DESIGN OF MACHINERY
6th Edition
ISBN: 9781260113310
Author: Norton
Publisher: RENT MCG
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Textbook Question
Chapter 2, Problem 2.11P
Use number synthesis to find all the possible link Combinations for 2 DOF, up to 9 links, to hexagonal order, using only revolute joints.
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(i) Determine binary link, ternary link for the given kinematic chain as shown in figure below and also find the number of degrees of
freedom by using Kutzbach criteria.
The link lengths and the value of 2 and offset for some fourbar crank-slide linkages are defined
in Table 1. The linkage configuration and terminology are shown in Figure 1. For the rows
assigned, find
(a) all possible solutions for angle and slider position d by vector loop method.
(b) the transmission angle corresponding to angle 83. (Hint: Treat the vector R4 as virtual rocker)
Show your work in details: vector loop, vector equations, solution procedure.
Table 1
Row
a
b
с
offset
02
Link 2
1.4
3
5
A
R2
0₂
Link 3
4
8
20
slider axis.
R3
Link 3
R₂
d
R₁
Figure 1.
0₁
Offset
1
2
-5
С
B
R4
T
84
X
Q2
45°
-30°
225°
For the 3-DOF Industrial manipulator arm as shown in Figure 3, determine
the joint displacements for known position and orientation of the end of the
arm point.
0.
0.
Y1A
Y2 A
Y3
X2
X3
21
22
23
Yo
xo
Figure 3. 3 DOF RRR Industrial manipulator arm
The link transformation matrices are given by
C3 -S3 0 a3C3
S3 C3
1
C2 -S2 0 a,C2
C1
S1
-S1
-C1
d1
S2
C2
2T3
%3D
T2
1
1
1
1
1
S1
C\C2a3+C1a2
C1C2C3 – C1S2S3 -C¡C2S3 – C1S2S3
S,C2C3 – S1S2S3 -SĄC2S3 – S1 S2C3 -C1 SịC2a3+ Sja2
Szaz + d1
1
OT3 =
= °T, 'T2 ?T3
S½C3 + C2S3
- S2S3 + C2C3
Chapter 2 Solutions
DESIGN OF MACHINERY
Ch. 2 - Find three (or other number as assigned) of the...Ch. 2 - How many DOF do you have in your wrist and hand...Ch. 2 - How many DOF do the following joints have? Your...Ch. 2 - How many DOF do the following have in their normal...Ch. 2 - Are the joints in Problem 2-3 force closed or form...Ch. 2 - Describe the motion of the following items as pure...Ch. 2 - Calculate the mobility of the linkages assigned...Ch. 2 - Identify the items in Figure P2-1 as mechanisms,...Ch. 2 - Use linkage transformation on the linkage of...Ch. 2 - Prob. 2.10P
Ch. 2 - Use number synthesis to find all the possible link...Ch. 2 - Prob. 2.12PCh. 2 - Use linkage transformation to create a 1-DOF...Ch. 2 - Use linkage transformation to create a 1-DOF...Ch. 2 - Calculate the Grashof condition of the fourbar...Ch. 2 - Prob. 2.16PCh. 2 - Describe the difference between a cam-follower...Ch. 2 - Examine an automobile hood hinge mechanism of the...Ch. 2 - Find an adjustable arm desk lamp of the type shown...Ch. 2 - The torque-speed curve for a 1/8 hp permanent...Ch. 2 - Find the mobility of the mechanisms in Figure...Ch. 2 - Find the Grashof condition and Barker...Ch. 2 - Find the rotatability of each loop of the...Ch. 2 - Find the mobility of the mechanisms in Figure...Ch. 2 - Find the mobility of the ice tongs in Figure P2-6:...Ch. 2 - Prob. 2.26PCh. 2 - Prob. 2.27PCh. 2 - Find the mobility of the corkscrew in Figure P2-9.Ch. 2 - Figure P2-10 shows Watts sun and planet drive that...Ch. 2 - Figure P2-11 shows a bicycle handbrake lever...Ch. 2 - Figure P2-12 shows a bicycle brake caliper...Ch. 2 - Find the mobility, the Grashof condition, and the...Ch. 2 - The approximate torque-speed curve and its...Ch. 2 - Prob. 2.34PCh. 2 - Prob. 2.35PCh. 2 - Sketch the equivalent linkage for the cam and...Ch. 2 - Describe the motion of the following rides,...Ch. 2 - For the mechanism in Figure P2-1 a, number the...Ch. 2 - Repeat Problem 2-38 for Figure P2-1b.Ch. 2 - Repeat Problem 2-38 for Figure P2-1c.Ch. 2 - Prob. 2.41PCh. 2 - Find the mobility, the Grashof condition, and the...Ch. 2 - Find the mobility, the Grashof condition, and the...Ch. 2 - Figure P2-20 shows a Rube Goldberg mechanism that...Ch. 2 - All the eightbar linkages in Figure 2-11 part 2...Ch. 2 - Prob. 2.46PCh. 2 - Prob. 2.47PCh. 2 - Find the mobility of the mechanism shown in Figure...Ch. 2 - Find the mobility of the mechanism shown in Figure...Ch. 2 - Find the mobility of the mechanism shown in Figure...Ch. 2 - Find the mobility of the mechanism shown in Figure...Ch. 2 - Prob. 2.52PCh. 2 - Prob. 2.53PCh. 2 - Repeat Problem 2-38 