From BlenderWiki

Limit Distance Constraint

Description

The Limit Distance constraint forces its owner to stay either farer than, nearer than, or exactly at a given distance from its target. In other words, the owner’s location is constrained either outside, inside, or at the surface of a sphere centered on its target.

When you specify a (new) target, the Distance value is automatically set to correspond to the distance between the owner and this target.

Note that if you use such a constraint on a connected bone, it will have no effect, as it is the parent’s tip which controls the position of your owner bone’s root…

Options

Target

This constraint uses one target, and is not functional (red state) when it has none.

(Bone Target)

When using a bone target, you can chose where along this bone lays the target point, using the Head/Tail numeric field.

Distance

This numeric field sets the limit distance, i.e. the radius of the constraining sphere.

R

When clicked, this small button will recalculate the Distance value, so that it corresponds to the actual distance between the owner and its target (i.e. the distance before this constraint is applied).

Clamp Region

The Limit Mode drop-down menu allows you to chose how to use the sphere defined by the Distance setting and target’s center:

Inside (default)

The owner is constrained inside the sphere.

Outside

The owner is constrained outside the sphere.

Surface

The owner is constrained on the surface of the sphere.

Examples

Objects

Limit Distance between objects example.

No constraint.	The Limit Distance constraint just added.
Inside clamp region…	Outside clamp region…
Surface clamp region…	Surface clamp region, with an enlarged Distance value.

A Limit Distance constraint applied to Owner empty, using Target_1 empty as target. The yellow dashed circle materializes the sphere defined by the Distance value and the target center. In (The Limit Distance constraint just added), as Distance is set to the distance between Owner and Target_1, the owner does not move.

Armature’s Bones

Limit Distance between bones example.

Two Limit Distance constraints with a same target.

Inside clamp region, moving the target nearer…

Inside clamp region, moving the target farer…

The two green constrained bones have a Limit Distance constraint, with the same target bone (the selected one). In the three pictures, the yellow dashed (arcs of) circles materializes their respective Distance spheres. In (Inside clamp region, moving the target nearer…), both owner bones are inside their sphere, everything’s perfect… In (Inside clamp region, moving the target farer…), the target is moved so that both owner bones are outside of their clamp sphere. As you can see, the unconnected (though parented) bone moves, to stay inside its sphere, whereas the connected bone cannot move, and hence is not effectively constrained…