Stiffness analysis, motion design and reconfiguration study of parallel mechanisms and manipulators

Parallel mechanisms, with their unique form of integration of mechanism loops and properties, attracted significant interest in the past 40 years. After a few decades of steady growth, the study of parallel mechanisms came to a crossroad at the beginning of the 21st century, when a new forum was needed to identify and address the fundamental issues and to open a discussion on future research directions for parallel mechanisms and manipulators. At that moment, in 2002, Clement Gosselin and Imme Ebert-Uphoff initiated the first of a workshop series on parallel mechanisms and manipulators at Laval University, in Quebec City, Canada. Experts from around the world attended this international forum during which open discussions on the fundamental issues and future research directions took place. With more than 100 participants, this workshop was a great success and raised a global attention which gave rise to a renewed interest on parallel mechanisms. Six years later, in 2008, Francois Pierrot, Nicolas Andreff, Olivier Company, Marc Gouttefarde and Sebastien Krut organized the second edition of this workshop series in Montpellier, France, which gave the opportunity to the participants to visit the LIRMM and see several successful prototypes of parallel mechanisms. The success of the first two workshops led to the third international workshop on fundamental issues and future research directions for parallel mechanisms and manipulators, which was held at Tianjin University, in Tianjin, China in 2014, organized by Tian Huang and Jian Dai as a platform for international experts to share common interests and discuss future research directions. The workshop brought together over 90 participants from 20 regions and countries with high-quality presentations and passionate discussions. This special issue includes 13 papers that were presented at the 2014 workshop on the theoretical development of parallel mechanisms and manipulators in parallel to the special issue on applications of parallel mechanisms which appears in the journal Meccanica. This special issue presents studies related to three main areas of research, namely stiffness, motion design and reconfiguration of parallel mechanisms and manipulators. Since stiffness is advocated as the main advantage of a parallel mechanism, its study has attracted the attention of researchers and various methods, integrated models, and designs have been proposed. Papers in this topic include Jacobian-based stiffness analysis based on the force equilibrium by Hoevenaars, Lambert and Herder, and stiffness evaluation based on the elasto-dynamic model by Zhao et al. The study of stiffness leads to the development of compliant parallel mechanisms by Hao, Li and Kavanagh that gives rise to the ingenious design of this monolithic type of parallel mechanisms. Stiffness analysis leads to the study of constraint and motion of parallel mechanisms. This could be seen in the continuous motion of a 3-CRC parallel mechanism presented by Chen et al., with the analysis of mirror symmetric triangles, and also in the instantaneous motion and constraint analysis presented by Liu, Zhao and Feng. The motion study leads to a revelation of transmission forces by Xie, Liu and Wang with a study of orientation capability and to a calibration of the Delta robot using distance measurements by Bai et al. with an error compensation strategy that reduces the source errors. Motion design is a challenging issue particularly with redundantly actuated parallel manipulators that raises an issue on homogenization of end-effector forces as revealed by Corves et al, leading to generating a design process and a linear mapping from the actuator space into the task space. As motions are dual to constraints, Muller and Shai presents a systematic method that transforms one mechanical system into another, with the duality concept based on the dual of a constraint graph that is the topological graph defining the kinematics, leading to a concept of

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