Architecture Chapter 16 Homework Explain in a short complete statement the function of each mechanism

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CHAPTER16 MECHANISMS:

LINKAGES, CAMS, GEARS,

ANDBEARINGS PROBLEMS

INSTRUCTIONS

Read each problem carefully before you begin working. Com-

plete each problem on an appropriately sized sheet with a border

and sheet block of your choice unless otherwise specified by your

instructor.

LINKAGE PROBLEMS

Print each problem page at 100% for use in making measure-

ments from the hard copy.

Part 1: Problems 16.1 Through 16.14

PROBLEM 16.1 Refer to the pictorial drawing and a linkage

schematic of a vise grip in the closed position. Reproduce the

schematic exactly as shown and also show the open position in

a second color.

A-B 5 2.5 IN

B-C 5 1.75 IN

C-D 5 1.75 IN

A-D vertical .25 IN

A-D horizontal 4.0 IN

2.5 1.75

4.0

.25

1.75

PROBLEM 16.2 Refer to the pictorial drawing and a linkage

schematic of a toggle clamp in the closed position. Reproduce

the schematic exactly as shown and also show the open posi-

tion in a second color.

A-B 5 1.7 IN

B-C 5 1.6 IN

C-D 5 1.75 IN

A-D vertical .4 IN

A-D horizontal 2.6 IN

1.7 IN 1.6 IN

1.75 IN

.4 IN

2.6 IN

PROBLEM 16.3 Determine the extreme right and left posi-

tions of link CD in the given problem. Determine and label the

angle through which CD oscillates. Measure the problem

drawing using a 1/20 5 19200 scale and transfer the measure-

ments to your final drawing.

PROBLEM 16.4 Draw the mechanism in the position

shown. Use different colors to draw the mechanism in the ex-

treme right and left positions. Dimension the stroke (in.).

PROBLEM 16.5 Draw the combination bell crank slider

mechanism in the position shown. Determine the stroke of the

slider if A moves to position A1. Note: Position of features in

the sketch may be out of proportion (in.).

408

258

ANGLE ABC=

808

AB = 1.500″

BC = 2.125″

CD = 3.375″

A’

1.625″

PROBLEM 16.6 The given drawing is a linkage schematic of

an oscillating lawn sprinkler. The spray tube, shown in section,

is part of link CD. Link AB moves through 3608, while points A

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through a total of 3608. Use a different color or line type or

both for each position (in.).

Dimension the angle through which CD oscillates.

BCP is a through link.

Point P slides on EF.

EF 5 6.5 IN

PROBLEM 16.7 Given the windshield wiper mechanism, de-

termine and dimension the angle of oscillation of the wiper

blades. The electric motor rotates link ED continuously

through 3608. ABC is one link with a 908 angle at B. A tension

spring is located in the center of link BG.

PROBLEM 16.8 Draw the given mechanism. Use different

colors to show the path of point D in a total of five equally

spaced positions, including the extreme right and left posi-

tions (in.).

2.5

PROBLEM 16.9 Draw the mechanism in the given position.

Draw the path of point P as linkage AB moves every 308

PROBLEM 16.10 Given the mechanism, rotate link BC at

608 intervals clockwise through 3608. Plot and draw the paths

of points D, E, and F. Dimension the angle of oscillation of link

AF. Measure the problem drawing using a 1/20 5 19 2 00 scale

and transfer the measurements to your final drawing.

and D are stationary. Determine and dimension the angle of

oscillation through which the spray moves (in.).

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PROBLEM 16.11 Given the assembly drawing of the

foundry flask handler, draw a mechanism schematic showing

the two extreme positions of movement. The handler is oper–

ated by a hydraulic piston with a 6 IN stroke.

a is welded to b.

b is welded to c (in.).

PROBLEM 16.12 Given the pivot hoist, measure and draw

exactly as shown using a 1/40 5 19 2 00 scale and transfer the

measurements to your final drawing. Rotate ADE clockwise so

link AE is horizontal. Determine and dimension the extended

length of the spring between C and E. Determine and dimen-

sion the angle between AE and CE when E is in the new

position.

PROBLEM 16.13 Given the linkage drawing, determine and

dimension the stroke of point E moving in a straight line as

link AB rotates 3608. In addition, dimension the angle of oscil-

lation of link CD (in.).

PROBLEM 16.14 Find two examples of linkage mecha-

nisms at home or school. Explain in a short complete state-

ment the function of each mechanism. Use schematic

representations to show and dimension the extreme posi-

tions of each mechanism.

