tarea 2. design_of_machinery norton

76

FIGURE P2-2

Problem 2-19

* Answers in Appendix F

DESIGN OF MACHINERY CHAPTER 2

2-10 Use linkage transformation on the linkage of Figure P2-1d (p. 74) to make it a 2-DOF mechanism.

2-11 Use number synthesis to find all the possible link combinations for 2-DOF, up to 9 links, to hexagonal order, using only revolute joints.

2-12 Find all the valid isomers of the eightbar 1-DOF link combinations in Table 2-2 (p. 38) having:

a. Four binary and four ternary links b. Five binaries, two ternaries, and one quaternary link c. Six binaries and two quaternary links d. Six binaries, one ternary, and one pentagonal link

2-13 Use linkage transformation to create a 1-DOF mechanism with two sliding full joints from a Stephenson's sixbar linkage in Figure 2-14a (p. 48).

2-14 Use linkage transformation to create a 1-DOF mechanism with one sliding full joint and a half joint from a Stephenson's sixbar linkage in Figure 2-14b (p. 48).

*2-15 Calculate the Grashof condition of the fourbar mechanisms defined below. Build cardboard models of the linkages and describe the motions of each inversion. Link lengths are in inches (or double given numbers for centimeters).

Part 1.

a. 2 4.5 7 9 b. 2 3.5 7 9 c. 2 4.0 6 8

Part 2. d. 2 4.5 7 9 e. 2 4.0 7 9 f. 2 3.5 7 9

2-16 What type(s) of electric motor would you specify

a. To drive a load with large inertia. b. To minimize variation of speed with load variation. c. To maintain accurate constant speed regardless of load variations.

2-17 Describe the difference between a cam-follower (half) joint and a pin joint.

2-18 Examine an automobile hood hinge mechanism of the type described in Section 2.14 (p. 57). Sketch it carefully. Calculate its mobility and Grashof condition. Make a cardboard model. Analyze it with a free-body diagram. Describe how it keeps the hood up.

2-19 Find an adjustable arm desk lamp of the type shown in Figure P2-2. Measure it and sketch it to scale. Calculate its mobility and Grashof condition. Make a cardboard model. Analyze it with a free-body diagram. Describe how it keeps itself stable. Are there any positions in which it loses stability? Why?

2-20 Make kinematic sketches, define the types of all the links and joints, and determine the mobility of the mechanisms shown in Figure P2-3.

*2-21 Find the mobility of the mechanisms in Figure P2-4 (p. 78).

2-22 Find the Grashof condition and Barker classifications of the mechanisms in Figure P2-4a, b, and d (p. 78).

2-23 Find the rotatability of each loop of the mechanisms in Figure P2-4e, f, and g (p. 78).

Dr. J. M. Rico

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KINEMATICS FUNDAMENTALS

FIGURE P2-3

Problem 2-20 Backhoe and front-end loader Courtesy of John Deere Co.

*2-24 Find the mobility of the mechanisms in Figure P2-5 (p. 79).

2-25 Find the mobility of the ice tongs in Figure P2-6 (p. 79).

a. When operating them to grab the ice block. b. When clamped to the ice block but before it is picked up (ice grounded). c. When the person is carrying the ice block with the tongs.

*2-26 Find the mobility of the automotive throttle mechanism in Figure P2-7 (p. 79).

*2-27 Sketch a kinematic diagram of the scissors jack shown in Figure P2-8 (p. 80) and determine its mobility. Describe how it works.

2-28 Find the mobility of the corkscrew in Figure P2-9 (p. 80).

2-29 Figure P2-IO (p. 80) shows Watt's sun and planet drive that he used in his steam engine. The beam 2 is driven in oscillation by the piston of the engine. The planet gear is fixed rigidly to link 3 and its center is guided in the fixed track 1. The output rotation is taken from the sun gear 4. Sketch a kinematic diagram of this mechanism and determine its mobility. Can it be classified by the Barker scheme? If so, what Barker class and subclass is it?

2-30 Figure P2-ll (p. 81) shows a bicycle handbrake lever assembly. Sketch a kinematic diagram of this device and draw its equivalent linkage. Determine its mobility. Hint: Consider the flexible cable to be a link.

2-31 Figure P2-12 (p. 81) shows a bicycle brake caliper assembly. Sketch a kinematic diagram of this device and draw its equivalent linkage. Determine its mobility under two conditions.

a. Brake pads not contacting the wheel rim. b. Brake pads contacting the wheel rim.

