Research Papers

Nonlinear Analytical Modeling and Characteristic Analysis of a Class of Compound Multibeam Parallelogram Mechanisms

[+] Author and Article Information
Guangbo Hao

School of Engineering-Electrical
and Electronic Engineering,
University College Cork,
Cork, Ireland
e-mail: G.Hao@ucc.ie

Haiyang Li

School of Engineering-Electrical
and Electronic Engineering,
University College Cork,
Cork, Ireland

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received June 3, 2014; final manuscript received January 5, 2015; published online April 6, 2015. Assoc. Editor: Anupam Saxena.

J. Mechanisms Robotics 7(4), 041016 (Nov 01, 2015) (9 pages) Paper No: JMR-14-1123; doi: 10.1115/1.4029556 History: Received June 03, 2014; Revised January 05, 2015; Online April 06, 2015

This paper deals with nonlinear analytical models of a class of compound multibeam parallelogram mechanisms (CMPMs) along with the static characteristic analysis. The CMPM is composed of multiple compound basic parallelogram mechanisms (CBPMs) in an embedded parallel arrangement. First, nonlinear analytical models for the CBPM are derived using the free-body diagram method through appropriate approximation strategies. The nonlinear analytical models of the CMPM are then derived based on the modeling results of the CBPM. Nonlinear finite element analysis (FEA) comparisons, experimental testing, and detailed stiffness analysis for the CBPM are finally carried out. It is shown that the analytical primary motion model agrees with both the FEA model and the testing result very well but the analytical parasitic motion model deviates from the FEA model over the large primary motion/force. It is also shown from the analytical characteristic analysis that the primary translational stiffness increases with the primary motion but the parasitic motion stiffness decreases with the primary motion, and the stiffness ratio of the parasitic motion stiffness to the primary translation stiffness also decreases with the primary motion. It is found that the larger the beam slenderness ratio is, the larger the stiffness or stiffness ratio is, and the more apparent the change of the stiffness or stiffness ratio is. The varied stiffness ratio indicates the mobility change of the CBPM.

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Fig. 1

Four types of parallelogram based leaf-type CTJs

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Fig. 2

A CBPM with actual geometry, loading and displacement indication

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Fig. 4

Parasitic translational displacement along the X-axis

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Fig. 5

Primary translational displacement along the Y-axis

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Fig. 6

Parasitic rotational yaw about the Z-axis

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Fig. 7

Testing rig for the primary motion

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Fig. 8

Parasitic translational stiffness (kx) along the X-axis

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Fig. 9

Primary translational stiffness (ky) along the Y-axis

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Fig. 10

Parasitic rotational stiffness (kr) about the Z-axis

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Fig. 11

Stiffness ratio: kx/ky

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Fig. 12

Stiffness ratio: kr/ky




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