Kinematics from the Active Point of View

There are essentially two ways to keep track of a rigid body. In the passive view each rigid body carries a coordinate frame and the position and orientation of the body is specified by giving the transformation which relates coordinates in a standard reference frame to the local frame moving with the body. In the active view there is a single fixed coordinate frame. The position and orientation of a rigid body is specified by the transformation which moves the body from a standard (home) position to its current position. When there are several bodies and when bodies also carry several different frames it can be hard to account for all the different frames. The alternative active view simplifies much of the labour of setting up the forward kinematics and dynamics of serial robots. This active view is completely equivalent to the passive view, but the passive view seems to be preferred in current texts on robotics