The Bounds and Realization of Spatial Stiffnesses Achieved with Simple Springs Connected in Parallel

Document Type

Article

Language

eng

Publication Date

6-1998

Publisher

Institute of Electrical and Electronics Engineers (IEEE)

Source Publication

IEEE Transactions on Robotics and Automation

Source ISSN

1042-296X

Original Item ID

doi: 10.1109/70.678455

Abstract

We identify the space of spatial compliant behavior that can be achieved through the use of simple springs connected in parallel to a single rigid body. Here, the expression “simple spring” refers to the set of compliant relations associated with passive translational springs and rotational springs. The restriction on the stiffness matrices is derived using the screw theory by investigating the compliant behavior of individual simple springs. We show that the restriction results from the fact that simple springs can only provide either a pure force or a pure torque to the suspended body. We show that the 20-dimensional subspace of “realizable” spatial stiffness matrices achieved with parallel simple springs is defined by a linear necessary and sufficient condition on the positive semidefinite stiffness matrix. A procedure to synthesize an arbitrary full-rank stiffness matrix within this realizable subspace is provided. This procedure requires no more than seven simple springs

Comments

IEEE Transactions on Robotics and Automation, Vol. 14, No. 3 (June 1998): 466-475. DOI.

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