...and the Chebyshev "paradoxical" linkage:
...and of course Kempe's "universality theorem", that there is a linkage that traces any polynomial curve.
I recently came across "Planar Linkages Following a Prescribed Motion":
...which looks awesome. Especially intriguing are sentences like:
"In modern terms, the procedure proposed by Kempe is a parsing algorithm. It takes the defining polynomial of a plane curve as input and realizes arithmetic operations via certain elementary linkages. In this work, we approach the question from a different perspective... ...By encoding motions via polynomials over a noncommutative algebra, we reduce this task to a factorization problem."
But currently the terminology used is considerably over my head. Anyone know what branches of math you should study to be able to understand things like:
"...we recall that one can embed SE2 as an open subset of a real projective space. This allows us to introduce a noncommutative algebra K whose multiplication corresponds to the group operation in SE2, hence mimicking the role played by dual quaternions with respect to SE3. A polynomial with coefficients in K therefore describes a family of direct isometries, which we call a rational motion."
...other suggestions for what to study to be able to synthesize new linkages? Places or forums for a beginner to ask questions about linkages?