PROBLEM 16.10

(Continued)

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CAM-DISPLACEMENT DIAGRAMS

Part 2: Problems 16.15 Through 16.25

PROBLEM 16.15 Construct a cam-displacement diagram for

a cam follower that rises in simple harmonic motion a total of

2.00 in. in 1508, dwells for 308, falls 2.00 in. simple harmonic mo-

tion in 1208, and dwells for 608. Draw the horizontal scale 6.00 in.

PROBLEM 16.16 Construct a cam-displacement diagram

for a cam follower that rises in uniform accelerated motion a

total of 2.00 in. in 1808, dwells for 308, falls 2.00 in. uniform ac-

celerated motion in 1208, and dwells for 308. Draw the horizon-

tal scale 6.00 in.

PROBLEM 16.17 Construct a cam-displacement diagram

for a cam follower that rises in modified constant velocity for

3.00 in. in 1808, falls 3.00 in. modified constant velocity motion

in 1208, and dwells for 608. Use a modified constant velocity

motion designed with one-third of the displacement.

PROBLEM 16.18 Construct a cam-displacement diagram

for a cam follower that rises 2.000 in. cycloidal motion in 1208,

dwells for 608, and falls 2.000 in. in cycloidal motion in 1808.

PROBLEM 16.19 Construct a cam-displacement diagram

for a cam follower that rises in simple harmonic motion a total

of 1.250 in. in 908, dwells for 608, rises .750 in. in 458 simple har–

monic motion, and falls 2.00 in. with cycloidal motion in 1208.

Draw the horizontal scale 12 in.

PROBLEM 16.20 Construct a cam-displacement diagram for

a cam follower that rises in modified constant velocity motion

(modified to one-third the displacement) for 3.000 in. in 1808,

dwells for 308, falls 3.000 in. simple harmonic motion in 1208, and

dwells to the end of the cycle. Draw the horizontal scale 12 in.

PROBLEM 16.21 Construct a cam-displacement diagram

for a cam follower that rises 3.500 in. in 908 cycloidal motion,

dwells for 458, falls 2.500 in. cycloidal motion in 1358, dwells for

308, falls 1.000 in. simple harmonic motion in 308, and dwells to

the end of the cycle. Draw the horizontal scale 12 in.

PROBLEM 16.22 Construct a cam-displacement diagram

for a cam follower that rises in cycloidal motion for 3.000in. in

908, dwells for 308, falls 1.000 in. in simple harmonic motion in

908, dwells for 308, and falls the remaining 2.000 in. in uniform

accelerated motion in 1208. Draw the horizontal scale 12 in.

PROBLEM 16.23 Construct a cam-displacement diagram

for a cam follower that rises in cycloidal motion a total of

2.1875 in. in 1508, dwells for 308, falls back to the original level

in simple harmonic motion in 1508, then dwells through the re-

mainder of the cycle. Use a 12 in. horizontal scale.

PROBLEM 16.24 Construct a cam-displacement diagram

for a cam follower that rises a .375 in. diameter inline roller fol-

lower 1.500 in. in uniform accelerated motion in 1508, dwells

458, falls with modified constant velocity (one-third displace-

ment) in 1208, and dwells the remainder of the cycle.

PROBLEM 16.25 Construct a cam-displacement diagram for

a cam follower that rises 3.500 in. in 908 cycloidal motion, dwells

for 308, falls 2.250 in. cycloidal motion in 1508, falls 1.250 in. sim-

ple harmonic motion in 608, and dwells for 308. Draw the hori-

zontal scale equal in circumference to a 3.000 in. diameter circle.

CAM PROFILE DRAWINGS

Part 3: Problems 16.26 Through 16.31

1. For the following problems requiring detail drawings use an

appropriate ASME sheet size with border and sheet blocks.

2. Draw and completely dimension the necessary views.

3. Provide a cam-displacement chart for cam drawings and

gear data chart for gear drawings.

4. Include the following general notes at the lower-left corner

of the sheet .5 in. each way from the corner border lines:

NOTES:

1. DIMENSIONING AND TOLERANCING PER ASME

Y14.5-2009.

2. REMOVE ALL BURRS AND SHARP EDGES.

Additional general notes can be required depending on the

specifications of each individual assignment. Use the follow-

ing for tolerances for unspecified inch values. A tolerance

block is recommended as described in Chapter 2 Drafting

Equipment, Media, and Reproduction Methods and shown in

problems for Chapter 10 Dimensioning and Tolerancing un-

less otherwise specified.

