Reduced inertial parameters in system of one degree of freedom obtained by Eksergian's method

Abstract

Abstract. The mechanisms of one degree of freedom can be dynamically analysed by setting out a single differential equation of motion which variable is the generalized coordinate selected as independent. In front of the use of a set of generalized dependent coordinates to describe the system, the method exposed in this work has the advantage of working with a single variable but leads to complex analytical expressions for the coefficients of the differential equation, even in simple mechanisms. The theoretical approach, in this paper, is developed from Eksergian's method and Lagrange's equations. The equation of motion is written by means of a set of parameters -reduced parameters -that characterize the dynamic behaviour of the system. These parameters are function of the independent coordinate chosen and its derivative and can be obtained numerically by direct calculus or by means of a kinetostatic analysis, as is proposed. Two cases of study of the method are presented. The first example shows the study of pedalling a stationary bicycle used in a rehabilitation process. The second one shows the analysis of a single dwell bar mechanism which is driven by an electric motor.

Simulation of Hydraulic Cylinder Cushioning

“…where F i is the inertial force and F m is the weight of the displaced reduced mass to the cylinder rod, considered constant. For the calculus of the inertial force, the general relationship between force and a reduced mass m reduced , for single degree of freedom systems, such as the studied one, is established according to the well-known Eksergian equation [21,22]:…”