Kinematic analysis of Active Ankle using computational algebraic geometry

Shivesh Kumar; Abhilash Nayak; Bertold Bongardt; Andreas Mueller; Frank Kirchner
In: Computational Kinematics. IFTOMM International Workshop on Computational Kinematics (CK-2017), May 22-24, Poitiers, France, Springer, 2017.


ACTIVE ANKLE is a novel 3 DoF parallel mechanism which works in an almost spherical manner. Its geometry provides various advantages like good stress distribution, low link diversity and robust construction. Determining all the solutions to the direct kinematics problem is an important and challenging step in kinematic analysis of any newly invented parallel manipulator due to the coupled nature of the constraint equations. In this paper, we make use of powerful methods in computational algebraic geometry to provide a rational univariate representation of direct kinematics solution in the form of a 40 degree univariate polynomial. In the presented analysis, up to 16 real solutions of the direct kinematics problem for this mechanism have been obtained. In addition, the results of its torsional motion analysis are presented and singularities of the mechanism are highlighted during this motion. Also, the assembly modes where this mechanism behaves as an almost-spherical device are identified, which is the main contribution of the paper.

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