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# Finite Element Analysis of Kinematics and Dynamics of Linkages

[+] Author Affiliations
Jiaxin Zhao

Indiana University-Purdue University Fort Wayne

Paper No. IMECE2005-81311, pp. 465-469; 5 pages
doi:10.1115/IMECE2005-81311
From:
• ASME 2005 International Mechanical Engineering Congress and Exposition
• Applied Mechanics
• Orlando, Florida, USA, November 5 – 11, 2005
• Conference Sponsors: Applied Mechanics Division
• ISBN: 0-7918-4212-6 | eISBN: 0-7918-3769-6
• Copyright © 2005 by ASME

## abstract

The kinematics and dynamics of two dimensional linkages is analyzed using an uniformed finite element approach in this paper. Each link in the linkage is a naturally discretized finite element and the joints are the nodes connecting elements. The analysis consists of two parts, namely the kinematics part and the dynamics part. In the first kinematics part, positions, linear velocities and linear accelerations of the joints are used as the solution variables in the finite element formulation. In order to have close-form solutions, the linkage must have only one degree of freedom. These joint variables are then solved for each input link configuration of angular position, velocity and acceleration. The angular positions, velocities and accelerations of the other links are then calculated from the joint variables. The position, linear velocity and acceleration of any point on the linkage, like the center of gravity for a particular link, can also be determined if desired. The second dynamics part uses joint forces as the solution variables in the finite element formulation. In each element, a third node is also defined to allow an external force or torque to be applied. Based on the solutions in the first kinematics part, the joint forces are solved for each input configuration. The forces inside each link can then be determined from the joint forces. A MATLAB program is developed for this finite element analysis on general four bar linkages and is posted on the author’s webpage.

Copyright © 2005 by ASME

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