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Point-joint coordinate formulation for the dynamic analysis of generalised planar linkages

Published online by Cambridge University Press:  17 February 2009

Hazem Ali Attia
Hazem Ali Attia
Affiliation:
Department of Mathematics, College of Science, Al-Qasseem University, P.O. Box 237, Buraidah 81999, KSA; e-mail: ah1113@yahoo.com.
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Abstract

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This paper presents a two-step formulation for the dynamic analysis of generalised planar linkages. First, a rigid body is replaced by a dynamically equivalent constrained system of particles and Newton's second law is used to study the motion of the particles without introducing any rotational coordinates. The translational motion of the constrained particles represents the general motion of the rigid body both translationally and rotationally. The simplicity and the absence of any rotational coordinates from the final form of the equations of motion are considered the main advantages of this formulation. A velocity transformation is then used to transform the equations of motion to a reduced set in terms of selected relative joint variables. For an open-chain, this process automatically eliminates all of the non-working constraint forces and leads to efficient integration of the equations of motion. For a closed-chain, suitable joints should be cut and some cut-joint constraint equations should be included. An example of a closed-chain is used to demonstrate the generality and efficiency of the proposed method.

Type
Research Article
Information
The ANZIAM Journal , Volume 46 , Issue 4 , April 2005 , pp. 575 - 589
Copyright
Copyright © Australian Mathematical Society 2005

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