blog ____________________________________

### Leonhard Euler, a Historical Figure in Pulleys

Thursday, March 9th, 2017
 Last time we ended our blog series on pulleys and their application within engineering as aids to lifting.   Today we’ll embark on a new focus series, pulleys used in mechanical devices.   We begin with some history, a peek at Swiss scientist and mathematician Leonhard Euler, a historical figure credited to be perhaps the greatest mathematician of the 18th Century.     Leonhard Euler, a Historical Figure in Pulleys         Euler is so important to math, he actually has two numbers named after him.   One is known simply as Euler’s Number, 2.7182, most often notated as e, the other Euler’s Constant, 0.57721, notated γ, which is a Greek symbol called gamma.   In fact, he developed most math notations still in use today, including the infamous function notation, f(x), which no student of elementary algebra can escape becoming intimately familiar with.     Euler authored his first theoretical essays on the science and mathematics of pulleys after experimenting with combining them with belts in order to transmit mechanical power.   His theoretical work became the foundation of the formal science of designing pulley and belt drive systems.   And together with German engineer Johann Albert Eytelwein, Euler is credited with a key formula regarding pulley-belt drives, the Euler-Eytelwein Formula, still in use today, and which we’ll be talking about in depth later in this blog series.     We’ll talk more about Eytelwein, another important historical figure who worked with pulleys, next time. Copyright 2017 – Philip J. O’Keefe, PE Engineering Expert Witness Blog ____________________________________