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Inverse kinematic solutions of 6-D.O.F. biopolymer segments

Published online by Cambridge University Press:  13 April 2016

Jin Seob Kim  and
Gregory S. Chirikjian
Jin Seob Kim
Affiliation:
Department of Mechanical Engineering, Johns Hopkins University Baltimore, MD 21218, USA. E-mail: jkim115@jhu.edu
Gregory S. Chirikjian*
Affiliation:
Department of Mechanical Engineering, Johns Hopkins University Baltimore, MD 21218, USA. E-mail: jkim115@jhu.edu
*
*Corresponding author. E-mail: gregc@jhu.edu
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Summary

We present two methods to find all the possible conformations of short six degree-of-freedom segments of biopolymers which satisfy end constraints in position and orientation. One of our methods is motivated by inverse kinematic solution techniques which have been developed for “general” 6R serial robotic manipulators. However, conventional robot kinematics methods are not directly applicable to the geometry of polymers, which can be treated as a degenerate case where all the “link lengths” are zero. Here, we propose a method which extends the elimination method of Kohli and Osvatic. This method can be applied directly to the geometry of biopolymers. We also propose a heuristic method based on a Lie-group-theoretic description. In this method, we utilize inverse iterations of the Jacobian matrix to obtain all conformations which satisfy end constraints. This can be easily implemented for both the general 6R manipulator and polymers. Although the extended elimination method is computationally faster than the Jacobian method, in cases where some of the joint angles are 180° (i.e., where the elimination method fails), we combine these two methods effectively to obtain the full set of inverse kinematic solutions. We demonstrate our approach with several numerical examples.

Keywords

Biopolymer structure6R manipulatorInverse kinematicsEigenvalue problemLie-group-theoretic methodJacobian matrix
Type
Articles
Information
Robotica , Volume 34 , Issue 8 , August 2016 , pp. 1734 - 1753
Copyright
Copyright © Cambridge University Press 2016 

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