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Homework2asol.spring11 - ME 352 - Machine Design I Spring...

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1 ME 352 - Machine Design I Name of Student____________________________ Spring Semester 2011 Lab Section Number_________________________ Homework No. 2. Parts (i) - (iv) are due at the beginning of lecture on Friday, January 28th. (20 points). Part (v) is due at the beginning of lab on Monday, January 31st, or Tuesday, February 1st. (20 points). Given a planar four-bar linkage (for typical notation of a four-bar linkage see Figure 2.15, page 62, and Figure 2.19, page 66, in the textbook) with the following link dimensions: Ground Link 1 14.0 inches Input Link 2 7.0 inches Coupler Link 3 10.0 inches Output Link 4 8.0 inches The fixed X and Y-axes are specified as horizontal and vertical, respectively, and the origin of this fixed Cartesian reference frame is coincident with the ground pivot of the input link 2. For the input angle D 60 2 = θ (counterclockwise from the X-axis): (i) Choose a suitable scale and accurately draw the four-bar linkage in its two possible configurations (open and closed). Measure the values of the joint variables 3 θ and 4 θ for each configuration. A similar problem of a sliding-block linkage is illustrated by Example 2.5, Section 2.12, see pages 77-79. (ii) Use the law of sines and the law of cosines to determine the joint variables 3 θ and 4 θ for the open configuration. (iii) Use the closed form solution to solve for the joint variables 3 θ and 4 θ . (Recall that the closed form solution for a planar four-bar linkage is commonly referred to as Freudenstein's equation, see Chapter 10, Section 10.11, Equations (10.23) - (10.26), pages 451 and 452, for one version of Freudenstein’s equation. Compare your answers for the two joint variables with the answers from Part (i). (iv) Set up and carry out the Newton-Raphson iteration procedure (see Chapter 2, Section 2.8, page 64) to solve for the joint variables 3 θ and 4 θ . Use the initial estimates for 3 θ and 4 θ for the open configuration given by Part (i) above. Continue to iterate until 3 θ and 4 θ converge to within 0.01 . D Clearly show all the steps for each iteration. (v) Using Matlab write a general computer program which uses the Newton-Raphson iteration procedure to solve for the joint variables 3 θ and 4 θ given initial estimates for these joint variables (and the input angle 2 θ and the link lengths). To check your computer program, use the initial estimates for the open configuration given by Part (i) above and print out the joint variables 3 θ and 4 θ .
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2 ME 352 - Machine Design I Name of Student_____________________________ Spring Semester 2011 Lab Section Number_________________________ Solution to Parts (i), (ii), (iii) and (iv) of Homework Set 2 (20 points). (i) The Graphical Method (3 Points). The link dimensions and the joint angles that are specified in the problem statement are: Ground Link: R 1 = 14.0 in θ 1 = 0 ˚ Input Link: R 2 = 7.0 in θ 2 = 60 ˚ Coupler Link: R 3 = 10.0 in θ 3 = ? ˚ Output Link: R 4 = 8.0 in θ 4 = ? ˚ For the specified input angle D 60 2 = θ , the two possible configurations of the four-bar linkage are as shown in Figure 1. The loop O 2 A B 1 O 4
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This note was uploaded on 04/23/2011 for the course ME 352 taught by Professor Staff during the Spring '08 term at Purdue.

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Homework2asol.spring11 - ME 352 - Machine Design I Spring...

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