I have the following path,

enter image description here

The smaller radius isn't a hard constraint but the other dimensions are. I have a continuous rotation as the input & would like to design a planar linkage where the end of the output link follows this path (or at least approximately).

I had a look at the Chebyshev lambda linkage which looks approximately right but I would like the quick return to happen on the linear segment not the curved. There are spatial constraints that mean the output link must be the only link to occupy the trajectory space, which eliminates the classic Chebyshev linkage & the like as a solution.

How should I go about this? Is there a known method for reverse linkage design like this?

  • $\begingroup$ Have you checked out 3 or 4 bar linkages? $\endgroup$
    – Solar Mike
    Jan 6, 2023 at 17:55
  • $\begingroup$ @SolarMike yes but so far everything appears to start with knowing the link lengths to start with, currently it seems like a trial & error process which I cant believe is the case in real mechanism design. $\endgroup$
    – DrBwts
    Jan 6, 2023 at 17:57
  • $\begingroup$ I can't speak for the case of mechanical linkages, but a lot of good designs are arrived at by "trial and error" also known as iterative design. You make something complicated that does precisely what you want, then loosen your requirements in ways that simplify the construction, or conversely, make it more complicated to get tighter requirements, until you arrive at the perfect balance of accuracy and simplicity. $\endgroup$ Jan 7, 2023 at 20:23

1 Answer 1


This is the classic point path linkage synthesis problem. Any kinematics textbook covers this topic. Design of Machinery - Robert Norton, Theory of Machines and Mechanisms - Uicker and Pennock, Mechanism Design - Erdman and Sandor. A new CAD based method is recently published called pole and rotation angle constraints. See the book Planar Linkage Synthesis - Ron Zimmerman. www.prclinks.com You could also reference Hrones and Nelson atlas of coupler curves and find one that matches yours.


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