[Mechanism Design] 4 bar linkage passing given 3 points

4 bar linkage passing given 3 pts

given: the trace of point A, B (A1, A2, A3, B1, B2, B3)

Fig.1

How to find?

A0 is a circumcenter of A1A2A3

B0 is a circumcenter of B1B2B3

Then, we can make the 4-bar linkage

A0B0(fixed) - B0B1(input) - A1B1(coupler) - A1A0(follower)

What if we can't set A0 point to one of pivots?

Fig.2

Put an arbitrary point, C3. Make use of kinematic inversion; now, we find C2 and C1.
Similarly, the fixed pivot point C0 is a circumcenter of C1C2C3.
Finally, we can make the 4-bar linkage
C0B0(fixed) - B0B1(input) - B1C1(coupler) - C1C0(follower)