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					                    ENG H191 Hands-on Lab
                    Lab 6: Gears


Background     Gears are important components in a large variety of devices. Music boxes,
               clocks, cars and CD players all have gears. The typical type of gear is a
               pinion gear however there are many other types of gears each of which meet
               the needs of certain applications.

Purpose        The purpose of this lab is to familiarize you with the concept of torque and
               rotational speed, and how these quantities may be manipulated using various
               types of gears. The uses of several types of gears will also be investigated.

Lab            The lab experience will encompass:
Experience        1. Applications of Worm Gears,
                  2. Application of Bevel gears and Rack & Pinion
                  3. Application of Spur gears and Sprockets.


Introduction   Gears are used to perform mechanical work. A common application of gears
               is to convert from one rotational speed to another through a gear train (or gear
               box or speed reducer). For example, a clock has two or three hands, each of
               which spin at different speeds but there is only one motor or power source
               turning the hands. The clock takes the speed of the input motor, gears it
               down and drives the second hand, gears it down again to drive the minute
               hand and down further to drive the hour hand. Several gears allow one power
               source to drive a variety of objects.

Torque         When rotational speed is changed through gearing, the rotational force that
               can be applied also changes. Consider a car traveling on a highway; the car is
               in high gear traveling fast but with low acceleration ability. When the car
               approaches a steep incline it down shifts, putting the car in a lower gear,
               which produces more torque but the car cannot go as fast (the engine must
               turn much faster to maintain speed).

               The transmission in a car transfers power from the engine to the drive train
               and moves the car. Power (or energy) is always conserved in any system, so
               this must also be true for a car's power train. Power, in a rotational system is
               represented by rotational speed and rotational force (or torque).

Interplay of   In linear motion the relationship of Power, Force, Work and Speed are as
Torque and     follows:
                     Power = Work / time

                     Work = Force * Distance

                      Power = Force * Distance / time

               In rotational motion the formulas are identical; we just have some different
               terms. Rotational force is called Torque and rotational distance is measured
               in radians or degrees.

                      Power = Torque * (Rotational Speed)

               A car is equipped with an engine capable of delivering a certain horsepower;
               the gear that the car is in determines how the power is converted into speed
               and torque. For a fixed power, if you need more torque the speed must go
               down or if more speed is needed then the torque available must decrease.

               A bicycle is another perfect example of how gearing controls torque and
               speed. Shifting gears on a bicycle is done to make the rider as efficient as
               possible. Low gear is for going up hills, high gear is used to go fast on
               smooth flat land.


Spur Gears    A pinion or spur gear is a simple gear used to mesh with another gear in the
              same plane. The smaller gear is commonly referred to as the pinion, while
              the larger gear is simply called the gear.

              Figure 1: Spur Gear                         Figure 2: Symbolic Representation

              The symbolic representation is used to simplify diagrams. The value, Dp, is
              optional. Dp is the pitch diameter, which can be used to find the gear ratio,
              (Dpgear / Dppinion). Gear ratio can also be found counting the number of teeth
              on each gear:

                    Dp gear        NumberOfGearTeeth
                   Dp pinion       NumberOfPinionTeeth

Bevel Gears   Bevel gears are designed to mesh with each other at different angles
              (commonly 90°). This type of drive is used to change the axis of rotation. A
              differential (which is discussed later in this lab) uses bevel gears to control its

              Figure 3: Bevel Gears

Rack and         A pinion turns and moves a rack in order to convert rotational motion into
Pinion           linear motion. Rack and pinion steering is just one of many applications of
                 this gear set.

                 Figure 4: Rack and Pinion Gear Set

Worm gears       This type of gear, like the bevel gears, converts the axis of rotation by 90°. A
                 worm gear is used for high ratio speed reduction. When a worm rotates, it
                 moves just one tooth on its meshing gear. (Double helix worms move two
                 teeth.) Because of the shape of worm gear, the driven gear must be specially
                 made in order to mesh properly.

                 Figure 5: Worm Gear

A note on gear When expressing the ratio of some gearbox, the convention is normally to
ratios         write the output rotational speed over the input rotational speed. So high gear
               would be used for faster speeds in a car or on a bicycle for example, and low
               gear would output more torque.

                                    OutputSpeed    InputTorque
                      GearRatio                
                                     InputSpeed   OutputTorque

Make sketches of all equipment used in class; include them in your lab report.

of Worm         Automobile Window Lift Motor
                     Take the gear assembly apart. Watch out for messy grease!
                     Observe how the given gear head motor unit would move and which
                       gears are the input/output, respectively.
                     Determine the gear ratio. # of teeth on the output gear : # of worm gears.

                Using Legos™
                     Observe the motion of the Lego™ robot gripper that is given.

                     Use the robot gripper to grab items. Notice how the worm gear is used to
                     provide holding power without energizing the motor.

                     What is the gear ratio of the window lift motor? How did you determine

                     How does the Lego™ worm gear robot gripper still hold objects without
                     a continuously applied force? Compare this mechanism to a crescent
                     wrench. Use the word 'back-driven' in your answer.

Bevel Gears     A differential is used to transfer power from the drive shaft to the wheels of
and Racks       the car. When a car turns a corner the wheels travel different distances and so
                move at different speeds. Move the Lego™ differential unit provided to
                prove this to yourself. A differential provides equal force to each wheel while
                allowing different speeds at each wheel. For more information on
                differentials, a very good description with animations can be found at

                     Understanding a differential: Explain what would happen to the simple
                     differential used in lab if one tire is sitting on ice and the other tire is on
                     clean pavement and the drive shaft is spinning? Will the car move?

Pinions and
Sprockets     Bicycle Gearing
              A bicycle demonstrates the trade off of speed and torque. Experiment with the
              speed and force attainable at different gear ratios. Since a bicycle uses a
              chain the direction of rotation of the output shaft (sprocket) is not reversed as
              it is with a pair of gears. For the given bicycle, find the gear ratio (sprocket
              combination) for:
                                a) Max Torque
                                b) Max Speed
                                c) Redundant combinations
              For this experiment, create a table that shows all the possible gear
              combinations. Show which ones are redundant. (Measure wheel diameter
              and length of pedal arm).

              Gear Boxes
              Using the Legos™ set provided build a simple gearbox that has a gear ratio of


                 Draw a sketch of the gearbox you made for the 1:75 gear ratio. Be sure
                  you could reproduce the gearbox from this sketch.
                    (Advice: Use symbolic representations for the gears (no teeth), and use
                    a top view.)

                 If a rider can pedal no faster than 5 revolutions per second, what is the
                  fastest he/she can make the bicycle in the lab go.
                  Hint: determine the diameter of the rear tire and the length of the pedal.

                 A biker weighs 175 lbs and his bike weighs 25 lbs. What is the steepest
                  hill the rider can climb? (Assume the rider can put all of his/her weight
                  on the pedal.)

                 Would a wrench driven by an electric motor have a very high or a very
                  low gear ratio?
                   Hint: Read the note on gear ratios earlier in this write up.


Format          Lab report format (INDIVIDUAL or TEAM) will be announced in lab.
                Follow the sample lab report format provided.

General          Include sketches of all mechanisms studied and built.
                 Be sure to provide answers to all questions presented.


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