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Mechanical Engineering QUESTION #2482
Question 1
The Cartesian method for position analysis of a planar link AB of length \(L_{AB}\) with angle \(\phi\) to the horizontal uses the constraint equation:
  • \((x_B - x_A)\sin\phi + (y_B - y_A)\cos\phi = L_{AB}\)
  • \((x_B - x_A)^2 + (y_B - y_A)^2 = L_{AB}^2\)✔️
  • \(x_B - x_A = L_{AB}\sin\phi\) and \(y_B - y_A = L_{AB}\cos\phi\)
  • \(\sqrt{x_B^2 + y_B^2} = L_{AB}\)
Correct Answer Explanation
For a rigid link AB of fixed length \(L_{AB}\), the geometric constraint is \((x_B-x_A)^2+(y_B-y_A)^2=L_{AB}^2\). This Pythagorean distance constraint is the foundation of the Cartesian method.