3-Position Motion Generation Four-Bar Linkage Synthesis using Unigraphics NX4 Sketch

In the real design problem, it will be more practical with 3 specified positions of a line in sequential order than 2-position synthesis. We can use a logical extension of the linkage synthesis technique described in [Four-bar linkage Synthesis using Unigraphics NX4 Sketch] to do the linkage synthesis with 3 positions.

Assume that we have to design the mechanism that move the link AB through 3 positions as shown below. The rectangle represents the limit of link AB, so link AB cannot interfere with the rectangle.

1) Draw link AB in its three design positions A₁B₁, A₂B₂, and A₃B₃ as shown above.
2) Draw construction lines from point A₁ to A₂ and A₂ to A₃

3) Bisect line A₁A₂ and line A₂A₃ and extend their perpendicular bisectors until they intersect with each other. Label the intersection O₂.
4) Draw line O₂A₁. It's link 2.
5) Repeat the same for another end of the link. Draw construction lines from point B₁ to B₂ and B₂ to B₃

6) Bisect line B₁B₂ and line B₂B₃ and extend their perpendicular bisectors until they intersect with each other. Label the intersection O₄.

7) Draw line O₄B₁. It's link 4.

8) Draw line O₂M and set the same length as O₂A₁.

9) Draw line O₄N and set the same length as O₄B₁.

10) Draw line MN and set the same length as A₁B₁.

11) Set angular dimension between O₄B₁ and O₄N to any desired value e.g. 15 degrees.

12) Select "Animate Dimension" Command in Unigraphics NX4 sketch and set lower limt to 0 and Upper limit to 56.355 (or any other value) and Steps/Cycle to 150 (the more steps, the smoother simulation).

See the results of four-bar linkage from three-position motion generation synthesis in the following video clip.

Further reading:

• Kinematic Synthesis of Linkages (Mechanical Engineering Series)
• Graphical solution of the branch and order problems of linkage synthesis for multiply separated positions
• Analysis of the Four-Bar Linkage: Its Application to the Synthesis of Mechanisms
• Kinematic Synthesis of Linkages
• Computer-aided synthesis of kinematic linkages (Massachusetts Institute of Technology. Dept. of Mechanical Engineering. Thesis. 1975. M.S)
• Computerized synthesis of straight-line four-bar linkages from inflection circle properties

Sponsored links