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  1. Position Analysis of a 4 bar RRRR Linkage Using Complex Numbers Q P Im q3 q4 q2 q1 Re O Viewing the point P from two directions in the complex plane

  2. Position Analysis of a 4 bar RRRR Linkage Using Complex Numbers Q P Im q3 q4 q2 q1 Re O Separating the real And the imaginary parts We have two unknowns And two scalar equations to solve for them

  3. Position Analysis of a 4 bar RRRR Linkage Using Complex Numbers Q P Im q3 q4 q2 q1 Re O Rearranging terms Squaring and adding

  4. Position Analysis of a 4 bar RRRR Linkage Using Complex Numbers Q P Im q3 q4 q2 q1 Re O Rearranging terms Rearranging further

  5. Position Analysis of a 4 bar RRRR Linkage Using Complex Numbers Q P Im q3 q4 q2 q1 Re O Substitute And To get Or

  6. Position Analysis of a 4 bar RRRR Linkage Using Complex Numbers Q P Im q3 q4 q2 q1 Re O Solving we get two roots! And The signs of sinq3 and cosq3 will let us determine the quadrant in which q3 lies