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3-Position Motion Generation Synthesis with Alternate Moving Pivots using Unigraphics NX4 Sketch

In the previous post [3-Position Motion Generation Four-Bar Linkage Synthesis], the locations of the fixed ground pivots (O2 and O4) were mathematically determined by the positions of points A and B.

The Problem: Sometimes, these calculated fixed pivots land in impossible locations—inside another machine part, off the machine base, or too far away.

The Solution: We use Alternate Moving Pivots. Instead of using the endpoints of the line AB, we create new points (C and D) that are rigidly attached to the moving body. By adjusting the location of C and D, we can steer the fixed pivots (O2 and O4) to desirable locations.

Step 1: Define the Desired Motion

Draw the coupler link AB in its three design positions: A1B1, A2B2, and A3B3.

Step 2: Define Alternate Moving Pivots (C and D)

This is the critical step. We attach a "virtual" rigid shape to line AB to define new points C and D.

Procedure:
1. Draw points C1 and D1 relative to A1B1.
2. Replicate this geometry for positions 2 and 3.
3. Use Geometric Constraints (Equal Length, Fixed Angle) to ensure the triangle ABC is identical in all three positions.

Step 3: Synthesize Fixed Pivot O2

Now we treat C as our moving pivot instead of A.

  • Draw construction lines from C1 to C2 and C2 to C3.
  • Construct perpendicular bisectors for both lines.
  • The intersection is the fixed pivot O2.
  • Draw Link 2 as line O2C1.

Step 4: Synthesize Fixed Pivot O4

Repeat the process for point D.

  • Bisect lines D1D2 and D2D3.
  • The intersection is the fixed pivot O4.
  • Draw Link 4 as line O4D1.

Step 5: Construct the Mechanism

1. Draw line O2M equal to O2C1.
2. Draw line O4N equal to O4D1.
3. Draw the rigid coupler triangle M-N-A-B. Ensure it is dimensionally identical to the shape C1-D1-A1-B1.
4. Apply an angular driving dimension (e.g., 20 degrees) to the input link.

Simulation and Verification

Use the Animate Dimension command to sweep the input angle. You should see the target line AB pass perfectly through all three desired positions.

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