DESIGN OF MACHINERY (LL) >C<
6th Edition
ISBN: 9781264001330
Author: Norton
Publisher: MCGRAW-HILL LEARNING SOLN.(CC)
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Textbook Question
Chapter 4, Problem 4.17P
Repeat Problem 4-16 except solve by the
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Re-work Problem 4 on Homework 2 using Lagrange's equations (see Figure 4 below). As
indicated in the original problem statement, find the equations of motion and the constraint force
(Hint: to find the constraint force, introduce an additional generalized coordinate and associated
Lagrange multiplier).
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
Problem 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
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@2
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Chapter 4 Solutions
DESIGN OF MACHINERY (LL) >C<
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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- 3-4 Design a fourbar mechanism to give the two positions shown in Figure P3-1 of coupler motion. (See Example 3-3, p. 105.) Build a model and determine the toggle positions and the minimum transmission angle from the model. Add a driver dyad. 2.409 2.656 B2 0.751 0.470 1.750 A2 B. 1.721 FIGURE P3-1arrow_forwardUse rotation about the current frame to calculate the transformation matrix for a rotation of 90° about yo axis and then 90° about zo axis.arrow_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_forward
- Problem 2 The linkage in Figure P7-5b has o4A = 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, AA, AB, Ac for the position shown for w2 = 15 rad/sec and a2 = 10 rad/sec^2 in the directions shown using an analytic 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 contactarrow_forwardProblem 2 The linkage in Figure P7-5b has O4A = 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, AA. AB,Ac for the position shown for w2 = 15 rad/sec and a2 = 10 rad/sec^2 in the directions shown using an analytic 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 contactarrow_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_forward
- The 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_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_forwardFigure below shows a four-bar linkage (non-scaled diagram) at an instant. The input angle is equal to the output angle (02 - 04) and the transmission angle is 30°. The input link is extended beyond joint B and an input force (Fin) is applied at the end of it, while an output force is drawn from the midpoint of the output link. If an output force of 30 N is desired from an input force of 10 N, how far the input link should be extended, i.e., what is the distance from point B to the point where Fin is applied. Fin B out undefined 02 04 A. Non-scaled diagram; AB = 10, CD=r4 = 30 (output), all in mmarrow_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_forwardSolve the following problem using both analytical(vector or scalar) and graphical (IC center)methodsarrow_forward2 Task Task 1 (40%): Get the Jacobian of the three-link manipulator below. As shown in the figure, all three joints are revolute. Joint 1’s axis is not parallel to the other two. Instead, there is a twist of 90 degrees in magnitude between axes 1 and 2. Write in terms of a frame {4} located at the tip of the hand and having the same orientation as frame {3}. Derive the Jacobian in three different ways: velocity propagation from base to tip, static force propagation from tip to base, and by direct differentiation of the kinematic equations. Compare these three approaches and discuss their pros and cons. 83 62 L1 Fig. 1. A 3R nonplanar armarrow_forward
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