Research Papers

Dynamic Balancing of Spherical 4R Linkages

[+] Author and Article Information
Brian Moore1

 ATR Computational Neuroscience Laboratories, 2-2-2 Keihanna Science City, Soraku-gun, Kyoto 619-0288, Japanmoore@atr.jp

Josef Schicho

RICAM, Austrian Academy of Sciences, A-4040 Linz, Austriajosef.schicho@oeaw.ac.at

Clément M. Gosselin

Département de Génie Mécanique, Université Laval, Québec, QC, G1V 0A6, Canadagosselin@gmc.ulaval.ca

A Laurent polynomial is a polynomial where the exponent of the monomial can be negative integer.

A rational function is simply the quotient of two polynomials.

Section 3, Theorem 1.

We use the toric polynomial division algorithm described in Ref. 16 (Algorithm 1, Sec. 3.4). A detailed example can be found in Ref. 25.

The method has been implemented in MAPLE , except step 3 where MATHEMATICA has been used.

In Ref. 24, exercises of Chap. 3.


Corresponding author.

J. Mechanisms Robotics 2(2), 021002 (Apr 15, 2010) (8 pages) doi:10.1115/1.4001090 History: Received October 17, 2008; Revised October 14, 2009; Published April 15, 2010; Online April 15, 2010

A mechanism, which, for any motion, does not apply reaction forces on the base, is said to be statically or force balanced. It is moment balanced or dynamically balanced if, moreover, it does not apply torques on the base. In this paper, an approach to determine the complete set of statically balanced spherical four-bar linkages is presented. Furthermore, it is shown that for all possible design parameters, it is not possible to dynamically balance such linkages.

Copyright © 2010 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 3

Mirror linkage of the spherical 4R linkage

Grahic Jump Location
Figure 1

Spherical linkage: parameters and variables

Grahic Jump Location
Figure 2

Computation of q2′




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