17 Cams and Gears Chapter Objectives Explain the purposes and applications of cams. Describe the three main types of cam motion. Develop a cam- related displacement diagram and profile. Describe the infor- mation needed for a typical gear drawing. Draw gear teeth using the simplified board- drafting method. Create a CAD- generated gear-tooth drawing. • • • • • • Section 17.1 Cams and Cam Drawings Section 17.2 Gears and Gear Drawings From Controversy to Acceptance Like many designs, the one for the Vietnam Memorial was controversial. Over the years, however, the memorial itself has come to be accepted. Why do you think this has happened? 576
Transcript
17 Cams and Gears
Chapter ObjectivesExplain the purposes and applications of cams.Describe the three main types of cam motion.Develop a cam-related displacement diagram and profi le.Describe the infor-mation needed for a typical gear drawing.Draw gear teeth using the simplifi ed board-drafting method.Create a CAD-generated gear-tooth drawing.
•
•
•
•
•
•
Section 17.1 Cams and Cam Drawings
Section 17.2 Gears and Gear Drawings
From Controversy to Acceptance Like many designs, the one for the Vietnam Memorial was controversial. Over the years, however, the memorial itself has come to be accepted. Why do you think this has happened?
576
Drafting Career
Maya Lin, then a 21-year-old Yale student, submit-ted the design for the Vietnam memorial. She pro-posed cutting a wedge in the earth from which two long, horizontal, perpendicular granite walls appeared to grow. She envisioned that the healing process in the earth would parallel the healing of visitors to the memorial.
Lin’s concept was chosen and built. As designed,
the granite walls were inscribed with the names of approximately 60,000 men and women who lost their lives during the Vietnam confl ict. She hoped ‶these names, seemingly infi nite in number, [would] convey the sense of overwhelming numbers, while unifying these individuals into a whole.″
Academic Skills and AbilitiesMathEnglishSocial studiesPhysicsSocial studiesComputer useDrafting, drawing
Career PathwaysA bachelor’s degree is required for most entry-
level positions. After licensure and three to fi ve years of on-the-job training, architects eventually manage entire projects, advance to supervisory or managerial positions, become partners in estab-lished fi rms, or set up their own practices.
•••••••
Go to glencoe.com for this book’s OLC to learn more about Maya Lin and the Vietnam Memorial.
Preview A basic element in a machine, a cam, is noted by its irregular outline or curved groove. What challenges would this design present to you as a drafter?
Content Vocabulary• cam• follower• displacement
diagram
• uniform motion• harmonic
motion
• uniformly accelerated and decelerated motion
• rectangular array
• polar array
Academic VocabularyLearning these words while you read this section will also help you in your other subjects and tests.• transmit • minimum
Graphic Organizer
Use a chart like the one below to organize notes about cams.
Go to glencoe.com for this book’s OLC for a downloadable version of this graphic organizer.
Cams and Cam Drawings
English Language Arts
Apply strategies to interpret texts (NCTE)
Use written language to communicate eff ectively (NCTE)
Mathematics
Measurement Understand measurable attributes of objects and the units, systems, and
processes of measurements (NCTM)
Measurement Apply appropriate techniques, tools, and formulas to determine measurement (NCTM)
CamsHow is a cam’s shape relevant to the motion it produces?
A mechanism is a system of mechanical parts connected to a motion or drive source such as a motor. Its parts include cams, gears, belts, linkages, shafts, bearings, and housings (see Figure 17-1). Most of these parts are of little use alone, but in combination they serve many purposes and are therefore important elements of machine design.
When a machine part known as a camrotates, it transmits a specifi c, continu-ous motion to another machine part, thefollower. The cam drives the follower. Both parts make up the cam mechanism. The cam’s design determines the follower’s motion and path. A cam usually has an irregular curved outline or a curved groove but can have an unlimited variety of shapes.
This motion is needed in all automatic machinery. Therefore, cams are important to
Figure 17-1
Cams and gears are necessary parts of machines.
the automatic control and accurate timing found in many types of machinery.
Figure 17-2 illustrates how the cam works. The rise, also called the stroke, takes place within one-half of a full revolution, or 180°. The movement is repeated every 360°, or once during each full revolution.
Cams and FollowersAll cams can be thought of as simple
inclines that produce or transmit a prede-termined motion. Depending on its specifi c shape and size, a cam transmits motion to its follower in a particular way. For example, a plate cam such as that in Figure 17-3 has a follower that moves up and down as the cam turns on the shaft. A cylindrical cam (see Figure 17-3) has a follower that moves back and forth parallel to the axis of the shaft. A grooved cam (see Figure 17-3) has a follower that follows the groove, moving in an irregu-lar pattern as the cam turns on a shaft.
Several other types of cams have been devel-oped for specialized uses, such as a cam for operating the valve of an automobile engine (see Figure 17-4). This cam has a fl at follower that rests against the face of the plate cam. SeeFigure 17-5 for several other types of cams:
A slider cam moves the follower up and down as the cam moves back and forth.
•
Figure 17-2
Cam action and terminology
Section 17.1 Cams and Cam Drawings 579
PLATE CAM
CYLINDRICAL CAM
GROOVED CAM
SLIDER
PIVOTEDROLLER CYLINDRICAL
ROLLER
OFFSET PLATE
FOLLOWER
A B C
CAM
VALVE
CAM UP – VALVE OPEN Figure 17-3
Common types of cams
Figure 17-4
Automobile valve cam
Figure 17-5
Types of cams
Figure 17-6
Plate cam followers
An offset plate cam has as an off-center point follower.A cam with a pivoted roller follower trans-mits motion at a 90° angle.A cylindrical roller cam may employ a swinging follower.
Refer to Figure 17-6 for three types of fol-lowers for a plate cam. The roller follower (17-16A) reduces friction to a minimum, so it transmits force at high speeds. The point follower (17-16B) and the fl at-surface follower (17-16C) are made with a hardened surface to reduce wear from friction. These followers are generally used with cams that rotate slowly.
Plate cams require a spring-loaded follower to ensure that contact is made throughout a full revolution. The cam’s lifting of the fol-lower occurs as the result of direct contact between the cam and follower. However, the cam and follower are normally not in con-tact during a drop (fall) or dwell (rest) unless an outside pressure causes contact. Outside pressure is exerted by a spring pushing the follower against the cam to ensure direct contact.
Identify In what pattern does a grooved cam follower move?
•
•
•
Courtesy of C
amco
580 Chapter 17 Cams and Gears
TRAVEL
RISE
A
B C
DE
F
ROLL CENTERS
ROLLER Ø
CAM FACE
RISE 1.875120°
3'
2'
1 '
B'
30°DWELL
90°DROP 1.250
30°DWELL
90°DROP .625
RISE 1.875
B
32
1A
A
X
D5
4C
4'
5'
YD'
F
7'
6'
E67
O
W
B'B
1.875
RISE120° 30°
DWELL30°
DWELL360°
90°DROP
90°DROP
1.250
.625
A
B
CAM DISPLACEMENT DIAGRAM
A
D' E
C
BASECIRCLE
Displacement DiagramsA cam’s shape determines the direction of
the follower’s motion (see Figure 17-7A). Adisplacement diagram such as the one in Figure 17-7B shows the motion the cam pro-duces through one revolution. The length of the displacement diagram represents one revolution of 360°. The height of the diagram represents the total displacement stroke of the follower from its lowest position—in this case, 1.875�.
Cam MotionCams can be designed so that the follow-
ers have three different types of motion. A displacement diagram can be used to plot the different types of motion.
Uniform MotionCams that follow uniform motion
(steady motion) are suitable for high-speed operations. Technically, uniform motion is “straight-line” movement in which time and distance are directly proportional. In other words, equal distances on the rise are made for equal distances on the travel. However, to avoid a sudden jar at the beginning and end of the motion, designers use arcs to change it slightly. The magenta line of the displacement diagram in Figure 17-8 represents uniform motion that has been modifi ed in this way.
