by fango on 7/25/17, 11:50 AM with 11 comments
by pavel_lishin on 7/25/17, 2:34 PM
by GregBuchholz on 7/25/17, 8:07 PM
by GregBuchholz on 7/25/17, 7:02 PM
https://en.wikipedia.org/wiki/Peaucellier%E2%80%93Lipkin_lin...
...and the Chebyshev "paradoxical" linkage:
https://www.futilitycloset.com/2015/01/03/chebyshevs-paradox...
...and of course Kempe's "universality theorem", that there is a linkage that traces any polynomial curve.
https://arxiv.org/abs/1511.09002
I recently came across "Planar Linkages Following a Prescribed Motion":
https://arxiv.org/abs/1502.05623
...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?