Introduced in this paper is a robust algorithm to solve the five-pose planar Burmester problem. The proposed algorithm functions even in the presence of special conditions of the prescribed poses that lead to algorithmic singularities otherwise. In order to show the applicability and to validate the robustness of the proposed algorithm, some examples are included.

This contribution presents a comprehensive theory for the type synthesis of fully parallel platforms. The theory deals with both types of platforms, 6 D.O.F. parallel platforms and lower mobility platforms. The theory is based on an analysis of the subsets and subgroups of the Euclidean group, SE(3). It is likely that the theory can be also developed based on an analysis of the subspaces and subalgebras of the Lie algebra, se(3), of the Euclidean group, SE(3).

In the last five years Prof. Shai has developed a comprehensive theory of the duality among different areas of engineering science, in particular between mechanisms and trusses. In this contribution, it is shown a different approach that, in the opinion of the authors, generalize the approach presented by Prof. Shai and clear some misconceptions.