Kinematic analysis of Active Ankle using computational algebraic geometry
Shivesh Kumar, Abhilash Nayak, Bertold Bongardt, Andreas Mueller, Frank Kirchner
In Computational Kinematics, (CK-2017), 22.5.-24.5.2017, Poitiers, 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.
parallel manipulator, kinematic analysis, direct kinematics, algebraic geometry