عنوان مقاله [English]
This paper proposes a systematic algorithm, based on the interval analysis concept, in order to optimize the maximal singularity-free circle within the workspace of 3-DOF planar parallel mechanisms. A 3-RPR parallel mechanism is
considered as the case study. Two approaches are presented, namely, interval analysis with four algorithms and a geometric constructive approach. A new concept in applying interval analysis is introduced, which could be of great help in other optimization contexts.
The proposed algorithm in the interval analysis section is divided into four sub-algorithms, which eases the understanding of the main concept and leads to a more effective and robust algorithm to solve the problem. First, the
workspace of the mechanism is obtained, using the branch and prune method. Then, by the same token, the singularity locus of the mechanism under study will be obtained. Afterwards, the maximal singularity-free circle for a
constant orientation and a prescribed guess box is found. Finally, the maximal singularity-free circle for all orientations of the end-effector is achieved. Moreover, a geometric approach, referred to as the offset curve approach, is presented, which can be implemented either in CAD software or in a computer algebra system. This method is quite fast and can be applied to more complicated mechanisms. As it is a geometric approach, it can be easily extended to higher degrees of freedom parallel robots.The main contribution of this work can be regarded as a combination of the maximal singularity-free circle with the workspace analysis, upon considering the stroke of the actuators, as additional constraints to the latter problem. The results of this paper reveal that the singularity-free circle of any parallel mechanism can be readily obtained upon following the proposed algorithm, and, as a case study, a 3-DOF planar parallel mechanism is presented.