Unspecified Tolerances

Decimals In.

X6.1

XX 6.01

XXX 6.005

ANGULAR 6309

FINISH 125 μin.

For metric drawings, provide a general note that states TOL-

ERANCES FOR UNSPECIFIED DIMENSIONS COMPLY WITH

ISO 2768-m. Provide a general note that states SURFACE FINISH

3.2 mm UNLESS OTHERWISE SPECIFIED.

DRAFTING

TEMPLATES

To access CADD template

files with predefined drafting

settings, go to the Student

Companion Website, select

Student Downloads and

Drafting Templates, and then

select the appropriate

template file.

59728_ch16_EOC_ptg01.indd 5 2/3/16 2:25 PM

PROBLEM 16.26 Use the displacement diagram con-

structed in Problem 16.15 and the information given in the il-

lustration to lay out the plate cam profile drawing. The cam

rotates counterclockwise. Make a two-view detailed drawing of

the cam and dimension it as shown in this chapter (in.).

INLINE ROLLER FOLLOWER

BASE CIRCLE

KEY SIZE USED

PLATE THICKNESS

HUB THICKNESS

HUB DIAMETER

SHAFT DIAMETER

.625

.626

[

.500

1.25

-28UNF-2B

[1.375

[.750

[2.000

1/4 3 1/4 SQ. KEY

.500

.750

.375

[.625/.626

PROBLEM 16.27 Use the displacement diagram constructed

in Problem 16.18 and the information given in the illustration

for Problem 16.26 to lay out the plate cam profile. The cam is ro-

tating counterclockwise. Make a two-view detailed drawing of

the cam, properly dimensioned and toleranced.

PROBLEM 16.28 Make a two-view detailed drawing of a

plate cam using the displacement diagram from Prob-

lem16.24. Completely dimension the drawing using the follow-

ing information:

The cam rotates counterclockwise.

Inline roller follower 5 [.375

Base circle 5 [2.750

Shaft 5 [1.000

Hub diameter 5 [1.250

Hub projection 5 .500

Plate thickness 5 .375

All dimensions in inches.

PROBLEM 16.29 Make a two-view detailed drawing of a

plate cam using the displacement diagram from Prob-

lem16.20. Completely dimension the drawing using the follow-

ing information:

The cam rotates counterclockwise.

Inline roller follower 5 [.750

Base circle 5 [2.000

Shaft 5 [.625

Hub diameter 5 [1.250

Hub projection 5 .500

Plate thickness 5 .500

All dimensions in inches.

PROBLEM 16.30 Make a two-view detailed drawing of a

plate cam using the displacement diagram from Problem 16.18.

Completely dimension the drawing using the information

shown below (in.).

.75

1.00

.50

Ø.750

Ø.625

Ø1.250

Ø2.000

BASE CIRCLE

PROBLEM 16.31 Use the displacement diagram con-

structed in Problem 16.25 and the following illustration to lay

out the profile of the groove in the drum cam. The cam rotates

clockwise. Make a two-view detailed drawing of the drum cam,

with tolerances and dimensions as discussed and shown in

this chapter (in.).

Ø3.00

5.00

.500

.375 (GROOVE DEPTH)

.500

.750

3/8-24 UNF-2B

WIDTH)

(GROOVE

.504

.501

.156

Ø1.250

HALF OF OBJECT SHOWN

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GEAR PROBLEMS

Part 4: Problems 16.32 Through 16.37

PROBLEM 16.32 Given the gear train and chart, calculate

or determine the missing information to complete the chart.

GEAR A GEAR C GEAR D

GEAR F

GEAR E

GEAR B

Gear

Diametral

Pitch

(P)

Number

of Teeth

(N)

Pitch

Diameter

(D) RPM Direction

Center

Distance

Gear

Ratio

A 4 7.5” 240 Clockwise

B18

C 10.0” 400

D540

F 14 1500

Gear

Pitch

Diameter

No. of

Teeth

Diametral

Pitch RPM

Ctr. Distance

Between

Mating

Gears Direction

A 3.00 3600 Counter–

clockwise

B 5 4.00

C 48

D 12 1080

E 4.00 40

F100

G 5.00 6.00

H 6

I 4

J 40 108

PROBLEM 16.33 Given the 10-gear power transmission and

chart, calculate or determine the missing information to com-

plete the chart.

