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Mechanical Sciences An open-access journal for theoretical and applied mechanics

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Mech. Sci., 8, 91-100, 2017
http://www.mech-sci.net/8/91/2017/
doi:10.5194/ms-8-91-2017
© Author(s) 2017. This work is distributed
under the Creative Commons Attribution 3.0 License.
Research article
30 Mar 2017
Reduced inertial parameters in system of one degree of freedom obtained by Eksergian's method
Salvador Cardona Foix, Lluïsa Jordi Nebot, and Joan Puig-Ortiz Mechanical Engineering Department, ETSEIB, Universitat Politècnica de Catalunya, Barcelona, 08028, Spain
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.

Citation: Cardona Foix, S., Jordi Nebot, L., and Puig-Ortiz, J.: Reduced inertial parameters in system of one degree of freedom obtained by Eksergian's method, Mech. Sci., 8, 91-100, doi:10.5194/ms-8-91-2017, 2017.
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Short summary
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 mechanisms of one degree of freedom can be dynamically analysed by setting out a single...
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