12 th International Research/Expert Conference ”Trends in the Development of Machinery and Associated Technology” TMT 2008, Istanbul, Turkey, 26-30 August, 2008 REDUCED PARAMETERS FOR THE DYNAMIC STUDY OF A SYSTEM OF ONE DEGREE OF FREEDOM Lluïsa Jordi, Enrique Zayas, Salvador Cardona Department of Mechanical Engineering Technical University of Catalonia Av. Diagonal, 647. Barcelona Spain ABSTRACT In the machine field, it is usual to use mechanisms of one degree of freedom in which their configuration, and therefore any geometrical condition, is defined by a unique variable or independent coordinate. Usually, this variable corresponds with the movement of the input member of the mechanism that, often, coincides with a crank that is driven by a rotary motor. In order to obtain, both the movement equation of the mechanism and the constrain actions, Lagrange’s equations are used. This implies to define a set of dynamic parameters, reduced parameters of the system, which are function of the independent coordinate. In this paper, a procedure to determine these parameters using PAM –Program of Analysis of Mechanisms– is exposed. This program makes static, kinematic and kinetostatic analysis of planar mechanism of one or more degrees of freedom that are controlled by the same number of actuators, angular or linear. This program obtains and allows exporting all the kinematic and dynamic variables of the mechanism, for all the time steps, from which it is possible to obtain the reduced parameters. The exposed procedure increases the possibilities of a program easy to use as PAM, which does not have the capacity for making a direct dynamic analysis. As example, the study of the direct dynamic of a single-dwell bar mechanism is exposed. Keywords: reduced parameters, Lagrange’s equations, dynamic, single-dwell bar mechanism 1. INTRODUCTION The dynamic analysis of mechanisms by means of manual procedures is, usually, hard and tough, either by the number of equations to propose if Newton’s laws are used, or by the difficulty to determine inertial forces if virtual work method is used, or by the difficulty to find the kinetic energy if the chosen method is the Lagrange’s equations [1, 2, 3]. In these two last cases the situation becomes worth if some constraint action is needed. The use of specific software to study multibody systems may be not justified or, even, may be unfeasible in some cases, as in the case that the study of the mechanism must be done in real time as part of a simulation and control of a productive process. In these cases, a model of low cost, both in implementation and computational point of view, is necessary. In this paper, the dynamic study of the mechanisms of one degree of freedom using a set of reduced parameters, function of the independent coordinate used in the kinematic analysis of the mechanism, is exposed. These reduced parameters are determined by means of a kinetostatic analysis and using them the dynamic of the system is written as a second order differential equation easy to integrate. If some constraint action is needed, it is obtained by means of an algebric expression that includes the reduced parameters as well as the velocity and the acceleration obtained through the integration process. 1049