Page 427 - Marks Calculation for Machine Design

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Brown˙C10
CHAPTER 10
MACHINE MOTION

10.1 INTRODUCTION

In this chapter, the motion of three major groups of machine elements will be discussed:
linkages, gear trains, and wheels and pulleys. Virtually every machine has one or more
elements from one of these groups as part of its critical design requirements. All three
groups are very important to the machine designer; therefore, each group will be discussed
with examples in both the U.S. Customary and SI/metric system of units.
Linkages comprise almost an endless variety of ingenious devices used in countless
ways by machine designers to achieve specific desired motions. Virtually all these linkages
were discovered or invented rather than being formally created from an analytic analysis.
Therefore, there is usually great mystery concerning how these linkages actually achieve
the motions they produce. The purpose of this book is to uncover the mystery of machine
design formulas; therefore, this will be the purpose of this chapter. While the motion of
every conceivable linkage cannot be discussed here, there are fundamental principles and
formulas that allow machine designers to uncover for themselves the mystery of a particular
linkage of interest. These fundamental principles and formulas, which relate the relative
motions between elements of a linkage, will be discussed in detail and then will be applied
to the most classic of the linkages, the slider-crank mechanism.
Gear trains fall into two main categories: spur and planetary. There are certainly other
types of gear arrangements: bevel, hypoid bevel, and worm; however, these gear sets do
not tend to be combined in multiple configurations, and therefore, their motion is rather
straightforward. In contrast, spur-type gears, including helical and double helical gears,
are usually arranged so that more than one gear is on each shaft and more than two shafts
comprise the overall assembly. Determining the ratio of the input motion to the output
motion can be daunting for the machine designer. Even more complex motion is present in
a planetary gear train, where spur-type gears rotate about their own axis while rotating about
another axis in a planetary motion and that is where the name derives from. Determining
the ratio of the input motion to the output motion can be very intimidating to the machine
designer.
Wheels and pulleys are two of the truly fundamental machine elements, along with the
lever and fulcrum and the inclined plane. It is almost trivial to say that the motion of the
rolling wheel is important to the machine designer; however, it is, and therefore its complete
motion along a variety of paths will be presented in detail. Pulleys can either rotate simply
about a fixed axis or be combined in complex arrangements where some pulleys will rotate
about their own axis while rolling up or down a cable or belt like a rolling wheel. The usual
purpose of pulley systems is to provide a mechanical advantage, that is, provide a large
output force from a small input force; however, this typically means that the speed of the
motion is greatly reduced. These and other design considerations will be discussed.

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