SHAFT

SHAFT 2

SHAFT 1

MOTOR

MACHINE

“A”

SHAFT 4

HOUSING

SHAFT

SHAFT 3

MACHINE

“B”

PROBLEM 16.34 Given the following information, use

ASME standards to make a detail drawing of the spur gear us-

ing the instructions provided with these problems (in.):

20 teeth

Diametral pitch 5 5

208 pressure angle

Face width 5 2.500 IN

Shaft diameter 5 [1.125

Keyway for a .25 IN square key

Place the centerline of the keyway in line with a radial line

through the center of one tooth (one tooth profile needed to

show alignment). Include the necessary spur gear data in a chart

placed over the title block. Use the formulas given in this chapter

to solve for unknown values.

2.500 .875

Ø3.00

2X .12

2X 308

5/16-18 UNC-2B

.44

MATERIAL: SAE 4320

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MATERIAL: SAE 4320

1.750 2.00

2.500

PROBLEM 16.36 Use ASME standards to make a detail

drawing of a straight bevel gear given the following informa-

tion and the illustration shown below (in.):

Pitch diameter 5 [8.000 in.

Pressure angle 5 208

32 teeth

Diametral pitch 5 4

Face width 5 1.400

Shaft diameter 5 [1.125 in.

Use a .250 square key.

Core distance 5 4.401

Circular thickness 5 4.0939

Pitch angle 5 658

Root angle 5 62.158

Addendum 5 .3022

Whole depth 5 .5493

Chordal addendum 5 .0496

Chordal thickness 5 .7841

5/16–13UNC–2B

1.563 2.688

4.250

MOUNTING

DISTANCE

3.750

[

(8.233)

PROBLEM 16.37 Prepare a detail drawing of the pinion and

gear using the following gear data.

Dimensions for 208 straight bevel gear 908 shaft angle

Feature Pinion Gear

Number of teeth 22 75

Diametral pitch 10 10

Face width 1.25 1.25

Pressure angle 208208

Shaft angle 908908

Working depth 0.200 0.200

Whole depth 0.221 0.221

Pitch diameter 2.200 7.500

Pitch angle 16.3488 73.6528

Cone distance 3.908 3.908

Circular pitch 0.314 0.314

Addendum 0.142 0.058

Dedendum 0.077 0.161

Clearance 0.021 0.021

Dedendum angle 1.12682.3568

Face angle of blank 18.704874.7788

Root angle 15.222871.2968

Outside diameter 2.473 7.533

Pitch apex to crown 3.710 1.044

Circular thickness 0.188 0.126

Backlash 0.002 0.002

Chordal thickness 0.186 0.125

Chordal addendum 0.146 0.058

Tooth angle 107.149 min 107.149 min

Limit point width 0.046 0.046

Tool advance 0.002 0.002

BEARING PROBLEMS

Part 5: Problems 16.38 Through 16.41

PROBLEM 16.38 Use the charts shown in this chapter to

establish the following medium-service bearing dimensions

for an approximate [1.25 in. shaft. Use a word processor to

type the problem number and the answer for each required

item.

Bearing catalog number ________________________________

Bore ________________________________________________

Outside diameter _____________________________________

Width ______________________________________________

Fillet radius __________________________________________

Shaft shoulder diameter ________________________________

PROBLEM 16.35 Use ASME standards to make a detail draw-

ing of a rack that mates with the spur gear in Problem 16.34.

Use the instructions provided with these problems. The overall

length is 24 in.

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Housing shoulder diameter ______________________________

Shaft diameter _______________________________________

Housing diameter_____________________________________

PROBLEM 16.39 Use the charts shown in this chapter to es-

tablish the following medium-service bearing dimensions for

an approximate [3.5 in. shaft. Use a word processor to type

the problem number and the answer for each required item.

Bearing catalog number ________________________________

Bore ________________________________________________

Outside diameter _____________________________________

Width ______________________________________________

Fillet radius __________________________________________

Shaft shoulder diameter ________________________________

Housing shoulder diameter _____________________________

Shaft diameter _______________________________________

Housing diameter _____________________________________

PROBLEM 16.40 Use the charts shown in this chapter to es-

tablish the following medium-service bearing dimensions for

an approximate [20 mm shaft. Use a word processor to type

the problem number and the answer for each required item.

