Natural coordinates for the computer analysis of multibody systems

In this paper we will describe a new method for the computer kinematic and dynamic analysis of a wide range of three-dimensional mechanisms or multibody systems. This method is based on a new system of non-independent coordinates that use Cartesian coordinates of points and Cartesian components of unitary vectors in order to describe the position and the motion of the system. Angular coordinates are not used. The kinematic constraint equation comes in two ways, from the rigid-body condition for each element and from the joints or kinematic pairs. The consideration of unitary vectors facilitates considerably the formulation of pair constraints when the pair is associated with a particular direction, as is the case with revolute (R), cylindrical (C), or prismatic (P) pairs. The constraint equations are quadratic in the problem coordinates and they never involve transcendental functions. The dynamic differential equations are obtained in a very simple and effective way from the theorem of virtual power. Finally, two examples will be presented.