Structural shakiness of nonoverconstrained translational parallel mechanisms with identical limbs
IEEE Transactions on Robotics
Parallel mechanisms with bifurcation of Schoenflies motion
IEEE Transactions on Robotics
Design and analysis of a totally decoupled flexure-based XY parallel micromanipulator
IEEE Transactions on Robotics - Special issue on rehabilitation robotics
1T2R parallel mechanisms without parasitic motion
IEEE Transactions on Robotics
The kinematic design of spatial, hybrid closed chains including planar parallelograms
Robotics and Computer-Integrated Manufacturing
Robotics and Autonomous Systems
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Mechanism synthesis is mostly dependent on the designer's experience and intuition and is difficult to automate. This paper aims to develop a rigorous and precise geometric theory for analysis and synthesis of sub-6 DoF (or lower mobility) parallel manipulators. Using Lie subgroups and submanifolds of the special Euclidean group SE(3), we first develop a unified framework for modelling commonly used primitive joints and task spaces. We provide a mathematically rigorous definition of the notion of motion type using conjugacy classes. Then, we introduce a new structure for subchains of parallel manipulators using the product of two subgroups of SE(3) and discuss its realization in terms of the primitive joints. We propose the notion of quotient manipulators that substantially enriches the topologies of serial manipulators. Finally, we present a general procedure for specifying the subchain structures given the desired motion type of a parallel manipulator. The parallel mechanism synthesis problem is thus solved using the realization techniques developed for serial manipulators. Generality of the theory is demonstrated by systematically generating a large class of feasible topologies for (parallel or serial) mechanisms with a desired motion type of either a Lie subgroup or a submanifold.