This paper presents a new methodology for specification and control of the motion of an articulated rigid body for the purposes of animation by coordinate transformations. The approach is to formulate the problem as a coordinate transformation from the joint space of the body to a user-defined animation space which is chosen for convenience in constraining the motion. Constraints are applied to the resulting coordinate transformation equations. It is sufficiently general so that it can be applied to all common types of control problems, including closed loop as well as open loop mechanisms. We also provided a new approach to simulate a closed loop mechanism, which is using animation space transformation technique. The method is formulated in detail and is demonstrated by animating the motion of an inchworm.