The cam in Figure 17-7A displays uniform motion. The length, or time, of a revolution is divided into convenient parts. The parts are proportional to the number of degrees for each action based on one full 360° revolution. Each part or division is called a time period. These pro-portional parts are identifi ed as A, 1�, 2�, B�, C, 4�, 5�, D�, E, 6�, 7�, and back to A, as shown. Each proportional part or time period is a 30° angular division of the base circle in Figure 17-7A.
In Figure 17-7A, point O is the center of the cam shaft, and point A is the lowest position of the center of the roller follower. The cen-ter of the roller follower must be raised 1.875�
with uniform motion during the fi rst 120° of a
Figure 17-8
Displacement diagram of uniform motion
Figure 17-7
Cam displacement diagram for one 360° revolution
Section 17.1 Cams and Cam Drawings 581
TRAVEL
RISE
A
B C
D
2
4
6
2
4
6
2 4 6
TRAVEL
RISE
A
B C
D1 2 3 4 5
12
34
5
revolution of the shaft. It must then dwell for 30°, drop 1.250� for 90°, dwell for another 30°, and drop .625� during the remaining 90°. The shaft is assumed to revolve uniformly (with constant speed).
Harmonic MotionOther cams follow harmonic motion,
which is a smoother-acting motion that fol-lows a harmonic curve. Like uniform-motion cams, harmonic-motion cams are suitable for use with high speeds. They are also used when a smooth start-and-stop motion is needed.
The method for plotting a harmonic curve is shown in Figure 17-9. To draw harmonic motion, fi rst draw a semicircle with the rise as the diameter. Divide the semicircle into eight equal parts, using radial lines. Then divide the travel into the same number of equal parts. Project the eight points horizontally from the semicircle until they intersect the correspond-ing vertical projections, as shown. Finally, draw a smooth curve through all eight points.
Uniformly Accelerated and Decelerated Motion
Cams that employ a steadily increasing and decreasing speed rather than a con-stant speed produce a uniformly acceler-ated and decelerated motion that is very smooth. A diagram of this motion would fol-low a parabola, or parabolic curve. Recall that a parabola is formed when a cone is sliced vertically at any place other than through the center.
To design a cam with uniformly accelerated and decelerated motion, fi rst divide the rise into parts proportional to 1, 3, 5, ... , 5, 3, 1 (see Figure 17-10). Note that the parts are not of
equal size. Then divide the travel into the same number of parts—in this case, into equal parts. Project the points horizontally from the rise until they intersect the corresponding vertical projections. Finish by drawing a smooth curve through all the points of intersection, as shown.
Identify Of the cams discussed, which are appropriate for high-speed use?
Creation of Cam Profi les What does a cam profi le include?
Before you begin to draw your own cam profi le, review the cam-related terminology in Figure 17-7. The cam there has fi ve impor-tant features: a rise, a dwell, a drop, another dwell, and another drop.
Draw a Cam Profi le Using
Board-Drafting TechniquesTo begin your drawing, follow these steps.
1. Rise. Divide the rise AB, or 1.875�, into a number of equal parts. The illustration uses four parts, but eight parts would make the layout more accurate. The rise occurs from A to W (120°). Divide it into the same number of equal parts as the rise (four at 30°) with radial lines from O. Using center O, draw arcs with radii O1, O2, O3, and OB until they locate 1�, 2�, 3�, and B� on the four radial lines. Use an irregular curve to draw a smooth line through these four points.
Figure 17-9
Displacement diagram of harmonic motion
Figure 17-10
Displacement diagram of uniformly accelerated and decelerated motion
582 Chapter 17 Cams and Gears
45°90°
DWELL
90°DWELL
HARMONICMOTION
HARMONICMOTION
R 7.00
.50 X .25KEYWAY
R 4.500
11.50
Ø2.25
Ø2.25
3.50
1.50 1.00
O4.00O4.00
2.0022.000O
2. Dwell. First draw an arc B�C (30°) using radius O�B�. This allows the follower to be at rest, because it will stay at the same distance from center O.
3. Drop. At C, lay off CD (1.250�) on a radial line from O. Divide it into any number of equal parts (three are shown). Next divide the arc XY (90°) on the base circle into the same num-ber of equal parts (three). Draw three radial lines from center O every 30°. Then draw arcs with center O and radii O4, O5, and OD to locate points 4�, 5�, and D� on the three radial lines. Using an irregular curve, draw a smooth line through points 4�, 5�, and D�.
4. Dwell. Draw an arc D�E� (30°) with radius OD. This will provide the constant dis-tance from center O to let the roller fol-lower be at rest.
5. Drop. In the last 90° of a full revolution, the roller will return to point A. It will move through a distance EF, or 6.25�. First divide EF into any number of equal parts (three are shown). Then divide arc FA into the same number of equal parts. Next draw radial lines every 30°. Draw arcs with radii O6 and O7 to locate points 6� and 7�. Using the irregular curve as a guide, draw a smooth curve through points E, 6�, 7�, and A. This fi nishes the roll centers.
6. Finish the Profi le. Using the line-of-roll centers as a centerline, draw successive arcs with the radius of the roller as inFigure 17-7. Then use an irregular curve
to draw the cam profi le. The profi le should be a smooth curve tangent to the arcs you drew representing the roller.
Refer to Figure 17-11 for another drawing for a face, or plate, cam. Note that the amount of movement, or rise, is given by showing the radii for the dwells (4.50� and 7.00�). Harmonic motion is used, and two rolls seem to be work-ing on this cam. See Figure 17-12 for drawing of a barrel cam (cylindrical cam) with a displace-ment diagram. The diagram shows two dwells and two types of motion. Note that the distance traveled from center to center, called throw, is 1.50�. Practice your technique by drawing the displacement diagrams for these two cams.
Defi ne What is throw?
Draw a Cam Profi le Using CADThe profi le of the cam in Figure 17-7 has
fi ve important features:
rise of 1.875� over 120°dwell, or rest period, over 30°drop of 1.250� over 90°dwell over 30°drop of .625� over 90°
The development of this cam profi le is an interactive process that involves creating an accompanying cam displacement diagram. Follow these steps to create both of these.
•••••
Figure 17-11
A drawing of a plate cam
Section 17.1 Cams and Cam Drawings 583
.750 .001+
R.88
R.88
.750
.750
1.5003.000
O.7502.7500
140°
360°
110°
90°DWELL
DWELL20°
.25 X .12
20°DWELL
CIRCUMFERENCE OF CAM
90°DWELL
110°UNIFORMMOTION
140°HARMONIC
MOTION
TH
RO
W
O2.50
O1.75
1. Set up a drawing fi le with limits of 0,0 and 15,12.
2. Create the base circle for the cam profi le with a diameter of 3.88�.
3. Place the hole in the center of the cam by creating a Ø1.000 circle using the same center point as the base circle. Remember to use the Center object snap to locate the center.
The next step involves the use of the ARRAY command. AutoCAD provides two types of arrays for 2D drawings: rectangular and polar. A rect-angular array is one in which an object is cop-ied into a specifi ed number of rows and columns (see Figure 17-13A). A polar array copies the object a specifi ed number of times to fi ll a circle or arc that you specify (see Figure 17-13B).
4. Divide the circle into 30° increments. To do this, fi rst create a vertical 4� line
with its starting point at the center of the base circle (see Figure 17-14). Then enter the ARRAY command and pick the vertical line. Enter P to select a polar array. Divide the circle’s 360° into equal 30° divisions. Enter 12 (360° � 30 �
12 items in the array) as the number of items, and accept the default angle to fi ll of 360°. Enter Y (Yes) to rotate the arrayed objects. The arrayed lines appear, dividing the circle into perfect 30° increments.
