For engineers who already know the math—but still lose projects. For the last few years, I’ve been sharing technical guides here on Mechanical Design Handbook —how to size a motor, how to calculate fits, and (as you recently read) how to choose between timing belts and ball screws. But after 25 years in industrial automation, I realized something uncomfortable: Projects rarely fail because the math was wrong. They fail because: The client changed the scope three times in one week. A critical vendor lied about a shipping date (and no one verified it). The installation technician couldn’t fit a wrench into the gap we designed. University taught us the physics. It didn’t teach us the reality. That gap is why I wrote my new book, The Sheet Mechanic . This is not a textbook. It is a field manual for the messy, political, and chaotic space between the CAD model and the factory floor. It captures the systems I’ve used to survive industrial projec...
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.
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Step 1: Define the Desired Motion
Draw the coupler link AB in its three design positions: A1B1, A2B2, and A3B3.
Figure 1: Defining the three target positions. Sometimes standard pivot locations are invalid or obstructed.
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.
Figure 2: Defining alternate moving pivots C and D relative to the coupler AB using rigid triangles.
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
Figure 3: Locating the fixed ground pivots O2 and O4 using the bisectors of the alternate pivot paths.
Repeat the process for point D.
- Bisect lines D1D2 and D2D3.
- The intersection is the fixed pivot O4.
- Draw Link 4 as line O4D1.
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Step 5: Construct the Mechanism
Figure 4: Building the final kinematic chain. The coupler is now a rigid triangle connecting the moving pivots to the functional link AB.
- Draw line O2M equal to O2C1.
- Draw line O4N equal to O4D1.
- Draw the rigid coupler triangle M-N-A-B. Ensure it is dimensionally identical to the shape C1-D1-A1-B1.
- Apply an angular driving dimension (e.g., 20 degrees) to the input link.
Simulation and Verification
Figure 5: Setting up the animation dimension to verify the motion path.
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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