Bearing catalog number ________________________________

Bore ________________________________________________

Outside diameter _____________________________________

Width ______________________________________________

Fillet radius __________________________________________

Shaft shoulder diameter ________________________________

Housing shoulder diameter _____________________________

Shaft diameter _______________________________________

Housing diameter _____________________________________

PROBLEM 16.41 Use the charts shown in this chapter to es-

tablish the following medium-service bearing dimensions for

an approximate [60 mm shaft. Use a word processor to type

the problem number and the answer for each required item.

Bearing catalog number ________________________________

Bore ________________________________________________

Outside diameter _____________________________________

Width ______________________________________________

Fillet radius __________________________________________

Shaft shoulder diameter ________________________________

Housing shoulder diameter _____________________________

Shaft diameter _______________________________________

Housing diameter _____________________________________

LINKAGE DESIGN PROBLEMS

Part 6: Problems 16.42 and 16.43

PROBLEM 16.42 Given the following drawing as an exam-

ple, design a backhoe that can dig a 20-ft.-deep trench. Draw

an assembly drawing with dimensions specified between link–

ages. Show the backhoe in the fully closed position, half ex-

tended position, fully extended horizontal, and fully extended

at the maximum trench depth.

PROBLEM 16.43 Given the following drawing as an exam

ple, design a similar material handling lift that can lift a maxi-

mum of 12 ft. vertically and 16 ft. horizontally. The telescoping

actuator can operate a maximum 4-ft. extension.

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GEAR DESIGN, BEARING SELECTION,

SHAFT DESIGN PROBLEM

Part 7: Problem 16.44

PROBLEM 16.44 Design a two-speed gear reducer that will

operate eight to ten hours per day and receive moderate shock

while in operation. Use the following information:

■ A 5-HP 1750 electric motor supplies the input power.

■ There are six gears arranged approximately as shown on the

following drawing.

■ Gear C-D is a cluster gear sliding on the countershaft.

■ The output speed is 625 rpm when gear C is engaged with gear E.

■ The output speed is 437.5 rpm when gear D is engaged with

gear F.

■ Gear A has 32 teeth, gear B has 64 teeth, gear C has 25 teeth,

and gear D has 24 teeth.

Use the gear and bearing information from this chapter to design

the gear reducer and do the following:

1. Determine the diametral pitches for all six gears.

2. Determine the number of teeth for gears E and F.

3. Use tolerances, surface finishes, and fit as discussed in this

chapter.

4. Use manufacturers’ catalogs shown in this chapter or sup-

plied by your instructor to select standard parts.

5. Make a detailed drawing of the cluster gear, including spur

gear data charts for both gears on one sheet.

6. Make detailed drawings of the three shafts—input, output,

and countershaft—each on a separate sheet. The shafts are

approximately [1.250 in. Design the shafts based on bear–

ing specifications and fits. Design the keyseats based on the

shaft diameter given and as specified in the Machinery’s

Handbook or other source.

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MATH PROBLEMS

Part 8: Problems 16.45 Through 16.50

For the oblique triangle shown below (which is not drawn

to scale):

PROBLEM 16.45 Find side b given a 5 125, A 5 54.78,

B 5 65.28.

PROBLEM 16.46 Find side c given b 5 321, A 5 75.38,

C 5 38.58. (Hint: A 1 B 1 C 5 1808.)

PROBLEM 16.47 Find angle C given b 5 50.4, c 5 33.3,

B 5 118.58.

PROBLEM 16.48 Find angle A given b 5 51.5, a 5 62.5, B 5

40.78, and given that angle A is greater than 908.

PROBLEM 16.49 Find side b given a 5 320, c 5 475,

A 5 35.38, and given that angle C is less than 908.

(Hint: Find angle C first.)

PROBLEM 16.50 Find side a given b 5 50.4, c 5 33.3,

B 5 118.58.

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289



Chapter 16

Mechanisms: Linkages, Cams, Gears, and Bearings

Solutions to End-of-Chapter Problems

Linkage Problems

Part 1: Problems 16.1 Through 16.14

PROBLEM 16.1

PROBLEM 16.2

PROBLEM 16.3

290



PROBLEM 16.4

PROBLEM 16.5

PROBLEM 16.6

291



PROBLEM 16.7

PROBLEM 16.8

292



PROBLEM 16.10

293



PROBLEM 16.11

PROBLEM 16.12

294



PROBLEM 16.13

PROBLEM 16.14 Solutions will vary.

Cam Displacement Diagrams

Part 2: Problems 16.15 Through 16.25

PROBLEM 16.15

295



PROBLEM 16.16

PROBLEM 16.17

PROBLEM 16.18