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1 2 3 4 Viewing the point P from two directions in the complex plane P O Re Im Q Position Analysis of a 4 bar RRRR Linkage Using Complex Numbers.

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Presentation on theme: "1 2 3 4 Viewing the point P from two directions in the complex plane P O Re Im Q Position Analysis of a 4 bar RRRR Linkage Using Complex Numbers."— Presentation transcript:

1 Viewing the point P from two directions in the complex plane P O Re Im Q Position Analysis of a 4 bar RRRR Linkage Using Complex Numbers

2 Separating the real P O Re Im Q Position Analysis of a 4 bar RRRR Linkage Using Complex Numbers And the imaginary parts We have two unknowns And two scalar equations to solve for them

3 Rearranging terms P O Re Im Q Position Analysis of a 4 bar RRRR Linkage Using Complex Numbers Squaring and adding

4 Rearranging terms P O Re Im Q Position Analysis of a 4 bar RRRR Linkage Using Complex Numbers Rearranging further

5 SubstituteSubstitute P O Re Im Q Position Analysis of a 4 bar RRRR Linkage Using Complex Numbers AndAnd To get OrOr

6 P O Re Im Q Position Analysis of a 4 bar RRRR Linkage Using Complex Numbers Solving we get two roots! Solving AndAnd The signs of sin 3 and cos 3 will let us determine the quadrant in which 3 lies


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