This paper introduces a new modular software approach combining symbolical and numerical methods for the simulation of the dynamics of mechanical systems. It is based on an exact, noniterative object-oriented algorithm, which is applicable to mechanisms with any joint type and any topology, including branches and kinematic loops. The simulation of big well-partitioned systems has complexity O(N), where N is the total number of simulated bodies. A new design software Virtual System Designer (VSD) integrates this method with the three-dimensional computer aided design tool Autodesk Inventor, which minimizes the cost of the development of models and the training of design engineers. The most time-expensive routine of the simulation process in VSD is the calculation of the accelerations of each body, which needs to find the roots of matrix equations. Accounting for the sparsity of matrices can significantly improve the numerical efficiency of the routine. The preprocessing module, developed using Maple software, performs the symbolic simplification of the matrix multiplication’s and QR decomposition’s procedures. The new coordinate projection method is demonstrated. The results of the simulation of the dynamics of a double insulator chain example show the method’s stability and effectiveness.