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Research Papers

Parameter Analysis and Normalization for the Dynamics and Design of Multibody Systems

[+] Author and Article Information
József Kövecses

Department of Mechanical Engineering and Centre for Intelligent Machines, McGill University, 817 Sherbrooke Street West, Montréal, QC, H3A 2K6, Canadajozsef.kovecses@mcgill.ca

Saeed Ebrahimi

Department of Mechanical Engineering and Centre for Intelligent Machines, McGill University, 817 Sherbrooke Street West, Montréal, QC, H3A 2K6, Canadaebrahimi@cim.mcgill.ca

These points are usually equally spaced in time, but this is not a primary requirement.

Consider, for example, that our system is a beam of unit length attached to the inertial frame with a revolute joint, and zi represents a point mass at the tip of the beam, while zj is a point mass at the center of mass of the beam. The investigated performance measure is the joint torque. In this case, zi and zj will combine in the dynamic equation as zi+14zj.

These figures show only the curves that have noticeable deviation from the reference torque curves.

J. Comput. Nonlinear Dynam 4(3), 031008 (Jun 04, 2009) (10 pages) doi:10.1115/1.3124785 History: Received May 16, 2008; Revised January 08, 2009; Published June 04, 2009

In this paper, we introduce a novel concept for parametric studies in multibody dynamics. This includes a technique to perform a natural normalization of the dynamics in terms of inertial parameters. This normalization technique rises out from the underlying physical structure of the system and the trajectory investigated. This structure is mathematically expressed in the form of eigenvalue problems. It leads to the introduction of the concept of dimensionless inertial parameters. This, in turn, makes it possible to introduce an analysis approach for studying design and control problems where parameter estimation and sensitivity are of importance.

FIGURES IN THIS ARTICLE
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Copyright © 2009 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

A geometric representation of a possible quadratic form

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Figure 3

Time history of the first joint torque

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Figure 4

Time history of the second joint torque

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Figure 5

Time history of the first joint torque

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Figure 6

Time history of the second joint torque

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Figure 7

Time history of the variation of the first joint torque

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Figure 8

Time history of the variation of the second joint torque

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Figure 9

Time history of the variation of the first joint torque

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Figure 10

Time history of the variation of the second joint torque

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Figure 11

Dual-pantograph system: CAD model and physical setup

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Figure 12

Horizontal plane view of the system

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Figure 13

Torque profiles for the trajectory segment

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Figure 14

Time history of the variation of torque 3

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