P0324 - Kinematics and Dynamics of Machinery SOLUTION...

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Kinematics and Dynamics of Machinery SOLUTION MANUAL 3-24-1 PROBLEM 3-24 Statement: Draw the Roberts diagram and find the cognates for the linkage in Figure P3-9. Given: Link lengths: Coupler point data: Ground link L 1 2.22  Crank L 2 1.0  A1P 3.06  31.00 deg  Coupler L 3 2.06  Rocker L 4 2.33  Solution: See Figure P3-9 and Mathcad file P0324. 1. Calculate the length BP and the angle  using the law of cosines on the triangle APB . B1P L 3 2 A1P 2 2 L 3 A1P cos   0.5  B1P 1.674 acos L 3 2 B1P 2 A1P 2 2 L 3 B1P  109.6560 deg 2. Use the Cayley diagram (see Figure 3-24) to calculate the link lengths of the two cognates. Note that the diagram is made up of three parallelograms and three similar triangles L 5 B1P  L 5 1.674 L 6 L 4 L 3 B1P  L 6 1.893 L 10 A1P  L 10 3.060 L 9 L 2 L 3 A1P  L 9 1.485 L 7 L 9 B1P A1P  L 7 0.812 L 8 L 6 A1P B1P  L 8 3.461 Calculate the coupler point data for cognates #2 and #3 A3P L 8  A3P 3.461 A2P L 2  A2P 1.000 180 deg 
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