5. Use the DIST command to measure the distance from the intersection of the base circle and one of the 30° division lines to the intersection of the base circle and the next division line as in Figure 17-15. This provides the length for each 30° increment on the displacement diagram. Each incre-ment will be 1.00�.
6. Start the cam displacement diagram by laying out the base line AA. Begin the line near the lower left corner of the drawing area. It should be equal to 12 segments of 1.00� each, or 12.00� total. Enter the PDMODE command and enter a new value of 4. This value creates tic marks at the location of points and divi-sions. Then enter the DIVIDE command, select the base line, and divide it into 12 parts. The tic marks appear at the required 30° intervals.
Figure 17-12
A drawing of a cylindrical cam
A B
Figure 17-13
(A) A rectangular array and (B) a polar array
Figure 17-14
Create a 4� vertical line up from the center of the base circle.
584 Chapter 17 Cams and Gears
1.875
120°RISE
30°DWELL
90°DROP
30°DWELL
90°DROP
1.250
.625
B
3
21A
7. Using the base line and the rise, dwell, and drop information in the bulleted list at the beginning of this section, com-plete the cam displacement diagram as in Figure 17-16. Add a small fi llet with a radius of .30 at each end of each segment of the diagram, as shown in the fi gure. Note: For the fi llet at the beginning of the base line, you will need to create a tem-porary line starting at the left end of the base line and extending to the left. Fillet the displacement line to this line to get the appropriate curve. Then delete the temporary line and, if necessary, extend the base line to meet the fi llet.
8. Dimension the displacement diagram as shown in Figure 17-16.
Explain For what purpose would you use the DIST command?
Now you can return to the cam profi le and continue to develop it. To do this, you will actually develop the follower’s path fi rst. Notice that the follower in this case is a roller.
The roller path is the most critical part of the profi le because the purpose of the entire cam development is to create a cam that makes the roller exhibit the specifi c rise, dwell, and drop behavior stated in the bulleted list at the beginning of this section. Follow these steps:
1. Trim the vertical division line to the top of the base circle. Then extend a new line AB from the intersection of the vertical divi-sion line with the top quadrant point of the circle, extending upward by 1.875� (the specifi ed rise). Use the DIVIDE command to divide this line into four equal segments, corresponding to the four 30° segments in the rise as in Figure 17-17. Change PDMODE to 3 to see the division points. Note: The points in Figure 17-17 are labeled with letters for your reference only. There is no need to add them to the drawing.
2. Using base circle center O, create circles with radii O1, O2, O3, and OB to locate points 1�, 2�, 3�, and B� on the four radial lines (see Figure 17-18).
3. Enter the ARC command, and create an arc that starts at point A, has a center point at point 1�, and ends at point 2�. Be sure to use the Intersection object snap to place the arc exactly. Then create a second arc that starts
Figure 17-15
Measure the distance between two consecutive radial lines along the base circle by entering the DIST command and picking the points shown here.
Figure 17-16
The fi nished displacement diagram
Figure 17-17
Divide line AB into four equal parts. Note: In this and the following illustrations, some elements are shown in color for clarity. It is not necessary to use these colors in your CAD drawing.
Section 17.1 Cams and Cam Drawings 585
B
3
2
1
A1'
2'
3'
B'
B
3
2
1
A 1'2'
3'
B'
B
3
2
1
A1'
2'
3'
B'
0
C
at point 2�, has a center point at point 3�, and ends at point B�. The result is a smooth curve that connects point A with point B�
as in Figure 17-19. This line defi nes the path of the center of the roller through the rise segment of the cam revolution. Delete the circles with radius 1, 2, and 3, but do not delete the circle with radius B.
4. The next phase is a dwell of 30° duration. Throughout a dwell, the roller remains at exactly the same distance from the cen-ter O. Therefore, you can use a portion of the circle with radius B to defi ne the path of the roller. Trim the circle so that only arc B�C remains as in Figure 17-20.
5. Now the roller needs to drop by 1.250�
over the next 90°. The procedure will be similar to the one used to defi ne the rise. First delete radial line OC. Then create a new line CD. The line should start at point C and extend toward center point O for 1.250� (the specifi ed drop), which means that the line should be at a 120° angle. At the To point prompt, enter @1.25 < 120.
6. Divide line CD into three equal parts using the DIVIDE command. Create three circles with center O and radii of O4, O5, and OD to locate points 4�, 5�, and D� as in Figure 17-21.
7. Enter the ARC command, and connect points C, 4�, and 5�. Reenter the ARC command and start the second arc at point 5�. Estimate a center point about halfway between point 5� and point D�, and end the arc at point D�. The arcs should form a smooth curve. If your
Figure 17-18
A smooth curve through points A, 1�, 2�, 3�, and B� defi nes the rise of the roller.
Figure 17-19
Create a smooth curve through the points using AutoCAD’s ARC command.
Figure 17-20
Trim the circle with radius B so that only the segment between B� and C remains.
586 Chapter 17 Cams and Gears
B
3
2
1
A1'
2'
3'
B'
0
C
D
54
4'
5'
D'
B
3
2
1
A 1'2'
3'
B'
0
C
D
54
4'
5'
D'
E
second arc does not connect smoothly with the fi rst one, pick the arc to select it, and pick the middle grip (blue box) so that the grip turns red. Move the grip as necessary to change the shape of the arc to provide a smooth curve. This com-pletes the fi rst drop. Delete the circles with radius 4 and 5, but do not delete the circle with radius D.
8. The next phase is another dwell of 30° duration. Trim the circle so that only arc D�E remains as in Figure 17-22.
9. The fi nal drop begins at point E and ends at point A; in other words, it drops by .625� over 90°. The portion of radial line OE that lies between the base circle and point E is, by defi nition, .625�. There-fore, trim away the remainder of line OE, leaving only segment EF. Then divide segment EF into three equal segments using the DIVIDE command, and create circles with center O and radii 6, 7, and F to create points 6�, 7�, and F�. Follow-ing the same procedure you used for the fi rst drop, defi ne the path of the roller through these points.
10. When you have completed the roller path, delete the remaining circles includ-
ing the base circle, but do not delete the Ø1.00� hole at the center of the cam. Also delete the radial lines and the division points. Enter the PEDIT command and pick anywhere on the roller path. When AutoCAD informs you that the selection is not a polyline, choose to convert it to a polyline. Then enter the J (Join) option, and select the remaining segments of the roller path following a counterclock-wise path to change the entire path into a single polyline. End the PEDIT com-mand and pick the roller path to ensure that all segments were added. Note: If the last segment did not add correctly, reen-ter PEDIT, pick the polyline, and enter C (Close). The closing segment will follow exactly the same path as the underlying segment. Delete the underlying segment. Then select the polyline and change its linetype to Center. With the polyline still selected, enter LTSCALE and change the linetype scale to .500. See Figure 17-23 for the completed roller path.
11. The actual cam profi le can now be cre-ated in one easy step. You know from the data in Figure 17-7 that the diam-eter of the roller is Ø.88�. By defi nition,
Figure 17-21
Create three additional circles to identify the path of the roller through the fi rst drop.
Figure 17-22
Connect points C, 4� 5�, and D� to complete the arc for the fi rst drop, and then trim the circle with radius D to create the second dwell.
Section 17.1 Cams and Cam Drawings 587
1.875
120°RISE
30°DWELL
90°DROP
30°DWELL
90°DROP
1.250
.625
then, the path of the center of the roller is .44� on the outside of the cam profi le. In other words, the cam profi le is .44� to the inside of the roller path. Enter the OFFSET command, enter an offset distance of .44, and pick the roller path. Then pick a point inside the roller path to create the actual cam
profi le. Pick the cam profi le and change its linetype to continuous.
