Inverse Kinematics of Anthropomorphic Arms Yielding Eight Coinciding Circles

  • B. BongardtEmail author
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 50)


In this paper it is demonstrated that the solution space of the inverse kinematic problem of an anthropomorphic, redundant 7R chain for a given pose does consist of eight different coinciding circles instead of a single circle that has been reported as of today. By modeling the structure using the convention by Sheth and Uicker, the displacements within the kinematics of the chain are partitioned in time-invariant displacements along rigid links and time-variant displacements along the seven rotative joints. In particular, the subchains of shoulder, elbow, and wrist are preserved. By respecting the ‘flips’ of these three substructures the eight-fold occupancy of the redundancy circle is obtained. The result corresponds to the eight IK solutions for regional-spherical arms and provides a prerequisite for using all capabilities of respective robots in practical applications.


Kinematic analysis Anthropomorphic robot arm Redundant manipulator Cyclic law of cosines Virtual joints 



The work was performed within the projects Capio and Recupera, funded with federal funds from the German Federal Ministry of Education and Research (BMBF) (Grant 01-IW-10001 and 01-IM-14006A). The author would like to thank Sankaranarayanan Natarajan, Wiebke Drop, and Arnaud Sengers for their contributions.


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© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Robotics Innovation CenterDFKI GmbHBremenGermany

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