The article devotes to t he construction of equations of motion of constrained mechanical systems. The constraint conditions are successively appended to the already defined systems. Therefore the algorithm is very flexible and allows studying the separate constraints more in detail. For illustration of consequent steps of the algorit hm one simple example is shown. | Vietnam Journal of Mechanics, NCST of Vietnam Vol. 24, 2002, No 2 (101 ·- 114) SUCCESSIVE ALGORITHM FOR CONSTRUCTION OF EQUATION OF MOTION OF CONSTR,AINED MECHANICAL SYSTEMS DINH VAN PHONG Department of Applied Mechanics, Hanoi University of Technology ABSTRACT. The article devotes to t he construction of equations of motion of const rained mechanical systems. The constraint conditions are successively appended to the already defined systems. Therefore the algorithm is very flexible and allows studying t he separate constraints more in detail. For illustration of consequent steps of t he algorit hm one simple example is shown. L Introduction Nowadays in technical application the constraints of mechanical systems are becoming increasingly important. They appear in the complex systems such as machines, robots and other multibody systems where the constraints can int roduce the interaction between mechanical problems and problems of other charact ers: control, electric and hydraulic law etc. Even for purely mechanical syst ems using constraints occurs when the redundant generalized coordinates are chosen. The equation of motion of constrained mechanical systems is mostly derived by using Lagrange multipliers. In combinat ion with various methods, e. g. NewtonEuler equations or Kane's equations for multibody systems etc., the full form or reduced forms of equation of motion are available. In the reduced form Lagrange multipliers are excluded from the equation. With the progress of comput er technology recursive methods are also developed, see . [7], [10], [11], [13] etc. In this article we will develop one new method for constructing t he equation of motion of constrained mechanical systems . The idea of the method is based on the principle of compatibility, see . [4], [5] . The equation of motion for the free system, . the system without constraints, is assumed to have been constructed before. Then the constraints can be added successively to the existing
