By R. J. Ellwood, D. Schütz, Annika Raatz, J. Hesselbach (auth.), Jadran Lenarcic, Michael M. Stanisic (eds.)

The booklet offers approximately 50 contributions within the region of robotic kinematics, the fundamental study sub-field of robotics. the most impetus is at the contemporary advances within the box. This most recent quantity of Advances in robotic Kinematics reviews the latest clinical and applicative effects. All contributions were peer reviewed.

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Extra resources for Advances in Robot Kinematics: Motion in Man and Machine: Motion in Man and Machine

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To eliminate all other variables from the system until an equation is obtained that contains only θ . Finally, a tangent-half-angle substitution is applied to translate sine and cosine functions of θ into rational polynomial expressions in a new variable t = tan(θ/2). Merlet was probably one of the first researchers to observe that the computation of the roots of this 6th-degree leads, J. M. V. 2010 23 24 N. Rojas and F. Thomas in some cases, to numerical instabilities and he also observed that the numerical robustness is improved by using a higher order polynomial [4].

In [12], the authors obtained analytically the conditions for the existence of cusp points in the joint space for the RPR-2PRR planar parallel manipulator. In this paper, the locus of cusp points for the general 3-RPR planar parallel manipulator will be obtained in a numeric way in the 3-dimensional joint space basing on the conditions developed in [12]. This way, it will be feasible to plan non-singular trajectories between assembly modes by varying the three input variables. Besides, it will be shown that not any path encircling a cusp point enables non-singular assembly mode change but that additional information about the singular curves which are crossed along the path is required.

Nevertheless, this kind of simplifications has an important drawback: the numerical conditioning of the resulting formulation depends on the chosen reference frame. This is why those formulations which are not linked to a particular reference frame – or coordinate-free formulations – are preferable. In this paper, we provide a way around the above difficulties by casting the problem into an equivalent problem fully stated in terms of distances which is solved by a sequence of bilaterations. As a result, a 6th-degree characteristic polynomial, which is not linked to any particular reference frame, is obtained in a straightforward manner without variable eliminations nor tangent-half-angle substitutions.

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