A Tooth For A Tooth

Written for aspiring Vex IQ teams, coaches and middle-and high schoolers, this is a handbook for designing compact, rigid and efficient gearboxes for robotics applications. The book presents a mathematically-rigorous analysis of multi-stage gear systems. Parts of the book are suitable for beginner teams and younger students - most chapters and concepts are summarized and simplified to a second grade level by Professor Gearhardt, who Loves To Simplify. This book is based upon an original STEM research project completed by the authors as part of the requirements of the 2014 VEX IQ Robotics Competition Challenge, Add It Up. This research project helped the team win the overall championship (the Excellence Award) at the 2014 VEX IQ State Championship in Virginia and propelled them to the VEX IQ World Championship. Team members have collectively won 9 robotics awards at regional, state and national levels over the past three years. This research is being published to help other teams use and build upon the authors' original research on designing gearboxes, and to inspire other top teams to publish and share their research. The book starts with a brief history of gears. Gears have been in use for almost 5,000 years! You can learn about the various types of gears and the rules of gearing. Gears also occur in nature. Did you know that the insect Issus Coleoptratus uses skeletal gears to jump? Starting with a simple explanation of simple and compound gears, the book proceeds to explain the mechanical structure of multi-stage gear systems. The fundamental relation between torque and speed is next explored. When a gear system is used to increase torque by a certain factor, the angular velocity (or speed) is reduced by inverse of the same factor. Gear reductions and gear ratios are analyzed next. This is followed by consideration of the basic set of spur gears in the Vex IQ set. Did you know that just three types of gears can be used to construct 819 different gear permutations in 1-3 stages. Even more surprisingly, only a few of these are unique. Two new concepts are next introduced - Minimum Spanning Beam and Stack Height. The Minimum Spanning Beam is the smallest beam or plate that can span all the axles of a gearing permutation. It is a measure of the rigidity of the gearbox. The Stack Height is the distance from the bottom of the lowest gear to the top of the highest gear. It is a measure of the overall size of a gear permutation. Formulae for calculating the Minimum Spanning Beam and the Stack Height for various stages of gearing are derived. Finally, nonlinear stacks are considered. A link to the source data spreadsheet is provided for further study. An author biography is appended.
About the Author: Rohit Narayanan is a sixth grader who attends the Potomac School in McLean, Virginia. He is 12. He has been interested in math, science and how things work since an early age. In 2011 he was one of the 20 World Finalists in the Google-LEGO-XPrize Moonbots competition. As a 2013 FLL Championship team, Matthew, Angela and he represent Virginia in select national and international competitions. Apart from technology, science and robotics, his interests include writing plays (thrillers, especially), theatre, opera, traveling at home and abroad, writing a travel blog with his sister Megha (at http: //traipestry.wordpress.com/) and swimming. This is his second book with Angela and Matthew. Angela Wei is sixth grader who attends the Potomac School. She is 11 years old. She has lived in both America and China and is fluent in Chinese. This is her second year of competitive robotics but her first year with this team. She is interested in science, technology, art and literature. She has won awards in calligraphy, essay and piano competitions. Besides robotics, her other hobbies include coming up with stories, doodling, writing songs or pieces, finding science jokes and reading dystopian novels. Last year, she illustrated a children's book (When Disasters Come Your Way) on natural disaster preparedness. Christopher Kang is a fifth grader at the Potomac School. His middle name is Korean and so is he, though he was born in Fairfax, Virginia. This is his second year of robotics but his first with VexIQ. He has been playing soccer since he was two. He also enjoys CAD design. Megha Narayanan is a third grader at the Potomac School. Her father has been coaching robotics teams for many years and she has been looking wistfully from the sidelines. She plays the piano and goes swimming three times a week. Her favorite hobbies are inventing things, making up jokes and reading. She created the Professor Gearhardt character. Matthew Cox is 13 years old, in seventh grade. He lives in McLean, Virginia and attends Longfellow Middle School in Falls Church, Virginia. He has been to the Virginia-DC FLL State Championship twice and is headed to the Science Olympiad Nationals soon. He can synthesize hydrochloric acid, scaring the rest of the team. He likes playing with chemistry kits. He has won several elementary school spelling bees, is fluent in Pig Latin and Ib, and has visited 45 states in an RV. He wants to be a scientist when he grows up.