Hint: Consider the flexible cables to be replaced by forces in this case.

77


Dr. J. M. Rico

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Dr. J. M. Rico

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Dr. J. M. Rico

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• 78

y

L1 = 174

L2 = 116

L3 = 108

L4 = 110

(a) Fourbar linkage

LJ=l50 L2=30 L3 = 150 L4 = 30

y

-box

X

(d) Walking-beam conveyor

Lt = 87

L2=49 L3 = 100

L4 = 153

L5 = 100

L6 = 153

2

X

y y

X

Lt = 162 L2 =40 L4 = 122 L3 = 96

(b) Fourbar linkage

A 3

0 2 0 4 =L3 = L5 = 160

0 80 4 = L6 = L7 = 120

0 2 A =02C = 20

0 4B=04D = 20

04E=04G = 30

OsF= OgH = 30

B

(e) Bellc rank mechanism

X


G

7

H

y

L2 = 19

L3 =70

£4=70

L5 = 70

L6= 70

(c) Radial compressor

(f) Offset slider crank

L1 =45.8

L2 = 19.8

L3 = 19.4

L4 = 38.3

L5 = 13.3

L7 = 13.3

L8 = 19.8

£9=19.4

(g) Drum brake mechanism (h) Symmetrical mechanism

I all dimensions in mm I FIGURE P2-4

Problems 2-21 to 2-23 Adapted from P. H. Hill and w. P. Rule. (1960) Mechanisms: Analysis and Design. with permission


Link 6 moves horizontally in a straight line

FIGURE P2-5

(a) (b)

79

Link 8 moves horizontally in a straight line

Problem 2-24 Chebyschev (a) and Sylvester-Kempe (b) straight-line mechanism Adapted from Kempe, How to Draw a Straight Line, Macmillan: London, 1877

2-32 Find the mobility, the Grashof condition, and the Barker classification of the mechanism in Figure P2-l3 (p. 82).

2-33 Figure P2-14 (p. 82) shows a "pick-and-place" mechanism in combination with a "walking beam." Sketch its kinematic diagram, determine its mobility and its type (i.e., is it a fourbar, a Watts sixbar, a Stephenson's sixbar, an eightbar, or what?) Make a cardboard model of all but the gear train portion and examine its motions. Describe what it does. (Xerox the page and enlarge it, or print it from the PDF file on the CD-ROM. Then paste the copies on cardboard and cut out the links.)

2-34 Figure P2-15 (p. 83) shows a power hacksaw, used to cut metal. Link 5 pivots at 0 5 and its weight forces the sawblade against the workpiece while the linkage moves the blade (link 4) back and forth within link 5 to cut the part. Sketch its kinematic diagram, determine its mobility and its type (i.e., is it a fourbar, a Watts sixbar, a Stephenson 's sixbar, an eightbar, or what?) Use reverse linkage transformation to determine its pure revolute-jointed equivalent linkage.

FIGURE P2-7

F F

w

FIGURE P2-6

Problem 2-25

Problem 2-26. Adapted from P. H. Hill and W P Rule. (1960) Mechanisms: Analysis and Design, with permission

Dr. J. M. Rico

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Dr. J. M. Rico

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Dr. J. M. Rico

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80

FIGURE P2-9

Problem 2-28



FIGURE P2-8

Problem 2-27

*2-35 Figure P2-16 (p. 83) shows a manual press used to compact powdered materials. Sketch its kinematic diagram, determine its mobility and its type (i.e., is it a fourbar, a Watts sixbar, a Stephenson's sixbar, an eightbar, or what?) Use reverse linkage transformation to determine its pure revolute-jointed equivalent linkage.

2-36 Sketch the equivalent linkage for the cam and follower mechanism in Figure P2-17 (p. 83) in the position shown. Show that it has the same DOF as the original mechanism.

2-37 Describe the motion of the following rides, commonly found at an amusement park, as pure rotation, pure translation, or complex planar motion.