for Figure P2-1f.Ch. 2 - Repeat Problem 2-38 for Figure P2-1g.Ch. 2 - For the example linkage shown in Figure 2-4 find...Ch. 2 - For the linkage shown in Figure 2-5b find the...Ch. 2 - Prob. 2.58PCh. 2 - Figure P2-21b shows a mechanism. Find its mobility...Ch. 2 - Prob. 2.60PCh. 2 - Figure P2-21 d shows a log transporter. Draw a...Ch. 2 - Figure P2-21e shows a plow mechanism attached to a...Ch. 2 - Figure P2-22 shows a Hart inversor sixbar linkage....Ch. 2 - Figure P2-23 shows the top view of the partially...Ch. 2 - Figure P2-24a shows the seat and seat-back of a...Ch. 2 - Figure P2-24b shows the mechanism used to extend...Ch. 2 - Figure P2-24b shows the mechanism used to extend...Ch. 2 - Figure P2-25 shows a sixbar linkage. Is it a Watt...Ch. 2 - Use number synthesis o find all the possible link...Ch. 2 - Use number synthesis to find all the possible link...Ch. 2 - Prob. 2.71PCh. 2 - For the mechanism in Figure P2-26, number the...Ch. 2 - Figure P2-27 shows a schematic of an exercise...Ch. 2 - Calculate the mobility of the linkage in Figure...Ch. 2 - Calculate the Grashof condition of the fourbar...Ch. 2 - The drum brake mechanism in Figure P2-4g is a...
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- Determine binary, ternary link and quaternary link for the given kinematic chain as shown in figure below and also find the number of degrees of freedom by using Kutzbach criteria.arrow_forwardFor the 3-DOF Industrial manipulator arm as shown in Figure 1, determine the joint displacements using inverse kinematics approach for known position and orientation of the end of the arm point. The link transformation matrices are given byarrow_forward3 25 cm B P 25 cm A 25 cm 03 04 02 10 cm (crank) 20 cm FIGURE 1. Hoeken's linkage (a) Solve for 03 and 04 if the crank angle 02 = 120°. Show your work. (You may want to use the scripts to verify your answers.) (b) Find the position of point P when the crank angle is at 60 degrees.arrow_forward
- You have been provided with following types of kinematic links. Type of link Binary number = 8 Ternary number = 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.arrow_forward6- if A=[ and B is 3x3 uit matrix -2 Pind AB)arrow_forwardSolve and Draw the following. [Tech pen (0.2 light, 0.4 medium, 0.6 above heavy)] Consider a four bar linkage with the following links: L0 = 180mm, L1 = 40mm, L2 = 170 mm. Using grashof criterion, determine the ranges of values for L3 if the linkage is: a) crank-rocker mechanism b)drag link mechanism c) double rocker.arrow_forward
- Define: cartesian space Forward kinematics Matrixarrow_forwardOA 0.90 ● AB 3.25 BC 2.75 BD 5.50 CG Length [m] 0.55 OE 1.85 CE H 2.20 2.581 3.15 В Angle 4. 60.99 Angle r = 159,81° Distance OC 2.88m - W ОА [deg] [rad/s] 160.0 3.0 m BD Mass [kg] 3000 Present a clearly labelled free body diagram for each rod and the slider; Calculate the magnitudes and directions of all reaction forces at the instant shown using accelerations obtained in acceleration analysis part; Calculate the instantaneous torque, T, required to drive the mechanism at the instant shown. J BD Mass moment of inertia [kg.m²] 2200arrow_forward4. A general fourbar linkage configuration and its notation are shown in the following figure and table. Find a 3, a 4,A¼, ABA, AB,Ap for open circuit by vector loop method. Row Link 1 Link 2 Link 3 Link 4 02 Rpa 63 6 2 7 9 30 10 6 30 - 12 - 15 7 3 8 85 25 3 10 6 8 45 -10 10 80 d 7 25 24 - 4 45 e 75 -50 10 300 Rp B A 03 2 X 04 NO O55arrow_forward
- Design linkages per the requirements below. Remember ground is also a link with the number of anchor points determining the type of link it is (i.e. binary, ternary, etc.). In each case, draw a clean kinematic diagram followed by a mobility calcula- tion verifying the design requirement:arrow_forwardEvaluate the 3-DOF wrist as shown in Figure 2, use the conventional method to determine 1. Linear velocity and 2. Angular velocity NOTE: for JOINT 3 ( 03 ) only Connected to robot arm Pitch Roll Yaw Figure 2: Wrist assembly The known position and orientation of the end of the arm point is. C, C2 [-C,S2C3 + S¼S3 -S;S2C3 – C1S3 C2C3 C¡S2S3 + S1C3 S4S2S3 + C,C3 -C2S3 01 S,C2 S2 1 °T3=°T¡'T2²T3arrow_forwardCalculate the mobility of the kinematic chain pleasearrow_forward
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