Dynamic Coupling Between the Joint and Elastic Coordinates in Flexible Mechanism Systems

Abstract

The aim of this investigation is to develop an efficient proce dure for decoupling the joint and elastic accelerations while maintaining the nonlinear inertia coupling between the rigid body motion and the elastic deformation. The inertia projec tion schemes used in most existing recursive methods for the dynamic analysis of flexible robotics and mechanism systems lead to dense coefficient matrices in the acceleration equations, and consequently there is a strong dynamic coupling between the joint and elastic coordinates. When the number of elastic degrees of freedom increases, the size of the coefficient matrix in the acceleration equations becomes large, and consequently the use of these recursive methods for solving for the joint and elastic accelerations becomes less efficient. This investigation discusses the problems associated with the inertia projection schemes used in the existing recursive methods, and it is shown that decoupling the joint and elastic accelerations using these methods requires the factorization of nonlinear matrices whose dimensions depend on the number of elastic degrees of freedom of the system. An amalgamated formulation that can be used to decouple the elastic and joint accelerations is then used to obtain a reduced system of equations whose dimension is in dependent of the number of elastic degrees of freedom of the system. This system can be solved for the joint accelerations as well as the joint reaction forces. The use of the procedure de veloped in this article is demonstrated using a four-bar flexible mechanism.

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References

Book, W.J. 1984. Recursive Lagrangian dynamics of flexible manipulator arms. Int. J. Robot. Res. 3(3):87-101.

Changizi, K. , and Shabana, A.A. 1988. A recursive formulation for the dynamic analysis of open loop deformable multibody systems. ASME J. Applied Mechanics 55(3):687-693.

Hwang, Y.L. 1992. Projection and recursive methods in flexible multibody dynamics. Ph.D. thesis, Department of Mechanical Engineering, University of Illinois at Chicago.

Keat, J.E. 1990. Multibody system order n dynamics formulation based on velocity transform method. AIAA J. Guidance Control Dynamics 13(2):207-212.

Rodriguez, G. 1989. Recursive forward dynamics for multiple robot arms moving a common task object. IEEE Trans. Robot. Automation 5(4):510-521.

Rodriguez, G. 1990. Spatial operator approach to flexible multibody system dynamics and control. Proceedings of the 4th NASA Workshop on Computational Control of Flexible Space Systems, Williamsburg, VA, July 11, 1990.

Shabana, A.A. 1989. Dynamics of Multibody Systems. New York: John Wiley & Sons.

Shabana, A.A. 1990. Dynamics of flexible bodies using generalized Newton-Euler equations. ASME J. Dynamic Sys. Measurement Control 112(3):496-503.

Wehage, R.A. , and Shabana, A.A. 1989. Application of the generalized Newton-Euler equations and recursive projection methods to dynamics of deformable multibody systems . Proceedings of 15th ASME Design Automation Conference , Montreal, Canada, September 17-20, 1989.