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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.
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