12. To fi nish the cam profi le drawing, add the roller with a center point at any point along the roller path. Rememberthat its diameter is .88. Add vertical and horizontal centerlines. See the fi nished working drawing in Figure 17-24.
Figure 17-23
The completed roller path
Section 17.1 AssessmentAfter You Read
Self-Check 1. Explain the purposes and applications
of cams. 2. Describe the three main types of cam
motion. 3. Explain how to develop a cam-related
displacement diagram and profi le.
Academic Integration English Language Arts
4. Using the headers and text from this sec-tion, outline the mechanical process of drafting a cam. Be sure to include useful content and academic vocabulary.
Drafting Practice 5. Prepare a drawing of the displacement
diagram and the cam profi le in Figure 17-7. Shaft: Ø.62�; roller: Ø.56�; base circle: Ø2.50�; hub: Ø1.12�. Diagram line = 2.50 × 3.14.Go to glencoe.com for this
Go to glencoe.com for this book’s OLC for a downloadable version of this graphic organizer.
Connect Another motion-transmitting device is the gear, characterized by its teeth. What aspects of creating teeth for a gear are most likely to be of particular importance to drafters?
A device that transmits motion using a series of teeth is called a gear. See Figure 17-25 for several of the numerous types of gears.
Spur GearsOne of the most practical and dependable
machine parts for transmitting rotary motion from one shaft to another is the spur gear. The operation of a simple spur gear can be explained by describing how friction wheels, which provide a simple means of transmit-ting rotary motion from one shaft to another, work. When the rims of two wheels are incontact as in Figure 17-26, both wheels revolve even if only one is turned. If the small friction wheel’s diameter is two-thirds of the diameter of the larger wheel, the smaller wheel makes 1.50 revolutions for every 1.00 revolu-tion the larger wheel makes. This assumes that no slipping occurs. However, when the load on the wheel that is turned, or driven, increases, that wheel becomes harder to turn, and its rim begins to slip. Therefore, a friction wheel cannot be counted on to provide a smooth transfer of rotary motion. Adding teeth to the friction wheels in Figure 17-26 turns them into spur gears (see Figure 17-27). Teeth added to the wheels provide the same type of motion as rolling friction wheels but without the slipping.
Figure 17-25
Several gears that are used as typical machine elements are (A) rack and pinion, (B) spur , (C) planetary (internal) set, (D) spiral bevel, and (E) eccentric spur.
Figure 17-26
Friction wheels
Figure 17-27
A spur gear. Teeth added to friction wheels provide a more effi cient means of transmitting rotary motion.
590 Chapter 17 Cams and Gears
WORKING DEPTH
CHORDAL THICKNESS
ADDENDUM
DEDENDUM
WHOLE DEPTHCIRCULAR THICKNESS
EDGE ROUND
FACE W
IDTH
TOOTH FILLETCLEARANCE
OUTSIDE DIA
PITCH DIA
ROOT DIA
CIRCULAR PITCH
15° INVOLUTE
PITCH CIRCLE OF SPUR GEAR
45 6 7
8
9
10
1112
1
2
3 D
5 4 3 2 1 C 11 10 9 8 7 BA
Refer to Figure 17-28, which identifi es the parts of a spur gear, as you work with the gear formulas in this chapter.
Gear TeethThe basic forms used for gear teeth are invo-
lute and cycloidal curves, which are explained in the following paragraphs.
The gears in Figure 17-27 are good examples of involute gears. The smaller of two mating spur gears is called the pinion. The teeth on this gear type have an involute curve, which could be thought of as the curve made by taut string as it unwinds from around the circumference of a cylinder. This special shape lets the teeth mesh smoothly. See Figure 17-29 for an illustra-tion explaining an involute curve that is used in drawing gear teeth. A cycloidal curve can be thought of as the path of a curve formed by a point on a rolling circle (see Figure 17-30).
The information in this chapter is for an 14½° involute system but also can be used
for a 20° involute system, because the only practical difference between the two is the number of degrees of the pressure angle. The 14½° or 20° refers to the pressure angle as in Figure 17-31. The pressure angle and the distance between the centers of mat-ing spur gears determine the diameters of the base circles. The pitch diameter is the point of tangency of a gear with itsmating gear and is equal to the diameters of the rolling friction wheels that are replaced by the gears. The involute is drawn from the base circle, which is smaller than the pitch circle.
In Figure 17-32, RA is the radius of the pitch circle of the gear with the center at A. RB
is the radius of the pitch circle of the pinion with the center at B. The distance between gear centers is RA + RB. The line of pressure TATB is drawn through O, which is the point of tangency of the pitch circles. It makes the pressure angle π with the perpendicular to the line of centers. This angle is 14½°. Note that lines ATA and BTB are drawn from centers A and B perpendicular to the pressure-angle
Figure 17-28
Gear terms identifi ed
Figure 17-29
Involute of a circle Figure 17-30
A cycloidal curve
Section 17.2 Gears and Gear Drawings 591
CENTER DISTANCE
PRESSURE ANGLE 141 2°
141 2°RADIAL LINE
OUTSIDE CIRCLE
PITCH CIRCLE
BASE CIRCLE
ROOT CIRCLE
141 2°
INVOLUTE
PITCH CIRCLES
BASE CIRCLEFOR B
TB
RBRA
BASE CIRCLE FOR A
TA
BOA
O
O
O
X
CENTER DISTANCE
A pair of involute gears is to be drawn according to these specifi cations:
The pressure angle will be 14½°.The distance between parallel shaft centers will be 12.00�.The driving shaft will turn at 800 revolu-tions per minute (RPM).The diametral pitch (number of teeth per inch of pitch diameter) equals 4.
To fi nd the remaining information needed to draw the gears, follow these steps:
1. Find the pitch radius of the pinion and the spur gear. These calculations are based on the ratio of the velocity of the two cylinders. One cylinder drives the other. Thus, the ratio is obtained by dividing the velocity of the driver by the velocity of the driven member. The velocities are stated in RPM.
••
•
•
Figure 17-31
The pressure angle. Note that the center distance indicates the distance between shafts of mating gears.
line TATB. A point X on a cord (line of pres-sure line TATB) describes the points that form the involute curve as the cord unwinds. This represents the outlines of gear teeth outside the base circles. The profi le of the gear tooth inside the base circle is a radial line. Figure 17-32 shows the cord unwinding off the surface on the base circle.
Defi ne What is a cycloidal curve?
Spur-Gear FormulasTable 17-1 defi nes terms commonly used
in gear formulas, and Table 17-2 presents the actual formulas. Refer to these two tables as you apply the gear formulas.
Drafters apply these formulas to the written descriptions and information they are given. The following information is typical of the instructions a drafter might receive.
Figure 17-32
Gear tooth interaction; the rolling nature of surface contact
592 Chapter 17 Cams and Gears
Term Symbol Defi nition
N number of teeth
NG
number of teeth of gear
NP
number of teeth of pinion
pitch diameter D diameter of pitch circle
DG
pitch diameter of gear
Dp
pitch diameter of pinion
diametral pitch P number of teeth per inch of pitch diameter
addendum a radial distance the tooth extends above the pitch circle
dedendum b radial distance the tooth extends below the pitch circle
outside diameter Do
overall gear size: pitch diameter plus twice the addendum
root diameter Dr
pitch diameter minus twice the dedendum
whole path ht
radial distance from the root diameter to the outside diameter; equal to addendum plus dedendum
circular pitch p distance from a point on one tooth to the same point on the next tooth measured along the pitch circle; the distance of one tooth and one space
clearance c distance between the top of a tooth and the bottom of the mating space when gear teeth are meshing; the diff erence between the addendum and the dedendum
working depth hk
distance a tooth projects into the mating space; twice the radial distance of the addendum
pressure angle o direction of pressure between teeth at the point of contact
base-circle diameter Db
circle from which the involute profi le is developed
The velocity ratio therefore equals½(4.00�:8.00�).
