Research Papers

Analysis of a Gravity Compensated Four-Bar Linkage Mechanism With Linear Spring Suspension

[+] Author and Article Information
Theeraphong Wongratanaphisan

Department of Mechanical Engineering, Chiang Mai University, Chiang Mai, Thailand 50200twongrat@chiangmai.ac.th

Matthew O. Cole

Department of Mechanical Engineering, Chiang Mai University, Chiang Mai, Thailand 50200

J. Mech. Des 130(1), 011006 (Dec 07, 2007) (8 pages) doi:10.1115/1.2803653 History: Received August 04, 2006; Revised January 23, 2007; Published December 07, 2007

This paper presents the analysis of a gravity compensated four-bar linkage mechanism with zero-free-length linear spring suspension. The objective of the study is to seek the possibility of employing the four-bar linkage or similar mechanisms for assisting vertical planar motion of a load mass in a gravitational field. The analysis is based on the system potential energy framework. Firstly, an arrangement of springs for gravity compensation in a four-bar linkage mechanism is proposed. It is then shown that for a four-bar linkage with symmetric geometric and mass properties the potential energy of the system has interesting and useful characteristics near the configuration at which the middle link is horizontal: an ideal operating configuration. The study also covers more practical cases where there is asymmetry in the mass distribution. The potential use of the mechanism in these cases is validated through a study of the sensitivity of the system potential energy function around the equilibrium point. Finally, based on the results obtained a novel mechanism is proposed for achieving gravity compensated vertical plane motion of a load mass. The proposed mechanism can have a wide range of travel and has significant potential for use not only in low-speed mechanical systems but also in high-speed heavy automated systems, where operating accelerations are of the order of 1g or less.

Copyright © 2008 by American Society of Mechanical Engineers
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Figure 1

Pendulum suspended by a linear spring

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Figure 2

Four-bar linkage suspended by linear springs

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Figure 3

Four-bar linkage with linear guided end joint

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Figure 4

Geometry of spring attachment points

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Figure 5

Potential energy profiles for a range of L (b¯=1, c¯=1, p¯1=p¯3=0.5, p¯21=b¯∕2, p¯22=0, m¯2=1, m¯3=1)

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Figure 6

Two alternate configurations with the same ψ for the suspended four-bar linkage and the potential profile: (a) alternate configurations and (b) potential energy profile

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Figure 7

Stable and unstable equilibrium configurations

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Figure 8

Two geometric inversion configurations of a four-bar linkage for b¯=L¯

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Figure 9

Potential energy profiles for the case b¯=L¯ (c¯=1, p¯1=p¯3=0.5, p¯21=b¯∕2, p¯22=0, m¯2=1, m¯3=1)

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Figure 10

Potential energy profiles for a symmetric parameter set (b¯=1, c¯=1, p¯1=p¯3=0.5, p¯21=b¯∕2, p¯22=−0.5, m¯2=1, m¯3=1)

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Figure 11

Potential energy profiles for an asymmetric parameter set (b¯=1, c¯=1,p¯1=p¯3=0.5, p¯21=0.8b¯, p¯22=0, m¯2=1, m¯3=1)

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Figure 12

Variation of the slope at ψ=0 for the system potential energy profiles (b¯=1,c¯=1, p¯1=0.25, p¯3=1, p¯21=b¯∕2, p¯22=0, m¯2=1, m¯3=1)

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Figure 13

A novel 1-DOF gravity compensated mechanism



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