Research Papers

Stiffness Evaluation of Machines and Robots: Minimum Collinear Stiffness Value Approach

[+] Author and Article Information
Vladimir T. Portman

Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beer-Sheva, Israelportman@bgu.ac.il

J. Mechanisms Robotics 3(1), 011015 (Feb 10, 2011) (9 pages) doi:10.1115/1.4003444 History: Received January 29, 2009; Revised January 09, 2011; Published February 10, 2011; Online February 10, 2011

New stiffness performance indices using the collinear stiffness value (CSV) associated with a given configuration of the machine are proposed. The minimal CSV (MinCSV) is applied to stiffness evaluation for all types of configurations. Similar to the determinant, the MinCSV equals zero in singular configurations. In regular configurations, the MinCSV is applied to evaluation of local stiffness for a given configuration and global stiffness in the workspace, wherein stiffness limitations are satisfied. A screw stiffness value, i.e., the CSV during a screw displacement, presents the general case of the CSV. There are two important special cases: rotational and translational stiffness values. Procedures for evaluation of the MinCSV are developed in natural and dimensionless forms. The CSV of the hexapod are simulated and compared with those of serial-type mechanisms. The proposed approach presents an effective design tool for evaluation and limitation of stiffness of machines and robots.

Copyright © 2011 by American Society of Mechanical Engineers
Topics: Stiffness , Machinery
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Figure 1

Rigid body resting on a set of linear elastic supports

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Figure 2

Classification of special configurations of machines and robots. Det[K] and Det[E] are the determinants of stiffness and compliance matrices, respectively.

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Figure 6

Dimensionless minimal TSV ξmin at heights h=150, 200, 300, and 500 mm. The areas lying in truncation planes satisfy requirement ξmin>1.

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Figure 3

The 6×3 Gough–Stewart platform, with the central configuration and horizontal orientation of the mobile platform: (a) kinematic model and (b) kinetostatic model

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Figure 4

Dimensionless minimal TSV ξmin versus height position h of the platform

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Figure 5

Dimensionless minimal SSV ζmin versus height position h of the platform



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