Static Balancing of Spatial Parallel Platform Mechanisms—Revisited

[+] Author and Article Information
Imme Ebert-Uphoff

Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0405e-mail: ebert@me.gatech.edu

Clément M. Gosselin, Thierry Laliberté

Département de Génie Mécanique, Université Laval, Québec, PQ, G1K 7P4, Canada

J. Mech. Des 122(1), 43-51 (Jan 01, 2000) (9 pages) doi:10.1115/1.533544 History: Received June 01, 1998; Revised January 01, 2000
Copyright © 2000 by ASME
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Grahic Jump Location
Potential mechanism with elastic elements for the motion base of a flight simulator (Figure by Jiegao Wang)
Grahic Jump Location
Parallelogram mechanism for the ith leg with two springs attached
Grahic Jump Location
Notation and glossary of terms for the mechanism. Glossary of terms: D: number of legs of the mechanism, θi1i2i3: angles that describe the configuration of the ith leg, Pi0: attachment point of the ith leg at the base, Pi5: attachment point of the ith leg at the mobile platform, Q : rotation of the mobile platform with respect to the global coordinate system, p : translation of the mobile platform with respect to the global coordinate system. As reference point on the platform we use the attachment point of one of the legs on the platform: p=P15, bi: local vector from the reference point on the mobile platform to the attachment point of the ith leg in the local reference frame of the platform, bi=Pi5−p, (all bi are constant), lij: length of the jth link of leg i, (note that li1=li4,li2=li3 and that length li5 includes li3), cij: vector to the center of mass of the jth link of leg i, written in a local coordinate system of the jth link of leg i, (ci3 is the c.o.m. of the whole link of length li5), cp: vector to center of mass of the platform, written in the local coordinate system of the platform rij, rp: center of mass in global coordinate system.
Grahic Jump Location
Affine space of three vectors
Grahic Jump Location
Mechanism with center of mass of the payload (indicated by sphere) far above the mobile platform (Figure by Kevin Johnson)




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