In the Lagrangian approach, the position vector of a point on an arbitrary body in a MBS application can be written in terms of a set of coordinates as , where are the coordinates used to describe the system configuration. These coordinates for large constrained system or a simple closed loop system can be related by algebraic equations. For complex systems, the identification of independent coordinates (degrees of freedom) can be difficult, and for smaller systems with closed loops, singularities can be also encountered if one set of independent coordinates are used during the entire simulation. For example, in the case of a four-bar linkage, the two loop-closure equations are expressed in terms of three angles while the mechanism has one degree of freedom ; a single angle cannot be used as the degree of freedom during the entire simulation of the mechanism. Sheth and Uicker pioneered the use of numerical methods in identifying the independent coordinates . The Jacobian matrix of the algebraic constraint equations was used to identify the dependent and independent coordinates of the system. Sheth and Uicker implemented this approach in one of the first general purpose mechanism program called IMP (Integrated Mechanism Program). There were attempts to commercialize IMP, but these attempts were not very successful. It is worth mentioning also that Sheth, after completing his Ph.D., joined University of Michigan as a postdoc, where he taught a course that was attended by Nicolae Orlandea. Sheth later joined the faculty of the University of Virginia. Sadly, he passed away in 2009.