Link frame and joint definitions

The ERobot is a general way to represent a rigid-body tree that can be a single serial-link chain or a branched mechanism.

Every link in the model has:

• a parent, except the root link
• zero, one or more children
• has a link coordinate frame in which inertial properties such as centre-of-mass and inertia are defined

This is shown diagrammatically below

where everything in red is a property (attribute) of link k, and everything in blue is a property of its parent link.

We borrow Featherstone's notation where the function is the parent of link k.

A robot joint connects two links. It connects coordinate frames on each side of the joint: the parent-side one expressed in the parent link's coordinate frame, and the child-side one is the child link's link coordinate frame.

is a constant transform, with respect to the parent frame, that describes the location of the parent-side of the joint. It is a property of the child link, since the parent link may have multiple children.

Frame can be expressed with respect to frame using an elementary-transform sequence (ETS). It comprises zero or more constant transforms and only one variable transform. It is parsed and processed at ELink construction time and is accessed via attributes:

• v is a variable elementary transform representing the joint. v.eval(q) is an SE3 object representing the joint transform .
• Ts is an SE3 object, possibly identity, from precomputing the constant part of the ETS
• A(q) is an SE3 object representing

With respect to Featherstone's notation.