DESIGN OF MACHINERY
6th Edition
ISBN: 9781260113310
Author: Norton
Publisher: RENT MCG
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Chapter 4, Problem 4.9P
The link lengths and the value of
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The general linkage configuration and terminology for an offset fourbar slider-crank linkage are shown in Figure below. The link lengths and the values of 02 and w2 are defined in. For the row(s) b and c, find the velocities of the pin joints A and B and the velocity of slip at the sliding joint using an analytical method. Draw the linkage to scale and label it before setting up the equations. y A 03 B Y 4 Link 3 A W2 Offset 02 04 = 90° Link 2 X 02 Slider position d TABLE P6-2 Data for Problems 6-6 to 6-7† Row Link 2 Link 3 Offset 02 02 a 1.4 4 1 45 10 2 -3 60 -12 3 8 2 -30 -15
The general linkage configuration and terminology for an offset fourbar
slider-crank linkage are shown in Figure below. The link lengths and the
values of 02 and w2 are defined in. For the row(s) b and c, find the
velocities of the pin joints A and B and the velocity of slip at the sliding joint
using an analytical method. Draw the linkage to scale and label it before
setting up the equations.
Link 3
Offset
04 = 90°
Link 2
02
Slider position d
TABLE P6-2 Data for Problems 6-6 to 6-7†
Row
Link 2
Link 3
Offset
02
1.4
4
1.
45
10
2
6.
-3
60
-12
3
8.
-30
-15
A general fourbar linkage configuration and its notation are shown in Figure
below. The link lengths, coupler point location, and the values of 02 and
w2 for the same fourbar linkages as used for position analysis in Chapter 4
are redefined in Table below. For the row c, draw the linkage to scale and
Using an analytical method calculate w3 and w4 and find the velocity of
point P. find the velocities of the pin joints A and.
RPA
AY
2
04
02
04
FIGURE P6-1
Configuration and terminology for the pin-Jointed fourbar linkage of Problems 6-4 to 6-5
TABLE P6-1 Data for Problems 6-4 to 6-5†
Row
Link 1
Link 2
Link 3
Link 4
02
02
Rpa
83
6.
2
7
30
10
6.
30
b.
9
3
8
85
-12
9.
25
10
6.
8
45
-15
10
80
O73
Chapter 4 Solutions
DESIGN OF MACHINERY
Ch. 4 - A position vector is defined as having a length...Ch. 4 - A particle is traveling along an arc of 6.5-in...Ch. 4 - Repeat problem 4-2 considering points A and B to...Ch. 4 - Repeat Problem 4-2 with the particles path defined...Ch. 4 - Repeat Problem 4-3 with the path of the particle...Ch. 4 - The link lengths and the value of 2 for some...Ch. 4 - Repeat Problem 4-6 except solve by the vector loop...Ch. 4 - Expand equation 4.7b and prove that it reduces to...Ch. 4 - The link lengths and the value of 2 and offset for...Ch. 4 - Repeat Problem 4-9 except solve by the vector loop...
