DESIGN OF MACHINERY
6th Edition
ISBN: 9781260113310
Author: Norton
Publisher: RENT MCG
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Textbook Question
Chapter 4, Problem 4.54P
Write a computer program or use an equation solver such as Mathcad, Matlab, or TKSolver to calculate and plot the angular position of link 4 with respect to the XY coordinate frame and the transmission angle at point B of the linkage in Figure P4-16 as a function of the angle of link 2 with respect to the XY frame.
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The link lengths, value of theta2, and offset for some fourbar slider-crank linkages are defined inTable P4-2. The linkage configuration and terminology are shown in Figure P4-2. For row a,draw the linkage to scale and graphically find all possible solutions (both open and crossed)for angles theta3 and slider position d.
The linkage in Figure P7-5b has 04A = O2A = 0.75 , AB = 1.5 , and AC = 1.2 in . The effective crank angle in the position shown is 77º and angle BAC = 30 ° . Find a3 , AA , AB , Ac for the position shown for m2 = 15 rad / sec and a2 = 10 rad / sec2 in the directions shown using an analytical method . ( Hint : Create an effective linkage for the position shown and analyze it as a pin - jointed fourbar . ) the linkage has a parallelogram form Assume rolling contact C 02 A 3 . B 02 02 T
Consider 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
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ZI,Zo
XI,Xo
Yı, Yo
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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- For 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_forwardWhat is the equivalent root of the system of the figure using the displacement of the block as a generalized coordinatearrow_forwardProblem 2 The linkage in Figure P7-5b has O,A = O2A = 0.75, AB= 1.5, and AC = 1.2 in. The effective crank angle in the position shown is 77° and angle BAC = 30°. Find a3, A4, AB,Ac for the position shown for @2 = 15 rad/sec and a2 = 10 rad/sec in the directions shown using an analytical method. (Hint: Create an effective linkage for the position shown and analyze it as a pin-jointed fourbar.)the linkage has a parallelogram form Assume rolling contact C @2 A 3 В a2 2 4 04arrow_forward
- A general inverted fourbar slider-crank linkage has links length: link 2 = a = 2, link 4 = c = 4, and link 1= d = 6 in. The input values are 02 = 60°, y = 90°. The linkage configuration and terminology are shown in figure below; note that this figure does not represent the real dimensions of the linkage We need to find the angular positions of link 4 (04), of link 3 (03) and the effective length of link 3 (b) for both open and crossed configurations. 03 Өд В 4 RB 02 02 1 02 04 Choose... For open configuration, the angle 04 measured form X axis CCW in degree = Choose... For open configuration, the angle 03 measured form X axis CCW in degree = Choose... + For open configuration, the absolute value of the effective length of link 3, b = Choose... For crossed configuration, the angle 04 measured form X axis CCW in degree = Choose... For crossed configuration, the angle 03 measured form X axis CCW in degree = Choose... For crossed configuration, the absolute value of the effective length of…arrow_forwardThe figure below shows an offset slider crank linkage. The links lengths are: link2 = a= 100 mm and link3 = b = 600 mm. The offset is c = 190 mm. we need to : 1. determine the maximum horizontal position of the slider B (dmax) and the corresponding input angle 02 2. determine the minimum horizontal position of the slider B (dmin) and the corresponding input angle 02 Y 03 y В R3 R4 R, 04 R2 02 d ► X R1 The maximum horizontal position of the slider is dmax = Choose... + The input angle 02 corresponding to dmax , in degree and measured CCW from X axis, is = Choose... + The minimum horizontal position of the slider is dmin = Choose... + The input angle 02 corresponding to dmin , in degree and measured CcW from X axis, is = Choose.. +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
- Find the transformation matrix for the following rotations: 1) Rotate a about the original x-axis (in frame 0). (Xo, Yo, Zo) → (X₁,Y₁,Z₁); 2) Followed by a rotation of B about current z-axis (in frame 1). (X₁,Y₁,Z₁)→ (X₂, X₂, Z₂); 3) Followed by a rotation of y about Xo -axis (in frame 0). (X2, Y, Z₂)→ (X3, Y, Z3); 4) Followed by a rotation of about Z3 - axis (in frame 3). (X3, X3,Z3) → (X,Y4, Z4). E F3 $ R F F4 Q Search DII % 5 F5 T F6 6 Y PRE F7 & H 7 PrtScn F8 U 8 Home Endarrow_forwardProblem 4.7 ( example on analytical position analysis of pinjointed fourbar linkage) The link lengths and the value of 0, for some fourbar linkages are defined in Table P4-1. 1. For row a, find all possible solutions (both open and crossed) for angles 0, and 0, using the vector loop method. R3 R4 R2 R1 04 FIGURE 4-6arrow_forwardFind the transformation matrix for the following transformations: 1) Rotate 45° about Xo-axis. (Xo, Yo, Zo) → (X₁, Y₁, Z₁); 2) Followed by a rotation of 90° about Xo-axis. (X₁, Y₁, Z₁)→ (X₂, Y₂, Z₂); 3) Followed by a rotation of 60° about Y₂-axis. (X₂, X2, Z2)→ (X3, Y, Z3); 4) Followed by a rotation of 60° about Z₂-axis. (X3, Y3, Z3) → (X, Y4, Z4). Note: give final answer in matrix multiplication form, no need to write out the elements of the matrices or multiply the matrices out. URALLY AND AFICIALLY LGarrow_forward
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