2. Find the number of teeth on the pinion:
NP = DP = 4 × 8 = 32
3. Find the number of teeth on the spur gear:
NS = DP = 4 × 16 = 64
4. Find the addendum:
a = 1 __ p = 1 __ 4 = .25�
5. Find the dedendum: b = 1.157 _____ p = 1 __ 4 = .289�
Involute gears are interchangeable as long as they have the same diametral pitch, pres-sure angle, addendum, and dedendum.
Table 17-2
Spur-gear formulas
Section 17.2 Gears and Gear Drawings 593
A
B
C D
Mark D
ieukel, Courtesy O
SU
Gear and
Mechanism
Lab
Defi ne What do the terms addendum and dedendum mean?
Involute Rack and PinionA rack and pinion is shown in Figure
17-33. A rack is a gear with a straight pitch line instead of a circular pitch line. The tooth profi les become straight lines. These lines are perpendicular to the line of action.
Worm and WheelA worm gear is similar to a screw. It may
have single or multiple threads. Figure 17-34shows how the worm and wheel mesh at right angles. This system is used to transmit motion between two perpendicular, nonintersecting shafts. The wheel is similar to a spur gear in design, except that the teeth must be curved to engage the worm gear.
Compare What does a worm gear resemble?
Bevel GearsWhen two gear shafts intersect, bevel gears
are used to transfer motion. See Figure 17-35for four sets of rolling friction cones. Think of
bevel gears as replacing the friction cones just as the spur gear replaced the circular friction wheels. Figure 17-36 illustrates mating bevel gears. The smaller gear is the pinion. When the
Figure 17-33
Rack and pinion Figure 17-34
Application of a worm and wheel
Figure 17-35
Rolling cones that represent bevel gearing
Figure 17-36
Bevel gear
594 Chapter 17 Cams and Gears
gears are the same size and the shafts are at right angles, bevel gears are referred to as miter gears.
Refer to Figure 17-37 for some basic infor-mation about bevel gears. Look for similarities and differences in the design of spur and bevel
Gear Ratio Calculate the mechanical advantage if a pinion has 12 teeth and a gear has 36 teeth. What is the gear ratio?
GEARPINION
GEAR TRAIN
The diameters of the gear and pinion can be used to determine the gear ratio. Calculating the gear ratio deter-mines the amount of increase or decrease in the speed of a combination of gears, or gear train. If the diameter of the gear is twice that of the pinion, it will have twice as many teeth as the pinion. Therefore, the gear ratio can also be determined by the relationship of the number of teeth on each. For example, the gear in the illustration has 24 teeth; the pinion has 12 teeth. Therefore, the pinion will make two complete turns for every one turn of the gear. This results in a gear ratio of 1:2. If the pinion is attached to a motor that rotates at 1000 revolutions per minute (RPM), the gear will turn at a speed
of 500 RPM, because the pinion rotates twice for every revolution of the gear.
Example:Here is how it works:
Mechanical advantage = Number of teeth on the driven gear/Number of teeth on the drive gear
In other words, by doubling the size of the driven gear, you increase the torque by a ratio of 2:1. Therefore, if a motor is driv-ing the pinion, the gear could carry a load double what it could carry without the gears.
The gear ratio is found by dividing the number of teeth on the gear by the number of teeth on the pinion. In this case, 24 ÷ 12 = 2. Thus, the gear ratio is 2:1, and the pin-ion ratio is 1:2. Clearly, mechanical advantage and gear ratio are closely related. If the pinion (drive gear) with 12 teeth is driving the gear (driven gear) with 24 teeth, the mechanical advantage is 2. In other words, the torque is doubled.
For help with this math activity, go to the Math Appendix located at the back of this book.
Academic Standards
Mathematics
Problem Solving Solve problems that arise in
mathematics and in other contexts (NCTM)
gears. The bevel gear’s circular pitch and diam-etral pitch are based on the pitch diameter just as they are in spur gears. The pitch diam-eter is the diameter of the pitch cone in the bevel-gear design. The symbols for important
Section 17.2 Gears and Gear Drawings 595
FACE CONEPITCH CONEROOT CONE
BACK CONE
BACKING
CROWNBACKINGb
a
F
RA
aN
DO
R
D
.25
2.12
2.12
9.00
8.006.00
2.881.88
1.38DATA TABLE.30 PITCH DIA 8.00
OUTSIDE DIA 9.00NO. OF TEETH 16DIA PITCH 2ADDENDUM .50WHOLE DEPTH 1.08
O
OO
OO
Figure 17-37
Bevel-gear terms. Note the cone shape of the gear.
bevel-gear features, such as the angles, are listed in Table 17-3. The two Greek letters used to represent bevel angles are α (alpha)and δ (delta).
Explain In a bevel gear, what do α and δ represent?
Gear DrawingsHow are gears usually indicated in drawings?
It is not usually necessary to show the teeth on typical gear drawings. Refer to Figure 17-38for a drawing for a cut spur gear. The gear blank
Table 17-3
Symbols for Bevel Gears
Symbol Defi nition
α addendum angle
δ dedendum angle
Γ pitch angle
ΓR
root angle
ΓO
face angle
a addendum
b dedendum
an
angular dedendum
A cone distance
F face
D pitch diameter
DO
outside diameter
N number of teeth
P diametrical pitch
R pitch radius
should be drawn with dimensions for making the pattern and for the machining operations. The spur-gear drawing should include infor-mation for cutting the teeth, the tolerances required, and a notation of the material to be used. On assembly drawings, a simplifi ed gear may be shown as in Figure 17-39. Although this drawing is simplifi ed, it should include all necessary notes for making the gear.
Figure 17-38
Simplifi ed profi le and cross-section of a spur-gear working drawing
596 Chapter 17 Cams and Gears
30T – 6P
15T – 6P
2.00
1.62
3.25
1.99651.2535
R.25
2.256•
FINISH ALL OVER
37°-22'35°-0'
2°-44'
2°-22'
35°-0'
32°-16'
O
OO
O
3.0489 26T 10P
1.12
.25
5°-6'
.62 1.0021.000
CIRCULAR PITCH
ADDENDUM CIRCLE
18/ PD 1
8/ PD
THIS LINE DRAWN TANGENTTO PITCH CIRCLE
14 (DRAWN 15 ) °
12/ °
FILLET
RADIAL LINE
ROOT CIRCLE
BASE CIRCLE
PITCH CIRCLE
CIRCULAR THICKNESS
On working drawings of bevel gears, the dimensions needed for machining the blank and all gear information must be given. An example of a working drawing for a cut bevel gear is shown in Figure 17-40.
The American National Standards Institute has established standards for satisfactorily detail-ing gear drawings. Refer to ASME Y14.7.1 and ASME Y14.7.2 for more study of gear detailing.
Drawing Gear TeethAlthough showing teeth on a gear drawing
is typically not necessary, sometimes drafters must include them. See Figure 17-41 for an example of a gear detail drawn using the sim-plifi ed method. To simplify the drawing of the involute curve, note that the radius in Figure 17-41 is drawn as 1 __ 8 of the pitch diameter. The procedure for drawing gear teeth using this method follows:
1. Draw the addendum circle, pitch circle, and root circle.
2. Draw a line tangent to the pitch circle at any point on it.
Figure 17-39
Simplifi ed drawing of mating spur gears. Note the tangent pitch circles, the number of teeth, and the pitch.
Figure 17-40
Simplifi ed profi le and detailed section of a bevel gear
Figure 17-41
Simplifi ed method of drawing a gear tooth
Section 17.2 Gears and Gear Drawings 597
Ø4.64
Ø5.16
Ø4.00
3. Draw a line through the intersection of the pitch circle and the tangent line at a 14 1 __ 2 ° (may be 15°) angle to the tangent line.