Ch. 4 - The link lengths and the value of 2 and for some...Ch. 4 - Repeat Problem 4-11 except solve by the vector...Ch. 4 - Find the transmission angles of the linkages in...Ch. 4 - Find the minimum and maximum values of the...Ch. 4 - Find the input angles corresponding to the toggle...Ch. 4 - The link lengths. gear ratio (). phase angle (),...Ch. 4 - Repeat Problem 4-16 except solve by the vector...Ch. 4 - Figure P4-5 shows the mechanisms for the following...Ch. 4 - For one revolution of driving link 2 of the...Ch. 4 - Figure P4-7 shows a power hacksaw, used to cut...Ch. 4 - For the linkage in Figure P4-8, find its limit...Ch. 4 - For the walking-beam mechanism of Figure P4-9,...Ch. 4 - For the linkage in Figure P4-10, calculate and...Ch. 4 - For the linkage in Figure P4-11, calculate and...Ch. 4 - For the linkage in Figure P4-12, find its limit...Ch. 4 - Prob. 4.26PCh. 4 - For the linkage in Figure P4-13, find its limit...Ch. 4 - Prob. 4.28PCh. 4 - For the linkage in Figure P4-15, find its limit...Ch. 4 - For the linkage in Figure P4-15, find its limit...Ch. 4 - Prob. 4.31PCh. 4 - Prob. 4.32PCh. 4 - Figure 4-22 plots the cubic function from equation...Ch. 4 - Write a computer program or use an equation solver...Ch. 4 - Prob. 4.35PCh. 4 - Prob. 4.36PCh. 4 - Write a computer program or use an equation solver...Ch. 4 - Write a computer program or use an equation solver...Ch. 4 - Prob. 4.39PCh. 4 - Prob. 4.40PCh. 4 - Write a computer program or use an equation solver...Ch. 4 - Prob. 4.42PCh. 4 - Prob. 4.43PCh. 4 - Prob. 4.44PCh. 4 - Model the linkage shown in Figure 3-37a in...Ch. 4 - Prob. 4.46PCh. 4 - Prob. 4.47PCh. 4 - Prob. 4.48PCh. 4 - Prob. 4.49PCh. 4 - Prob. 4.50PCh. 4 - Figure 3-29g shows Evans approximate straight-line...Ch. 4 - For the linkage in Figure P4-16, what are the...Ch. 4 - The coordinates of the point P1 on link 4 in...Ch. 4 - Write a computer program or use an equation solver...Ch. 4 - For the linkage in Figure P4-17, calculate the...Ch. 4 - Prob. 4.56PCh. 4 - Prob. 4.57PCh. 4 - The elliptical trammel in Figure P4-18 must be...Ch. 4 - Prob. 4.59PCh. 4 - Prob. 4.60PCh. 4 - Repeat Problem 4-60 except solve by the vector...Ch. 4 - Write a computer program or use an equation solver...Ch. 4 - Write a computer program or use an equation solver...Ch. 4 - Write a computer program or use an equation solver...Ch. 4 - Write a computer program or use an equation solver...Ch. 4 - Figure P4-20 shows a cut-away view of a mechanism...Ch. 4 - For the linkage in Figure 3-32a, calculate and...
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- A general fourbar linkage configuration and its notation are shown in Figure below. The link lengths, coupler point location, and the values of 02 and w2 for the same fourbar linkages as used for position analysis in Chapter 4 are redefined in Table below. For the row c, draw the linkage to scale and Using an analytical method calculate w3 and w4 and find the velocity of point P. find the velocities of the pin joints A and. RPA Y B 4 03 04 02 1 02 FIGURE P6-1 Configuration and terminology for the pin-jointed fourbar linkage of Problems 6-4 to 6-5 TABLE P6-1 Data for Problems 6-4 to 6-5† Row Link 1 Link 2 Link 3 Link 4 02 Rpa 83 02 a 2 7 9. 30 10 30 7 9. 8 85 -12 9 25 3 10 8 45 -15 10 80arrow_forwardConsider the figure as shown below. O-XoYoZo is the reference frame and O-X₁Y₁Z₁ is the frame attached to the tool. Sketch the tool position after each intermediate position of the operation of the tool about the reference frame: roll π/2(rotate about Zo), pitch -T/2(rotate about Yo), yaw π/2(rotate about Xo). Please write the final rotation matrix expression. ZI,Zo XI,Xo Yı, Yoarrow_forwardGiven the vectors in Figure P1-2, use a scale of 1 inch = 10 units, and determine the following vectors: Figure P1-2 B=10 ; 270⁰ C=15 ; 210⁰ D=12,5 ; 315⁰ E= 7,5 ; 75⁰ F = 10 ; 215⁰ G= 15 ; 100⁰arrow_forward