0

A

t

FIGURE P2-l 0

Problem 2-29 James Watt's sun and planet drive

) L1 = 2.15

L2 = 1.25

L3 = 1.80 3

L4 = 0.54

2

Section A-A


Fcah/e 3

cable

handlebar

FIGURE P2-11

Problem 2-30 Bicycle hand brake lever assembly

a. A Ferris wheel b. A "bumper" car c. A drag racer ride d. A roller coaster whose foundation is laid out in a straight line e. A boat ride through a maze f. A pendulum ride g. A train ride

FIGURE P2-12

Problem 2-31 Bicycle brake caliper assembly

wheel rim

81

brake lever

hand grip

frame

82

0204 = 108

02A = 40

L3 = 108

L4=40

0206 = 200

028 = 32

L5 = 260

06C = 96

c

FIGURE P2-14


FIGURE P2-13

Problem 2-32 Crimping Tool

Lt = 0.92

L2 = 0.27

L3 = 0.50

L4 = 0.60

Fcrimp

2-38 Figure P2-la (p. 74) is an example of a mechanism. Number the links, starting with 1. (Don't forget the "ground" link.) Letter the joints alphabetically, starting with point A.

a. Using your link numbers, describe each link as binary, ternary, etc. b. Using your joint letters, determine each joint's order. c. Using your joint letters, determine whether each is a half or full joint.

2-39 Figure P2-lb (p. 74) is an example of a mechanism. Number the links, starting with 1. (Don't forget the "ground" link.) Letter the joints alphabetically, starting with A.


product

Section A-A

Problem 2-33 Walking-beam indexer with pick-and-place mechanism Adapted from P. H. Hill and w. P. Rule. (7960). Mechanisms: Analysis and Design. with permission


I , Ws

FIGURE P2-15

workpiece

L2 =75 mm L3 =170 mm

83

Problem 2-34 Power hacksaw Adapted from P. H. Hill and W P Rule. (7960). Mechanisms: Analysis and Design, with permission

2-40 Figure P2-lc (p. 74) is an example of a mechanism. Number the links, starting with I. (Don't forget the "ground" link.) Letter the joints alphabetically, starting with A.

a. b. c.

Using your link numbers, describe each link as binary, ternary, etc. Using your joint letters, determine each joint's order. Using your joint letters, determine whether each is a half or full joint.

I

3 3 powder

die

FIGURE P2 - 16

Problem 2-35 Powder compacting press Adapted from P. H. Hill and w P. Rule. (7960). Mechanisms: Analysis and Design. with permission

follower

\

FIGURE P2-17

Problem 2-36

84

• This mechanism was created when the boss complained that the light was being left on overnight too frequently in the shop storeroom but refused to provide funds to buy an electronic solution. The shop technician solved the problem mechanically (and whimsically) from scrap parts. The boss was later promoted, perhaps because of hi s demonstrated mastery of budgetary control.


2-41 Figure P2-ld (p. 74) is an example of a mechanism. Number the links, starting with I . (Don't forget the "ground" linlc) Letter the joints alphabetically, starting with point A.


2-42 Find the mobility, the Grashof condition, and the Barker classification of the oil field pump shown in Figure P2-18.

2-43 Find the mobility, the Grashof condition, and the Barker classification of the aircraft overhead bin shown in Figure P2- 19. Make a cardboard model and investigate its motions.

2-44 Figure P2-20 shows a "Rube Goldberg" mechanism* that turns a light switch on when a room door is opened and off when the door is closed. The pivot at 02 goes through the wall. There are two spring-loaded piston-in cylinder devices in the assembly. An arrangement of ropes and pulleys inside the room (not shown) transfers the door swing into a rotation of link 2. Door opening rotates link 2 CW, pushing the switch up as shown in the figure, and door closing rotates link 2 CCW, pulling the switch down. Consider the spring-loaded cylinder at the switch to be effectively a single variable-length binary link. Find the mobility of the linkage.

2-45 Use Working model to create and animate the mechanism in Figure P2-14 (p. 82).

2-46 Use Working model to create and animate the mechanism in Figure P2-15 (p. 83).

2-47 Use Working model to create and animate the mechanism in Figure P2- 18.

2-48 Find the mobility of the mechanism shown in Figure 3-33 (p. 142).

2-49 1 Find the mobility of the mechanism shown in Figure 3-34 (p. 143).



76

12

FIGURE P2-18

Problem 2-42 An oil field pump - dimensions in inches

Dr. J. M. Rico

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KINEMATICS FUNDAMENTALS 85

6.95

9.17

9.17 ---~

FIGURE P2-19

Problem 2-43 An aircraft overhead bin mechanism - dimensions in inches

2-52 Find the mobility of the mechanism shown in Figure 3-37b (p. 144).

FIGURE P2-20

A 'Rube Goldberg" light switch actuating mechanism (Courtesy of Robert Taylor, WPI)

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