4. Draw the base circle tangent to the 14 1 __ 2 ° (15°) line.
5. Calculate or estimate the chordal thick-ness and step this distance off along the pitch circle.
6. With the compass set at a distance equal to 1 __ 8 of the pitch diameter, place the com-pass point on the base circle and strike the arcs (see Figure 17-41).
7. Add the short radial lines from the curve of the tooth to the fi llets. The size of the fi llet is estimated and can be drawn to any suit-able size that appears appropriate.
8. Darken all lines.
Restate What information for bevel gears must be given on a working drawing?
Drawing Gear Teeth Using CADGears are easier to draw using a CAD system
than with board drafting techniques because you can simply create one tooth in detail and then array it to form the entire gear. In this application, you will use a polar array to com-plete a drawing of a gear showing the individ-ual gear teeth. Follow these steps:
1. Draw the addendum circle, the pitch cir-cle, and the root circle using the dimen-sions shown in Figure 17-42.
2. Create a 2.00� line from the top quadrant point of the pitch circle at a downward 14.5° angle. (Use the Quadrant object snap for the fi rst point, and enter @2<345.5 at
Figure 17-42
Create the addendum circle, the pitch circle, and the root circle.
Figure 17-43
Use DIVIDE to create 24 equal segments on the base circle.
Smooth Circle Representations
When you zoom in to a small part of a circle, you may notice that the circle looks segmented at the higher zoom level. To fi x its appearance, you can enter the REGEN command to regenerate the drawing at the new zoom level. However, if you plan to use several diff erent zoom levels in a drawing, you can avoid the problem by setting VIEWRES to a higher level. VIEWRES is an AutoCAD system vari-able that controls the resolution of curved lines on a scale of 1 to 20,000. The default value is 1,000. By enter-ing a new, higher value, you can force the curved lines to be more accu-rate at high zoom levels. Try setting the zoom level at various levels. For this drawing, you may want to set VIEWRES to a value of 5,000.
598 Chapter 17 Cams and Gears
A
B
CENTER OFBASE CIRCLE
A B
the To point prompt.) Then create a circle with the same center point as the other cir-cles. Use the Tangent object snap to snap the circle to the 2.00� line. This becomes the base circle. Erase the 2.00� line.
3. This gear will have 12 teeth. To deter-mine the shape of the curved portion on the upper part of the tooth, fi rst divide the base circle into 24 equal segments (because each tooth has two sides). Before you do this, enter the PDMODE com-mand and change the point display to 3 so that the points will show up. Then enter the DIVIDE command and pick the base circle. Enter 24 for the number of segments. The drawing should look like the one in Figure 17-43.
4. Zoom in on a small portion of the circle. Create another circle with its center at one of the division marks on the base and a radius equal to 1 __ 8 of the pitch diameter, or .58�. Then create an identical circle with its center at the next division mark on the base circle (see Figure 17-44A). The area common to these two circles begins to defi ne a gear tooth. Trim away the excess portions of both circles as in Figure 17-44B.
5. Create a line from the center of the base circle tangent to one of the arcs that forms the tooth. Create a similar line
tangent to the arc that forms the other side of the tooth, as shown in Figure 17-45A. These lines are the radial lines that form the relatively straight portions near the tooth’s bottom. Then zoom in on the tooth and trim away the bottom part of the arcs and the part of the lines that extends below the root circle. The result should look like Figure 17-45B.
6. Add the fi llets at the bottom of the tooth. They can be estimated to give a good appearance in the drawing. In this case, try using a fi llet radius of .04�.
Figure 17-44
Begin the gear tooth by creating circles with a radius equal to 1 __ 8 of the pitch diameter at two consecutive division points on the base circle. Trim away the excess parts of the circle as shown.
Figure 17-45
Create the bottom sides of the tooth along radial lines from the center of the base circle.
Removing Division Marks
The fastest way to remove the division marks from the screen is to change PDMODE back to 0. Remem-ber, however, that if you simply change their display, the points still exist in the drawing database. If the drawing is to be used directly to drive certain machinery, the points can cre-ate problems. Therefore, if the draw-ing is intended to be used with a CAM or CIM setup, you should delete the points individually.
Section 17.2 Gears and Gear Drawings 599
Figure 17-46
The completed gear tooth
7. Trim away the addendum circle leaving only the portion that forms the top of the gear tooth. See Figure 17-46. This completes one tooth.
8. You can now array the tooth to com-plete the rest of the gear teeth automati-cally. Enter the ARRAY command. At the Select objects prompt, carefully pick all of the lines and arcs that make up the tooth, and press Enter. Then enter P to choose a polar array, and use the Cen-ter object snap to select the center of the base circle as the center point of the array. Enter 12 for the number of items in the array, and accept the default 360° angle to fi ll. Enter Y (Yes) to rotate the objects as they are arrayed. Zoom out to see the effect of the ARRAY operation: The remaining teeth appear, perfectly spaced around the gear.
9. Delete the pitch circle and the base circle, and remove the division marks.
10. Before trimming the base circle, use it as the basis for creating the hole at the center of the gear and the circles that defi ne the indented portion of the gear. Enter the CIRCLE command and use the Center object snap to snap to the center of the base circle. Create the hole with a diameter of 1�.
11. Trim away the base circle from the base of each tooth. The fi nished gear should look similar to the one in Figure 17-47.
Explain What is a quick way to remove division marks?
Creating 3D Gears and WheelsIn some cases, you may be required to
create a 3D model of a gear or wheel. The best way to create a gear that has teeth is to create a 2D drawing like the one in Figure 17-47 and then extrude it. Before you do so, however, be sure to use either the REGION command to create a region of the entire gear or PEDIT to join all of the individual lines and arcs to make a single polyline.
For simpler objects, such as the friction wheels shown in Figure 17-26, you can use AutoCAD’s REVOLVE command. The fi rst step is to create the profi le from which the revolu-tion can be constructed.
1. Create a new drawing, ZOOM All, and create two layers: Center and Wheel. Give the Center layer a CENTER linetype.
2. Draw a vertical centerline, as shown in Figure 17-48. The exact length of the centerline does not matter, but use Ortho to make sure the line is perfectly vertical.
3. Switch to the Wheel layer and draw the profi le using the dimensions shown in Figure 17-48. Use the PLINE command to create the entire profi le as a single object.
4. Enter the FACETRES system variable and specify a new value of 10.
Figure 17-47
The fi nished gear
600 Chapter 17 Cams and Gears
.25
2.002.75
4.75
Section 17.2 AssessmentAfter You Read
Self-Check 1. List the information needed for a typi-
cal gear drawing. 2. Describe how to draw gear teeth
using the simplifi ed board-drafting method.
3. Explain how to create a CAD- generated gear-tooth drawing.
Academic Integration Mathematics
4. Calculate Mechanical Advantage and Gear Ratio Calculate the mechani-cal advantage if a pinion has 24 teeth and a gear has 48 teeth. Then calculate the gear ratio.
Build Mathematical
Knowledge Through
Problem Solving
Recall from this section’s Do the Math activ-ity that Mechanical advantage � Number of teeth on the gear (driven gear)/Number of teeth on the pinion (drive gear). The gear ratio can then be found by dividing the number of teeth on the gear by the number of teeth on the pinion and expressing the result as a ratio.
Drafting Practice 5. Prepare a working drawing of the mat-
ing gears in Figure 17-39. Calculate the data necessary to draw the gear teeth and prepare a data table.
Go to glencoe.com for this book’s OLC for help with this drafting practice.
Figure 17-48
Friction wheel profi le
Figure 17-49
The fi nished friction wheel and axle
The angle of revolution is the portion of a circle through which you want to revolve the profi le. For this example, you will need to revolve the profi le 360 degrees.
