> For the complete documentation index, see [llms.txt](https://alpaca4d.gitbook.io/docs/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://alpaca4d.gitbook.io/docs/basics/constraints/equal-dof.md).

# Rigid Link

A **rigid link** ties one node to another through an infinitely stiff connection. It is the way to join two nodes that are offset from each other — a beam framing into the face of a column, a member with an eccentric connection — without adding a real element.

{% hint style="warning" %}
Earlier versions of this page described an **Equal DOF** component. There is no such component. `EqualDOF` exists inside Alpaca4d as a constraint class, used when [Deserialise](/docs/basics/utility/deserialise.md) reads an `equalDOF` command back from a `.tcl` file, but the only constraint you can build in Grasshopper node-to-node is the **Rigid Link** described here.
{% endhint %}

## 🔧 Grasshopper component

`Rigid Link (Alpaca4d)` — **Alpaca4d ▸ 03\_Constraint**

### Inputs

| Name             | Nick               | Type  | Default | Description                                                                                    |
| ---------------- | ------------------ | ----- | ------- | ---------------------------------------------------------------------------------------------- |
| RetainedPoint    | `RetainedPoint`    | Point | —       | The **retained** (master) node. Its motion drives the link.                                    |
| ConstrainedPoint | `ConstrainedPoint` | Point | —       | The **constrained** (slave) node. Its motion follows.                                          |
| Type             | `Type`             | Text  | `beam`  | `bar` or `beam`. Attach a **Value List** to the input and Alpaca4d fills it with both options. |

### The two types

| Type   | Constrains                                                       | Behaves like                                                                                                                    |
| ------ | ---------------------------------------------------------------- | ------------------------------------------------------------------------------------------------------------------------------- |
| `bar`  | The three translational DOFs only, in the direction of the link. | A pin-ended rigid bar. Transfers force, not moment.                                                                             |
| `beam` | All six DOFs.                                                    | A rigid offset. Transfers force and moment, and converts the retained node's rotation into translation at the constrained node. |

### Outputs

| Name       | Nick         | Type       | Description                                                                 |
| ---------- | ------------ | ---------- | --------------------------------------------------------------------------- |
| Constraint | `Constraint` | Constraint | Constraint object, to be connected to [Assemble](/docs/basics/assemble.md). |

## 📈 When to use it

**Use it when**

* Two nodes at different locations should move as one rigid body — a beam offset from a column centreline, a rigid bracket, a stiff connection zone.
* You want the coupling without meshing a stiff element, which would need a stiffness chosen by hand and can wreck the conditioning of the system.

**Do not use it when**

* Many nodes on one floor need tying → a [Rigid Diaphragm](/docs/basics/constraints/diaphragm.md) is one constraint instead of dozens.
* The connection has real flexibility — a rigid link has none.
* The link would close a loop with another constraint. Over-constraining gives a singular matrix, and the solver failure will not point back here.

## 🔗 Relation to OpenSees

```tcl
rigidLink $type $retainedNodeTag $constrainedNodeTag
```

`$type` is `bar` or `beam`. Node tags are resolved from the point coordinates by the [Assemble](/docs/basics/assemble.md) tolerance.

For completeness, the `EqualDOF` class writes:

```tcl
equalDOF $masterNodeTag $slaveNodeTag $dof1 $dof2 ...
```

but no Grasshopper component produces one.