# Questions tagged [linkage]

The linkage tag has no usage guidance.

10
questions

**11**

votes

**2**answers

579 views

### Which curves and surfaces are realizable by linkages? references?

Ok, so I try to formulate rigorously the question in the title, for which I am asking for references. My definitions may be flawed, so feel free to adjust/correct them! I care about dimensions 2 and 3 ...

**0**

votes

**3**answers

91 views

### Calculating radii allowing for circular placement of polygonal linkage's joints

Given a planar polygonal linkage defined by a sequence of $n$ hinge joints $(j_0,\,\cdots,\,j_{n-1},j_n = j_0)$ with links of fixed lengths $\lbrace\|j_{k+1}-j_k\|=d_k\ |\ 0\le k\lt n\rbrace$ between ...

**5**

votes

**1**answer

289 views

### Is there a relationship between the moduli space of spatial polygons and the moduli space of labeled points?

It is well known that the set of all polygons with consecutive side lengths $l_1, \dots, l_n$ in $\mathbb{R}^3$, considered up to rigid motions, is a compact complex manifold. Of course, I am assuming,...

**3**

votes

**1**answer

113 views

### The volume of a region arising from planar linkages

Let $x_0,\dots,x_n$ be a collection of variable points in $\mathbb{R}^2$ and let $c>0$ be a fixed constant. Is there any way I could compute an upper bound of the volume of the region in $\mathbb{...

**1**

vote

**0**answers

117 views

### Obstruction to Gorenstein Liaisons of space curves

Let $P_1,P$ be Hilbert polynomials of curves in $\mathbb{P}^3$. Denote by $H_{P_1,P}$ the flag Hilbert scheme parametrizing pairs $(C_1 \subset C)$ where $C_1, C$ are of Hilbert polynomials $P_1$ and $...

**2**

votes

**0**answers

93 views

### A basic question on complete intersection liaisons of curves

I am a beginner in the Linkage theory and would like to clarify certain points I am not sure of.
Let $P$ be the Hilbert polynomial of a curve in $\mathbb{P}^3$. Let $L$ be an irreducible component of ...

**4**

votes

**1**answer

393 views

### A.J. Galitzer's Ph.D. thesis: On the moduli space of closed polygonal linkages on the 2-sphere

Recently I became curious about moduli spaces of linkages and so I found and began reading some papers of Kapovich and Millson. In the paper Hodge theory and the art of paper folding, the Ph.D. ...

**7**

votes

**2**answers

374 views

### Calabi-Yau manifolds and polygonal linkage configuration spaces: related?

I was reading about Calabi-Yau manifolds, about which I know little, and was wondering
if these (or related complex manifolds, perhaps K3 surfaces) can be viewed as configuration
spaces (or moduli ...

**2**

votes

**0**answers

147 views

### When is the area of the convex hull of a tree-like linkage maximal?

This is inspired from this recent question. Given in the plane a tree-linkage (fixed length rigid edges, vertices are flexible joints, connected and no cycles) is there a simple description of when ...

**10**

votes

**5**answers

601 views

### Is the area of a polygonal linkage maximized by having all vertices on a circle?

Consider a (non-stellated) polygon in the plane. Imagine that the edges are rigid, but that the vertices consist of flexible joints. That is, one is allowed to move the polygon around in such a way ...