7. Enter 360 for the angle of revolution and press Enter to create the revolution.
8. Change to the SE Isometric view and enter the HIDE command to see the fi nished friction wheel and axle (see Figure 17-49).
5. Enter the REVOLVE command, select the profi le as the object to revolve, and press Enter.
6. For the axis start point, use the Endpoint object snap to select the top of the cen-terline, and snap to the other end of the centerline for the axis endpoint.
Section 17.1 Cams are designed to have uniform, harmonic, and uniformly accelerated and decelerated motion.A cam-related displacement diagram shows the motion a cam produces through one revolution, and a cam profi le shows its important features.
•
•
Section 17.2 Information needed for a typical gear drawing includes the tolerances required and a notation of the material to be used.Drawing gear teeth using the simplifi ed board-drafting method involves simplify-ing the drawing of the involute curve.A CAD-generated gear-tooth drawing cre-ates one tooth in detail and then forms the entire gear using the array method.
•
•
•
17 Review and Assessment
Review Key Concepts2. Explain the purposes and applications of cams.3. Describe the three main types of cam motion.
4. Explain how to develop a cam-related displacement diagram and profi le. 5. Describe the information needed for a typical gear drawing. 6. List the steps for drawing gear teeth using the simplifi ed board-drafting method. 7. Summarize the process for creating a CAD-generated gear-tooth drawing.
Chapter Summary
602 Chapter 17 Cams and Gears
True/False QuestionsDirections Read the following statements and determine whether each statement is true or false. 11. Cams and gears can transmit motion
and change the speed of motion.TF
12. Uniform and unsteady are similar in meaning.
TF
Engineering 8. Engineers in the Economy Economy is the production, distribution, and consump-tion of goods and services. What kinds of ser-vices to designers and engineers provide that add to the economy? Think of how design and engineering contribute to your neighbor-hood, your state, and the country? The design and engineering industries add to the econ-omy on all levels—local, state, and national. Write a fi ve-paragraph essay comparing the role of design and engineering on local, state, national and international economies.
9. Being an Informed ConsumerBeing a good consumer means making wise
choices about the products you buy. Select a product, such as a CD player, that you own or have access to. Identify the brand and model number. Then fi nd ads for the same prod-uct online and in local sources. Also read any reviews you can fi nd for it. Then prepare a table evaluating the accuracy of information you found according to the source (that is, ad or review) that you are citing and your personal experience.
Mathematics 10. Calculate Ratio
If gear x has 64 teeth and gear y has 24 teeth, what is the ratio of gear x teeth to gear y teeth?
Calculating Ratio
Remember that ratios, like fractions, should be reduced to their simplest form.
TEST-TAKING TIP
When you are taking a test, work on a prob-lem only until you get stuck. Think about it for a minute or two, and if nothing comes to mind, move on to another problem.
Prep For
Go to glencoe.com for this book’s OLC for more information about competitive events.
Win Competitive Events
13. CADOrganizations such as SkillsUSA offer a
variety of architectural, career, and draft-ing competitions. Completing activities such as the one below will help you pre-pare for these events.
Activity Design a device used to hold parts in place on a drill-press table. Use a cam arrangement for holding the part and for quick release. Design the unit to work on stock up to 100 mm thick and have a reach of at least 150 mm. Mate-rial optional.
Drafting ProblemsThe drafting problems in this chapter are designed to be completed using
board-drafting or CAD techniques.
1. Make a profi le of the radial plate cam shown in Figure 17-50. Prepare a displacement dia-gram similar to the one in Figure 17-7 to illustrate the travel patterns from the base circle.
NOTE: SCRIBE LINE .03 DP
R 2.875
23°–24'DWELL
12°–36'RISE .250"
R 3.125
32°–24'RISE .8125"
O1.00 FOLLOWER
R 3.9375
255°–36'DWELL
O3.0023.000
36°RETURN
21°–36'
TITLE:
FRAWN BY: CHECKED: DATE: SCALE:
MATERIAL: DWG. NO.:
MACHINES TOLERANCES
KEYWAYS SYM. TO C. L. W. I. .002
ALL SURFACES TO BE
PARALLEL, SQUARE, & CONCENTRIC
WITHIN T. I. R.
-- 32 MICROINCHES OR LESS
-- 63 MICROINCHES OR LESS
-- 125 MICROINCHES OR LESS
-- 250 MICROINCHES OR LESS
DECIMAL DIMENSIONS .003
ANGULAR DIMENSIONS .5
BREAK ALL SHARP EDGES .02 3
2
1
REV. DATE DESCRIPTION OF CHANGE BY
.38
O
4XØ.266 THRU (AT ASSEMBLY)ON A Ø3.50 BC
Figure 17-50
2. Prepare diagrams similar to those in Figures 17-8 through 17-10 to illustrate the three types of cam motion. Travel: 2.50�; rise: 1.25�.
3.
Draw the two views of the plate cam shown in Figure 17-11. Prepare a dis-placement diagram to illustrate the rises.
604 Chapter 17 Cams and Gears
4. Draw a cam for the conditions given in Figure 17-51. Draw the path of the roll centers and lay off the angles. From A to B, rise from 2.50� to 3.50�, with modifi ed uniform motion. From B to C, dwell, radius 3.50�. From C to D, drop from 3.50� to 2.50�, with harmonic motion. From D to A, dwell, radius 2.50�. Draw the groove, using a roller with a 1.00� diam-eter in enough positions to fi x outlines for the groove. Keyway: .50� � .12�.
DWELL
Ø1.OOOROLLER
.50
.50
1.50D 70°
R2.502.25O
O
R3.50
DWELL 30°
180°UNIFORM MOTION
80°HARMONIC MOTION
1.0021.000
.50
B
C
.50
A
Figure 17-51
5.
Prepare a two-view drawing of the spur gear in Figure 17-38. Make a simplifi ed profi le and section as shown. Using the given data, draw in two gear teeth after calculating circular thickness.
Problems 605
Problems17
6. Complete the gear data for the gears shown in Figure 17-52, using formulas from this chapter. Make an enlarged drawing of a mating spur and pinion as shown. Select a suitable scale. Use an involute to draw the gear tooth profi le or 1 __ 8 PD, as directed by your instructor.
12/14 °
12/14 °
O2.50
12/ ° 1
2/ °
GEAR DATA SPUR PINIONNO. TEETH 15 12DIA PITCH 1 1PITCH DIA 15.00 12.00ADDENDUMDEDENDUM
CIR. PITCHOUTSIDE DIA 17.00 14.00ROOT DIACLEARANCEPRESSURE 14 14
O2.00
B
C
A
Figure 17-52
7. Prepare the two views of the bevel gear in Figure 17-40. Review the simplifi ed profi le and insert the proper pitch circles as centerlines in the front view. Dimension the drawing.
606 Chapter 17 Cams and Gears
Teamwork
1. Design an automatic bubble-blowing machine that uses commercial bubble solution. It can be designed to use com-pressed air from a commercial compressor or from a built-in air pump (diaphragm or piston). Use a cam mechanism to open and close the opening where the air and solution form a bubble and exit the machine. Use your most creative imagi-nation in the development of this design.
Teamwork
2. Design a gear mechanism with a cable, powered by a hand crank or electric motor drive, used to raise and lower a 309'-0 steel fl agpole for maintenance pur-poses. The fl agpole is hinged at the base. Design the unit to attach to a concrete pad installed 159'-0 from the base of the pole.
Teamwork
3. Design a device for crushing aluminum beverage cans using a gear mechanism to reduce the effort required to crush the can. The power is to be supplied with a hand crank attached to the gear mecha-nism. Be aware of safety issues. Design appropriate sheet metal guards to enclose the gears. Add safety devices where needed to protect the operator from fl y-ing material.
