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Minimal realization of an arbitrary spatial stiffness matrix with a parallel connection of simple and complex springs

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1 Author(s)
Roberts, R.G. ; Dept. of Electr. Eng., Florida State Univ., Tallahassee, FL, USA

This article presents a method for determining a minimal realization of an arbitrary spatial stiffness matrix K through the use of a mechanism constructed of a parallel connection of springs. Two types of springs are used: simple and complex. The term simple spring refers to a purely translational or purely rotational passive spring while a complex spring couples translational and rotational components. Any symmetric positive definite spatial stiffness matrix can be realized with a parallel connection of such springs. However, to reduce the compliance mechanism's complexity, it is desirable to minimize the number of complex springs. This article presents a method for determining minimal realizations for any symmetric positive definite or semi-definite spatial stiffness matrix. These realizations are minimal in the sense that they minimize both the number of complex springs and the total number of springs

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Robotics and Automation, 2000. Proceedings. ICRA '00. IEEE International Conference on  (Volume:4 )

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