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Research Papers

An Inverse Dynamic Model of Over-Constrained Parallel Kinematic Machine Based on Newton–Euler Formulation

[+] Author and Article Information
Z. M. Bi

Department of Engineering,
Indiana University-Purdue University Fort Wayne,
Fort Wayne, IN 46805
e-mail: biz@ipfw.edu

Bongsu Kang

Department of Engineering,
Indiana University-Purdue University Fort Wayne,
Fort Wayne, IN 46805
e-mail: kang@engr.ipfw.edu

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received September 16, 2011; final manuscript received January 8, 2014; published online March 13, 2014. Assoc. Editor: Rama K. Yedavalli.

J. Dyn. Sys., Meas., Control 136(4), 041001 (Mar 13, 2014) (9 pages) Paper No: DS-11-1288; doi: 10.1115/1.4026533 History: Received September 16, 2011; Revised January 08, 2014

It has been known that redundant constrains in a mechanism can improve the rigidity and stiffness of the mechanism. Some Parallel Kinematic Machines (PKMs) have adopted redundant constraints to enhance their performance and stability. However, limited studies have been conducted on the dynamics of over-constrained mechanisms. While a dynamic model is not essential to machine control, a clear understanding of the dynamic behavior of the system can be useful in identifying the weakest components, optimizing the overall structure, and improving the quality of control. In this paper, the dynamic characteristics of an over-constrained PKM are investigated for the first time. The Newton–Euler formulation is extended to develop the dynamic model of the machine. It is shown that the compliance of deformations of the redundant constraints needs to be taken into account to build a complete and solvable dynamic model since the number of equations derived from the force and moment equilibrium of the PKM components is insufficient to determine all unknown variables. The proposed approach is generic in sense that it can be applied to model dynamic behaviors of other over-constrained machines with a combination of the Newton–Euler formulation and compliance conditions. Its effectiveness has been verified by the dynamic model established for Exechon PKM. The developed dynamic model has its potential to be integrated with control systems to improve accuracy and dynamic performance of real-time control.

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References

Figures

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Fig. 1

Virtual model of 5-DOF hybrid Exechon machine

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Fig. 2

Simplified structure of Exechon machine

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Fig. 3

Two redundancies caused by Leg_1 and Leg_3

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Fig. 4

The parametric model of the Exechon machine

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Fig. 5

Angular intermediate variables of Leg

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Fig. 6

Components and applied forces/torques in Exechon

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Fig. 7

The compliance equations of over-constrained Exechon machine

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Fig. 8

Linear deflection along the y-axis due to over-constraint

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Fig. 9

Twist angle along the z-axis due to over-constraint

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Fig. 10

Driving forces at the joints

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