3-Position Synthesis with Inversion Method using Unigraphics NX4 Sketch - Part 2

In previous posts, the fixed pivot points were determined from the moving pivot points. We can get result that can't be fitted in our design due to space limit. The principle of inversion can be applied to solve this problem. The first step is to find the three positions of the ground plan that correspond to the three desired coupler positions.

We start with our desired positions of fixed pivot points.

1) Draw desired fixed pivots (O₂ and O₄) and moving pivot points. Red lines are three desired positions of links (moving pivots).

2) Draw lines to make fixed relations between the ground plane (O₂O₄) and the second coupler position.

3) Transfer the ground position to the first coupler position using same relations developed in previous step as shown in dashed lines. Name new ground positions as O'₂ and O'₄ respectively.

4) Draw lines to make fixed relations between the ground plane (O₂O₄) and the third coupler position (A₃B₃).

5) Transfer the ground position to the first coupler position using same relations developed in previous step as shown in dashed lines. Name new ground positions as O''₂ and O''₄ respectively.

6) Draw lines O₂O'₂ and O'₂O''₂, bisect both lines and extend the perpendicular bisectors until they intersect. Label the intersection G.

6) Draw lines O₄O'₄ and O'₄O''₄, bisect both lines and extend the perpendicular bisectors until they intersect. Label the intersection H.

7) Draw O₂G, GH and O₄H. Now we get G and H as inverted fixed pivot points of moving link O₂O₄.

8) Re-invert the linkage to return to the original arrangement.

Let's see how it moves in [3-Position Synthesis with Inversion Method using Unigraphics NX4 Sketch - Part 3]

Further reading:

• Kinematic Design of Machines and Mechanisms
• Mechanism Design: Analysis and Synthesis (4th Edition)
• Compliant Mechanisms: Design of Flexure Hinges

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