Class LinkChain 

A LinkChain is a hierarchy of transformations. At the top is the 
RootLink and it is followed by a number of Link痴 . Each link, be it a
 RootLink or Link, evaluates to a matrix, called the link matrix 
(LinkMatrix). This matrix consists of two parts, one is a variable
 part (degrees of freedom) and the other is a relatively constant part,
 called rigid extend (RigidExtend). It can be graphically represented as:

 

 

RootLink 

The link variable is a rotation, rotXYZ. The link matrix is defined as

RigidExtend * Rx (rotXYZ.x) * Ry (rotXYZ.y) * Rz (rotXYZ.z)

where Rx (.) stands for rotation about the x-axis, etc.

 

Link 

The variable part of a Link is of one degree of freedom. It can be 
translational or rotational. A typical 3 degrees of freedom (xyz) 
rotational joint can be decomposed into 3 Links, with the first two being null links:

 

 

LinkChain 

A LinkChain consists of a RootLink and a number of Link痴. The reason
 that the LinkChain can start with rotation, the variable part of the
 RootLink, is that the IK system will collapse all the node 
transformations from the root of the scene to the parent matrix of the
 Start Joint and the translation part of the Start Joint, called the 
parent matrix, and transform the node hierarchy of the IK chain into 
this space. The author of the plugin solver does not have to be 
concerned about parentMatrix. They work on the problem as it is rooted 
at the origin of the world. The data structure of LinkChain should be 
sufficient for those solvers that DoesOneChainOnly() and UseSwivelAngle().

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