I Introduction
Computational mechanics of rigid and deformable bodies is being developed for already more than 50 years since first computers appeared. The major current directions of dynamics simulation theory development are analyzed in the review [1]. Among different closed forms equations of dynamics simulation the recursive Composite Rigid Body Algorithm (CRBA) and similar algorithm developed by Y. Stepanenko [2], [3] with computational efficiency where n is the number of system's degrees of freedom, are the most effective ones. They are based on repeated usage of simple algorithm for solving the inverse problem of dynamics. This efficiency is achieved only in case of equations character conversion. Another algorithm “Kerchief” based on recursive block matrixes arrangement has similar effectiveness [4]. The new algorithm for dynamics equations coefficients calculation of mechanical systems with simple kinematic chain structure is presented. It has effectiveness and based on analytic form of dynamics equations. Kane algorithm is the source for these equations [5]. It was considered to be perspective for the development of new mechanical systems dynamics modeling simulation algorithms in review [1]. There are many algorithms and dynamics simulation software packages for simulation of universal industrial and special robotic mechanisms, with rigid as well as flexible links [7], [8] using linear and parallel calculations [9], [10], and working in real time. Different implementations of Kane equations have either proprietary code or such a form that is inconvenient for further transformations. In this article I propose the matrix form of Kane equations, transformation method and the resulting equations that present a new recursive algorithm.