Timeline for Work on "Churning Polygons"
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 25, 2017 at 17:37 | vote | accept | Manfred Weis | ||
| Jun 25, 2017 at 16:10 | answer | added | j.c. | timeline score: 5 | |
| Jun 25, 2017 at 15:21 | comment | added | Gerhard Paseman | That is an interesting application, and probably has been explored by companies producing digital animation. You might consider looking for technical reports from such companies that are available through a web search. Also, the pentagon linkage has more degrees of freedom and thus there are up to four different possible values for area with some locations for the vertex opposite the fixed edge. However a quadrilateral linkage has essentially less than two degrees of freedom, so five is the minimal number of edges. Gerhard "State Spaces Can Be Weird" Paseman, 2017.06.25. | |
| Jun 25, 2017 at 15:08 | comment | added | Manfred Weis | @GerhardPaseman thanks for the reply; designing such polygons isn't the problem; I have found some interesting examples, which I can share. What fascinates me about those polygons is that they yield a primitive model for the motion of crustaceans filled with an incompressible liquid. | |
| Jun 25, 2017 at 14:58 | comment | added | Gerhard Paseman | I have no references, although Unsolved problems in geometry (edited by Croft and Guy I think?) may have something. I would think the term "adjusting" preferable to "churning". Finally, a nonconvex regular pentagon should be adjustable, as well as some convex ones: fix an edge and consider a linkage in which the opposite vertex corresponds to an area, and note that this gives a continuous function with lengthy level curves for all but the extreme values. Gerhard "Proving Propositions Through Picturing Pantographs" Paseman, 2017.06.25. | |
| Jun 25, 2017 at 9:56 | history | asked | Manfred Weis | CC BY-SA 3.0 |