- What is the equivalent root of the system of the figure using the displacement of the block as a generalized coordinatearrow_forwardFor the walking-beam mechanism of Figure P4-9, calculate and plot the xand y components of the position of the coupler point P for one complete revolution of the crank O2A. Hint: Calculate them first with respect to the ground link O204 and then transform them into the global XY coordinate system (i.e., horizontal and vertical in the figure). Scale the figure for any additional information neededarrow_forwardAll pertinent rigid dimensions are specified for the linkage shown. Note that the ground pivot for the input link is at the origin of the coordinate system. The input angle []in is currently 170° measured from the x axis as shown. The figure is not exactly to scale, but it is reasonably close for checking purposes. (a) Calculate the value of the angle []out as shown on the figure. Use the equations developed from the loop closure method. Note that you will need to incorporate a change of coordinate axes orientation to the axes defined for the loop closure equations. (b) Calculate the absolute location of point P with respect to the coordinate axes shown. 18 30° 9° 9 P 20 50° -170° Xarrow_forward
- The general linkage configuration and terminology for an offset fourbar slider- crank linkage are shown in the figure. The link lengths and the values of d, d.d and d..d are defined in the table. For row a, using graphical method, the value the acceleration of pin joint A is Row la b C d le If g 02 002 Link 2 1.4 2 3 3.5 5 3 0₂ Y Link 2 O 792.064 in/sec2 0₂ 291.385 in/sec2 O 1,593 in/sec2 O 1,779 in/sec2 Link 3 14 16 18 10 20 13 25 Link 3 Offset 1 -3 2 1 -5 10 10 Offset 03 Slider position d, d, d d 2.5 5 8 -8 15 -12 25 y B d.d d..d 10 -12 15 -15 -10 24 -4 -50 10 -45 50 100 18 04 = 90° 10 Xarrow_forwardSlide B travels along the center line XX'. Q2A = 18 cm, AB = 72 cm. 1. With the crank in the position shown, draw the four bar linkage. Name each link and show the finite and infinite cranks.2. Find the two extreme positions of block B. Express your answer in terms of the acute angle formed by crank Q2A with the horizontal axis (like the angle 45° in the figure)3. Determine the length of the stroke of B. Write your answer in two decimal places.arrow_forwardFigure out the 2D sketch of housing using AutoCAD and mention all the dimensions. Colour the hatched lines which are inside the curve (red) 37 30 14 R 2 holes 72 Dia 12R 60R 30 R 24 10 R 15R Housing 60 Rarrow_forward
- Plz answer this question Given the vectors in Figure P1-2 using a scale of 1 inch = 10 units, and determine the following vectors on the image below: Additional information A= 20 B= 270⁰ ; 10 C=210⁰ ; 15 D=315⁰; 12,5 E=75⁰ ; 7,5 F=215⁰ ; 10 G=100⁰ ; 15arrow_forward1. Find a combination of link lengths where motion of a point on output link is one quarter of a circle. 2. Find the value of all 0, 0, 0, and y in open and close configuration Read the value of link lengths and the input angle 8., then use the formulae given below to calculate the value of unknowns 03, 0, and y K₁ = = K₂= d K2 K3 = a²-b²+c²+d² 2ac A = cos 0₂ - K₁ - K₂ cos 0₂ + K3 B = -2 sin 0₂ C = K₁ (K₂ + 1) cos 02 + K3 -B± √B²-4AC 2A 0412 = 2tan-1 d K₁ = — K5 = c²d²a²-6² 2ab D = cos 0₂ - K₁ - K4 cos 0₂ + K5 E = -2 sin 0₂ FK₁+ (K₁ - 1) cos 02 +K5 0312 2 tan-1 (-E± -E± √E²4DF 2D Y = 04-03arrow_forwardQ3) You have been provided with following types of kinematic links. Can Type of link Numbers Binary 8 Ternary 3 Quaternary 2 Can you form a kinematic chain by selecting suitable number of links from the available quantity as indicated in the table above? Justify your answer. Note; (please provide an answer that is based on the Mechanics of Machines 1 handout MIME 3220)arrow_forward
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