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Research Papers

Perfect Static Balance of Linkages by Addition of Springs But Not Auxiliary Bodies

[+] Author and Article Information
Sangamesh R. Deepak

Department of Mechanical Engineering,  Indian Institute of Science, Bangalore 560012, Indiasangu@mecheng.iisc.ernet.in

G. K. Ananthasuresh

Department of Mechanical Engineering,  Indian Institute of Science, Bangalore 560012, Indiasuresh@mecheng.iisc.ernet.in

J. Mechanisms Robotics 4(2), 021014 (Apr 25, 2012) (12 pages) doi:10.1115/1.4006521 History: Received February 26, 2011; Accepted February 22, 2012; Published April 25, 2012; Online April 25, 2012

A linkage of rigid bodies under gravity loads can be statically counter-balanced by adding compensating gravity loads. Similarly, gravity loads or spring loads can be counter-balanced by adding springs. In the current literature, among the techniques that add springs, some achieve perfect static balance while others achieve only approximate balance. Further, all of them add auxiliary bodies to the linkage in addition to springs. We present a perfect static balancing technique that adds only springs but not auxiliary bodies, in contrast to the existing techniques. This technique can counter-balance both gravity loads and spring loads. The technique requires that every joint that connects two bodies in the linkage be either a revolute joint or a spherical joint. Apart from this, the linkage can have any number of bodies connected in any manner. In order to achieve perfect balance, this technique requires that all the spring loads have the feature of zero-free-length, as is the case with the existing techniques. This requirement is neither impractical nor restrictive since the feature can be practically incorporated into any normal spring either by modifying the spring or by adding another spring in parallel.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Three categories of perfect static balancing techniques shown on a lever and a multibody linkage

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Figure 2

Difference between zero-free-length spring and normal spring

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Figure 3

A lever under a constant load and a spring load

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Figure 4

Static balancing of a weight by a spring

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Figure 5

A body that is free to move in a plane

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Figure 6

A rigid body moving freely in a plane under a constant load is made to have θ-independent potential energy by addition of two zero-free-length springs

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Figure 7

Details of statically balanced gravity loaded 4R linkage and its modification into 3R and 2R linkage.

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Figure 8

Details of static balance of a 2R linkage under spring load

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Figure 9

Details of static balance of a 4R tree-structure linkage under a constant load and a spring load

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Figure 10

Potential Energy variation of spring loads, constant loads, and their sum

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Figure 11

Breaking a problem as a superposition of several problem with each problem being static balance of revolute-jointed tree-structured linkage with loads exerted by the root body

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