tailieunhanh - The method of determining internal forces at any cross section of links in mechanisms

In the paper it is introduced a method of determining internal forces at any cross section of the links of mechanisms. As known, so far it is used the method of D'Alembert, which consists of two steps, the determination of the acceleration states of links and the establishment of the equilibrium equations for the set of forces including the forces of inertia and the internal forces at the cross section. A. I. Lurie proposed a method of analytical mechanics for this problem. | . Vietnam Journal of Mechanics, VAST, Vol. 26, 2004, No 2 (111 - 121) THE METHOD OF DETERMINING INTERNAL FORCES AT ANY CROSS SECTION OF LINKS IN MECHANISMS Do SANH, Do DANG KttoA Hanoi University of Technology ABSTRACT. In the paper it is introduced a method of determining internal forces at any cross section of the links of mechanisms. As known, so far it is used the method of D'Alembert , which consists of two steps, the determination of the acceleration states of links and the establishment of the equilibrium equations for the set of forces including the forces of inertia and the internal forces at the cross section. A. I. Lurie proposed a method of analytical mechanics for this problem. Its concept is to make a new system called the released one by cutting the link at a cross section under consideration and adding some coordinates . Only one condition putting restriction on the released system is the additional coordinates must equal zero. Under this restriction the new created system is coincided to the original one. This restriction is equivalent to put the mechanical constraints, whose reaction forces are the components of internal forces at t he cross section under consideration. It is necessary emphasize that the Lurie's method is convenient only for opened loops, but is not applied for closed ones. Moreover, the Lagrange's multiplier equations applied by A. I. Lurie are unsuitable. In this paper it is presented the generalized Lurie's method, which is applied for the opened and closed loops by using the Principle of Compatibility. 1 Introduction The problem of determining internal forces at any cross section of links of mechanism is very important because in modern dynamics the cross section of links is designed increasingly small while their angular velocities are more and more larger. In t he past, for determining the components of internal forces (the tensible, shearing force and bending moment ) the D 'Alembert 's method is applied. For doing .