DESIGN OF MACHINERY
6th Edition
ISBN: 9781260113310
Author: Norton
Publisher: RENT MCG
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Chapter 4, Problem 4.58P
The elliptical trammel in Figure P4-18 must be driven by rotating link 3 in a full circle. Derive analytical expressions for the positions of points A, B, and a point C on link 3 midway between A and B as a function of
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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
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4
RB
02
02
1
02
04
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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…
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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- Problem 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_forwardThe 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 Tarrow_forwardFind 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_forward
- 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 expression. ZI,Zo XI,Xo Yı, Yoarrow_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_forwardDefine and show on the figure the necessary vectors and their angles for second mechanism and construct the corresponding vector-loop equation(s). please draw the vectors and angles and visually show them on mechanism you can name the angles theta1, theta2 etc. it should be looking exactly like the example( first mechanism).arrow_forward
- Oestion-1: An elliptical trammel is a double slider-crank mechanism used for drawing ellipses as shown in figure (a) below. Position vectors for various linkages are drawn as shown in figure (b). Where: R2: represents position vector for a Slider which can slide along x-axis only R4: represents position vector for a Slider which can slide along y-axis only R3 represents position vector for a crank (Take R3 = 10mm, 03 = 45°, V3 = 10mm/sec) Rix: This is aligned with x-axis and represents fixed position of slider (R4) from ground RIY: This is aligned with Y-axis and represents fixed position of slider (R2) from ground Take: R13= 20mm, Rịy=40mm. Assume crank is rotating with constant velocity Note: all angles are measured counterclockwise from x-axis. a) Formulate the vector loop, position, velocity and acceleration equations b) Simplify the equations by plugging in respective angles and solve to find R2, R4, linear velocities of both sliders and angular acceleration of crank. c) Identify…arrow_forwardThe kinematic scheme of the mechanism is given. Point C is the center of curvature of the link 3 at the point of the contact. Link 2 is with circular shape with center point B. Find the degrees of freedom.arrow_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
- What is the equivalent root of the system of the figure using the displacement of the block as a generalized coordinatearrow_forwardIn the figure, we apply a transformation matrix to box A to obtain box B. (a) Derive the 3 x 3 homogeneous matrix that achieves the transformation in the figure. (b) Compute its inverse. B a A barrow_forward3. The four bars of Figure A are initially free in the plane, then connecting to bars 2, 3 and 4, through their pivots, to bar 1, as shown in figure B. Choose a generalized coordinate system for these bars in design A and, depending on this system, determine the number of degrees of freedom after assembly, as shown in design B y 3 A B Xarrow_forward
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