Kinematics and dynamics of multibody system based on natural and joint coordinates using velocity transformations

The equations of motion are initially formulated using natural coordinates. These coordinates are used to define the position of the system, kinematic joints between bodies, and forcing functions on and between the bodies. When using this system of coordinates the definition of initial system is straightforward. The equations of motion are then expressed in terms of relative joint coordinates with the use of velocity transformation method. The velocity transformation matrix relates the relative coordinates to the natural ones. The kinematic relationships for each joint type and the graph theory for identifying the system topology are used in constructing the velocity transformation matrix. Use of both natural and relative coordinates produces an efficient set of equations without loss of generality, then the equations of motion can be efficiently integrated.