Design ProblemsDesign problems have been prepared to challenge individual students or teams of students. In
these problems, you are to apply skills learned mainly in this chapter but also in other chapters throughout the text. They are designed to be completed using board drafting, CAD, or a combi-nation of the two. Be creative and have fun!
Problems 607
Collect, Store, and Distribute Rainwater
Your Project Assignment
Harvest Rainwater and Help the Environment
Design a rainwater collection system using the rooftop of a home to store rainwater and use it to meet non-potable, outdoor water needs such as lawn and garden irrigation.
Use what you have learned in Chapters 11–17 to create a plan for a rainwater collection and distribution system. Your challenge is to:
Research the design and construction of rooftop rainwater collection systems for homes. Think through how you would design such a system for your home. List the materials you will need.
Calculate the yield of your rooftop catchment.
TIP! A typical rooftop catchment can yield about 600 gallons of water per 1000 square feet of roof area for one inch of rainfall.
Determine the best way to store the water you collect. What type of storage container is best for your system? Explain your choice.
•
•
•
Design a conveyance system using gutters and pipes to transport the water collected on the roof to the storage container. Calculate the volume of water that can be held in the storage container you chose.
Design a system to distribute the water as needed for lawn or garden irrigation using fi ttings, pipes, and hoses.
Create a pictorial drawing and a pipe drawing of your collection and distribution system.
Applied Skills
Research and write a paragraph about the benefi ts of using stored rainwater on lawns and plants in a garden.
Estimate the cost of materials for your system. Include barrels, pipes, pumps, fi ttings, and hoses.
List the steps, materials, and tools you used to create the drawings for your system.
The Math Behind the Project The primary math skills you will use to complete this project are geometry modeling, algebra, and measurement. To get started, remember these key concepts, and follow this example:
Algebra—Finding Area and Calculating Yield
To calculate the yield of your rainfall catch-ment, begin by determining its area in square feet. Your catchment area is equal to the total square feet of the area under your roof including the extension of the eaves.
•
•
•
•
•
•
Math Standards
Algebra Represent and analyze mathematical situations
and structures using algebraic symbols (NCTM)
Measurement Apply appropriate techniques, tools, and
formulas to determine measurements (NCTM)
NCTM National Council of Teachers of Mathematics
Thematic Project UNIT 3
608 Chapter 17 Cams and Gears
TIP! You do not need to consider the pitch of your roof because rain falls evenly on every part of the roof. The area you need to fi nd is the area under the roof’s edges.
Therefore, if your house is 40 feet by 60 feet, and it has eaves that extend 2 feet all around, the width of the catchment is 44 feet, and the length is 64 feet. The formula for area is A = l × w.44 × 64 = 2,816 square feet
Then, since one inch of rainfall provides about 600 gallons of water for a 1,000 square foot catchment, divide 2,816 by 1,000 and mul-tiply be 600 to fi nd the yield per inch of rainfall.
Now, to fi nd the yearly potential, or yield, multiply 1,690 gallons by the average yearly rainfall for your area. If average rainfall is
25 inches, then the potential collection over a year is:
1,690 × 25 = 42,250 gallons
Algebra—Finding Volume and Calculating Storage Capacity
If your storage container is shaped like a cyl-inder, you can use the formula for the volume of a cylinder to calculate the storage capacity of your system. The formula is: V = πr2h
TIP! The symbol r stands for radius. The radius of a circle is half its diameter. The symbol h stands for height. Use 3.1416 for π.
For example, if your system uses two barrels for storage, and each is 3 feet in diameter and 4 feet high, then the volume of the two is:
V = 2 × 3.1416 × 1.52 × 4V = 56.55 gallons
Rooftop GardensRespecting and maintaining the environment has
become a worldwide concern. Evidence of this can be
seen in various countries where legislation has been
passed to protect national forests. However, what
about the trees and vegetation that are removed dur-
ing city construction and expansion?
Landscape architects have discovered that the acres
of rooftops in urban areas represent a great resource
for counteracting some of this loss. Regulations in parts
of Europe now require green roofs on new industrial
buildings.
Research Activity Find out more about rooftop
environments. Where are they located? What factors
must landscape architects consider when designing
a green rooftop environment? Write a one-page sum-
mary of your fi ndings.
Bonus! Incorporate some of your fi ndings into your
ground-water recycling project.
Unit 3 Hands-On Math Project 609Car Culture/Corbis
UNIT 3 Thematic Project
Project Steps:
Design for the Environment
STEP 1 Research
Explain the environmental value of recycling rainwater for lawn and garden irrigation.
Find out or estimate how much water your family uses during the year. Estimate the savings you can achieve.
Find out more about different types of rain-water collection systems. List sources for and costs of materials you need to build one.
Calculate the yield of your catchment area.
TIP! Find out if there are any rainwater collection systems operating in homes nearby. Make an appointment to visit the site and discuss the design with those who use it.
STEP 2 Plan
Defi ne and write out your overall goal for this project.Gather the appropriate supplies and tools for board drafting.Set up your drawing fi le with AutoCAD.
Refer to the Math Concepts on the previous page, or go to glencoe.com for this book’s OLC for more informa-tion on the math concepts used in this project.
STEP 3 Apply
Make a pictorial drawing of your rainwater collection system.
Make a pipe drawing of your system.
•
•
•
•
•
•
•
•
•
TEAMWORK Collaborate: Ask a classmate to review the design of your system before you continue. Ask for feedback on the technical aspects of your drawing as well as the overall concept.
STEP 4 Present
Prepare a presentation combining your research with your completed drawings using the checklist below.
Presentation ChecklistDid you remember to…
state your objectives for your system?
describe the environmental value of recycling rainwater?
show and discuss your plan?
explain the process you used to create the system and what you hope to achieve with it?
explain how you created your pictorial and pipe drawings?
demonstrate the basic sketch or CAD drawing?
review the drafting principles involved in completing your system plan?
explain any problems you encountered and how you overcame them?
turn in your research and planning notes to your teacher?
✓
✓
✓
✓
✓
✓
✓
✓
✓
STEP 5 Build Your Portfolio
The purpose of a portfolio is to showcase your education, examples of your work, and your accomplishments.
Organize your drawings in a manner that will show your ideas well.
Organizing Work Experience Many students have a part-time job, participate in an internship, or have the opportunity to shadow a work-place mentor on the job. To prepare information about these job experiences for your portfolio, keep a diary to record what you learn about the world of work.
Job Diary: Keep a diary of your job or job shadowing experience. Describe what happens and your reactions to the events of the day. Identify skills that you need to develop in order to be successful in the job.
Interview a Mentor: Create a list of questions about the world of work and interview someone who works in a fi eld you are interested in. Record the questions and answers and write a summary of your fi ndings.
Samples of your work: Now that you have completed your rainwatercollection project for this unit, include your drawings as samples of your work in your portfolio.
Save Your Work In the following Units, you will add more elements to your portfolio. Keep items you want to use in a special folder as you progress through this class.
1.
2.
3.
Attach a written introduction and a descrip-tion of your design.
STEP 6 Evaluate Your Technical
Skills
Assess yourself before and after your presentation.
Is your research thorough?Did you plan your steps carefully?Did you organize your visuals so that they showcase your ideas?Is your presentation creative and effective?During your presentation, do you make eye contact and speak clearly enough?
Rubrics Go to glencoe.com for this book’s OLC for a printable evaluation rubric and Academic Assessment.
•
1.2.3.
4.5.
Unit 3 Hands-On Math Project 611Kim Karpeles/Alamy
![Index [] · 2 Red Shift® Cams Twin Cam® Applications & Specs Red Shift® Application Matrix for 1999-Up Twin Cam ® Engines Red Shift® Specs for 1999-Up Twin Cam ® Engines 1999-2006](https://static.documents.pub/doc/80x56/5f94d203b8690b2d316b27c1/index-2-red-shift-cams-twin-cam-applications-specs-red-shift-application.jpg)
