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Graphical Synthesis : 4 position path

Graphical Synthesis : 4 position path. P 2. P 3. P 1. P 4. y 14. P 14. O 4. Step I : Locate the 4 positions of crank. Step II : Choose P 1 and P 4 as the two working points.

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Graphical Synthesis : 4 position path

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  1. Graphical Synthesis : 4 position path P2 P3 P1 P4 y14 P14 O4 Step I : Locate the 4 positions of crank. Step II : Choose P1and P4 as the two working points Step III : Pole P14 is chosen at a convenient location on the perpendicular bisector of P1P4. We chose O2 to coincide with P14 Measure the angle y14

  2. Graphical Synthesis : 4 position path P2 P3 P1 P4 A4 y14 O2 Y14 / 2 Y14 / 2 P14 O4 A1 Step IV : Choose a convenient direction for O2O4. Step V : Choose O2. Step VI : With P14 as center two lines are drawn at angles of Y2/2 with O2 O4. Two points A1 and A2 are chosen on these lines. These lines correspond to the locations of the coupler after inversion.

  3. Graphical Synthesis : 4 position path P2 P3 P1 P4 A4 y14 A3 O2 Y14 / 2 Y14 / 2 A2 P14 O4 A1 Step VII : Draw an arc with O2 as center and radius A1O2=A4O2. Step VIII : Draw an arc with P2 as center and P2A2 as radius to locate A2 in the inversion. Repeat with P3 to locate A3. Note that two possibilities exist for each case. We chose one.

  4. Graphical Synthesis : 4 position path P2 P3 P1 P4 A4 y14 A3 O2 Y14 / 2 O”’4 Y14 / 2 A2 P14 O”4 O4 A1 O’4 Step IX : Choose O’’’4to coincide with P14. Step X : Fix the coupler and locate relative positions of O4 for positions 2 and 3 by constructing DA1P1O’4~DA2P2O4 and DA1P1O’’4~DA3P3O4.

  5. Graphical Synthesis : 4 position path P2 P3 P1 P4 A4 y14 A3 O2 Y14 / 2 O”’4 Y14 / 2 A2 P14 O”4 O4 A1 B1 O’4 Step XI : Find the center of O4, O’4, O”4. This is B1.

  6. Graphical Synthesis : 4 position path P2 P3 P1 P4 A4 y14 A3 O2 Y14 / 2 O”’4 Y14 / 2 A2 P14 O”4 O4 A1 B1 O’4 Assembled Mechanism

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