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Mechanical Engineering QUESTION #2492
Question 1
For an open kinematic chain with \(n\) links forming a vector loop from point A to point B, the closure equation in scalar form (x-projection) is:
  • \(\sum_{k=1}^{n} r_k\sin\phi_k = y_B - y_A\)
  • \(\sum_{k=1}^{n} r_k\cos\phi_k = x_B - x_A\)✔️
  • \(\prod_{k=1}^{n} r_k\cos\phi_k = x_B - x_A\)
  • \(\sum_{k=1}^{n} r_k = |r_B - r_A|\)
Correct Answer Explanation
The vector loop equation projected onto the x-axis yields \(\sum_{k=1}^n r_k\cos\phi_k = x_B - x_A\) and onto y gives \(\sum_{k=1}^n r_k\sin\phi_k = y_B - y_A\).