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 real-world engineering, a mechanism often needs to guide a part through more than just a start and end point. It usually requires passing through 3 specified positions to clear obstacles or perform complex tasks.
This technique is known as 3-Position Motion Generation. We can extend the logic from our previous post [Four-bar linkage Synthesis using CAD Sketcher] to solve this problem geometrically within a modern CAD environment like Siemens NX, SolidWorks, or CATIA.
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The Design Challenge
Assume we must design a mechanism to move Link AB through three specific positions (A1B1, A2B2, A3B3) while avoiding an obstacle (represented by the rectangle below).
Figure 1: Defining the three target positions (A1B1, A2B2, A3B3) relative to the obstacle.
Step-by-Step Synthesis
1. Define the Positions:
Draw Link AB in its three design positions: A1B1, A2B2, and A3B3.
2. Geometric Synthesis for Pivot O2:
To find the fixed pivot that allows point A to move through all three locations, we must find the center of the circle that passes through A1, A2, and A3.
- Draw construction lines connecting A1 to A2 and A2 to A3.
- Create Perpendicular Bisectors for both lines.
- The intersection of these bisectors is the fixed pivot O2.
- Draw line O2A1. This is your Input Link (Link 2).
Figure 2: Intersecting the bisectors of A1-A2 and A2-A3 locates the first ground pivot O2.
3. Geometric Synthesis for Pivot O4:
Repeat the exact same logic for point B to find the Follower Link pivot.
- Draw construction lines connecting B1 to B2 and B2 to B3.
- Create Perpendicular Bisectors for both lines.
- The intersection is the fixed pivot O4.
- Draw line O4B1. This is your Follower Link (Link 4).
Figure 3: Finding the second ground pivot O4 using the positions of Point B.
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Building and Validating the Kinematic Chain
Now we construct the linkage geometry to verify the motion path.
Figure 4: Building the constraint network. Links O2M, O4N, and MN form the mobile mechanism.
- Draw line O2M equal in length to O2A1.
- Draw line O4N equal in length to O4B1.
- Draw coupler line MN equal in length to A1B1.
- Set an angular driving dimension (e.g., 15 degrees) between O4B1 and O4N.
Simulation via "Animate Dimension":
In the CAD Sketcher, select the angular dimension and set the limits based on the synthesized range.
Example: Lower Limit: 0 | Upper Limit: 56.355 | Steps: 150
Figure 5: Configuring the animation parameters to drive the linkage through the synthesized path.
Video Result: 3-Position Synthesis
Watch how the synthesized mechanism perfectly guides the link through all three positions while avoiding the obstacle.
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