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Minimal realization of a spatial stiffness matrix with simple springs connected in parallel

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1 Author(s)
Roberts, R.G. ; Dept. of Electr. Eng., Florida Atlantic Univ., Boca Raton, FL, USA

This article presents a method for determining a minimal realization of an arbitrarily specified stiffness dominated spatial impedance through the use of a mechanism constructed of passive springs. This mechanism consists of simple springs connected in parallel where the term simple spring refers to a purely translational or purely rotational passive spring. Not every stiffness matrix K can be realized with a parallel connection of simple springs. The characterizing condition is that the upper right 3×3 submatrix of K has zero trace. Using this condition, the author shows how one can always synthesize any realizable spatial stiffness matrix with r parallel simple springs, where r is the rank of K. These results are also applicable to realizing a spatial damping matrix

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Robotics and Automation, IEEE Transactions on  (Volume:15 ,  Issue: 5 )