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Sensitivity Analysis: Generalized Coordinate Kinematic Systems

  • Daniel A. Tortorelli
Chapter
  • 1.7k Downloads
Part of the CISM International Centre for Mechanical Sciences book series (CISM, volume 511)

Abstract

We now apply the afore developed analysis and sensitivity analysis to kinematically driven rigid body mechanisms. Initially we perform a position analysis, i.e. we determine the mechanism configuration for a given time. This analysis parallels the nonlinear static finite element analysis of Section 9.2. Through differentiation we then perform velocity and acceleration analyses. This procedure is akin to our sensitivity analysis if we view time t as the parameter d i of interest. Next we evaluate reaction forces in an inverse dynamic analysis. Such forces are often used in subsequent finite element analyses to determine the stress distribution in the mechanism’s components. And finally we perform a sensitivity analysis in its own right to determine how the generalized position, velocity, acceleration and generalized reaction force vectors change as we perturb a model parameter d i , e.g. a link dimension.

Keywords

Reaction Force Position Analysis Adjoint Method Joint Constraint Lagrange Multiplier Vector 
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References

  1. Haug, E.J. (ed) Computer Aided Analysis and Optimization of Mechanical Systems Dynammics, F9 Proceedings of NATO ASI, Iowa City, 1983.Google Scholar
  2. Haug, E.J.: Computer-Aided Kinematics and Dynamics of Mechanical Systems. Allyn and Bacon, Needham Heights 1989.Google Scholar
  3. Minaar, R.J., Tortorelli, D.A., Snyman, J.A.: On Non-Assembly in the Optimal Dimensional Synthesis of Planar Mechanisms. Structural and Multidisciplinary Optimization, Vol. 21, 345–354, 2001.CrossRefGoogle Scholar
  4. Nikravesh, P.: Computer-Aided Analysis of Mechanical Systems. Prentice-Hall, Englewood Cliffs, 1988.Google Scholar

Copyright information

© CISM, Udine 2009

Authors and Affiliations

  • Daniel A. Tortorelli
    • 1
  1. 1.Department of Mechanical SciencesUniversity of Illinois at Urbana-ChampaignUrbanaUSA

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