Homework8asol.spring11

Homework8asol.spring11 - ME 352 - Machine Design I Spring...

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ME 352 - Machine Design I Name of Student ______________________________ Spring Semester 2011 Lab Section Number ___________________________ Homework No. 8 (30 points). Due at the beginning of lecture on Monday, March 28th. Solve Problem 13.7, on page 603, for the crank position o θ 45 = using the Graphical Method. Assume that gravity is acting into the paper (i.e., the negative Z-direction) and the effects of friction in all of the lower pairs in the mechanism can be neglected. The recommended procedure for performing a static force analysis of this linkage using the graphical method is as follows: (i) Draw a scaled figure of the linkage and measure the orientations (i.e., the angles) of links 3, 4, and 5. (Please check the accuracy of your measurements by using trigonometry, such as, the law of sines and the law of cosines). (ii) Draw free body diagrams of each of the moving links. (iii) Identify all two-force members, three-force members, and/or four-force members. (iv) Draw all the force polygons accurately to scale. Clearly state the scales that you use for your polygons. (v) Determine all the unknown internal reaction forces. Specify the magnitudes and the directions of these forces. (vi) Determine the magnitude and direction of the torque 12 12 M( o r T) acting on the crankshaft at 2 . O (vii) Specify whether the two-force members are in tension or in compression.
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2 Solution to Homework 8. The crank-shaper mechanism is drawn half-full size in the figure below.
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3 Position Analysis. First, determine the angles that links 4 and 5 make with the positive X-axis. The angle 24 45 90 135 oo o AO O ∠= + = (1) From measurements of the scaled drawing, the angle 42 AO O 13 (2) and the angle CBE 3 (3) where point E is as shown in Figure 1. Figure 1. The Geometry of the Mechanism. The accuracy of the measurements given by Equations (2) and (3) can be checked from trigonometry. The cosine rule for the 2 4 OA O Δ can be written as 22 2 2 4 2 2 4 2 4 AO AO O O 2 (AO ) (O O ) cos A O O =+ (1) Sunbstituting the given data into this equation gives 2 2 4 AO 2.5 6 2 2.5 6 cos135 63.463 in o × × × = (2) Therefore, the distance between pin A and the ground pin 4 O is
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4 4 AO 7.966 in = (3) Now applying the sine rule to the 2 4 OA O Δ gives 24 42 sin AO O sin AO O AO AO = (4)
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Homework8asol.spring11 - ME 352 - Machine Design I Spring...

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