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Position Analysis of a 4-Bar RRRR Linkage Using Complex Numbers

This study explores the position analysis of a 4-bar RRRR linkage by leveraging complex numbers. The approach involves viewing point P from two directions in the complex plane, effectively separating real and imaginary parts. We formulate two scalar equations to solve for two unknowns. By rearranging terms, and employing squaring and adding techniques, we simplify the analysis. The resulting calculations yield two roots, allowing us to determine the quadrant for angle q3 based on the signs of sine and cosine. This method offers a robust framework for analyzing complex linkages.

curran-marquez
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Position Analysis of a 4-Bar RRRR Linkage Using Complex Numbers

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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

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