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Determination of reaction forces at kinematical joints
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Determination of reaction forces at kinematical joints
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The determination of reaction forces at kinematical joints of mechanism plays an important role in dynamics of machines. In the paper a method of determining the reaction at kinematical joints is presented. It is established a set of equations that are divided into two groups. The one describes the motion of the system and the other allows to calculate the reaction at kinematical joints. | Vietnam Journal of Mechanics, NCNST of Vietnam T. XX, 1998, No 1 (47 - 55) DETERMINATION. OF REACTION FORCES AT KINEMATICAL JOINTS Do SANH Hanoi University of Technology, Hanoi ABSTRACT. The determination of reaction forces at kinematical joints of mechanism plays an important role in dynamics of machines. In the paper a method of determining the reaction at kinematical joints is presented. It is established a set of equations that are divided into two groups. The one describes the motion of the system and the other allows to calculate the reaction at kinematical joints. 1. Introduction The determination of reaction forces at kinematical joints has investigated in many works. In engineering the D'Alembert's method is usually applied for calculating the reaction forces at kinematical joints. However, such a method depends on each concrete structure of mechanisms. There was an idea of making a general method for the problem. That is to apply the method of analytical mechanics for determining reaction forces at kinematical joints of a chain of links [7]. However, such method hasn't yet taken clearness and simplicity from engineering point of view. 2. Equations of motion of a constrained mechanical system Let us consider a holonomic mechanical system of n degrees of freedom. Denote generalized coordinates of the system under consideration by q; (i = 1, n). Assume that the matrix of inertia of the system is denoted by A, which is an n X n positive define symmetric matrix. The elements of the matrix A depend on generalized coordinates, i.e. A = A( q); where q is an n x 1 matrix of generalized coordinates, that is: (2.1) the notation T denotes a transpose of matrix. 47 Suppose that the expression of kinetic energy of the system is written in the form: (2.2) where q is an n x 1 matrix of generalized velocities, of q, i.e.: q is the transpose of the matrix (2.3) Denote the generalized forces of applied ones by Q;(t, q, q) and Q is their matrix notation, that .
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