Abstract
Singularity is an inherent characteristic of parallel robots and is also a typical mathematical problem in engineering application. In general, to identify singularity configuration, the singular solution in mathematics should be derived. This work introduces an alternative approach to the singularity identification of lower-mobility parallel robots considering the motion/force transmissibility and constrainability. The theory of screws is used as the mathematic tool to define the transmission and constraint indices of parallel robots. The singularity is hereby classified into four types concerning both input and output members of a parallel robot, that is, input transmission singularity, output transmission singularity, input constraint singularity, and output constraint singularity. Furthermore, we take several typical parallel robots as examples to illustrate the process of singularity analysis. Particularly, the input and output constraint singularities which are firstly proposed in this work are depicted in detail. The results demonstrate that the method can not only identify all possible singular configurations, but also explain their physical meanings. Therefore, the proposed approach is proved to be comprehensible and effective in solving singularity problems in parallel mechanisms.
Highlights
In theory, parallel robots, compared with their counterparts, have the potential to answer the increasing need for high stiffness, compactness, load-to-weight ratio, and so forth
There is no doubt that screw theory is an efficient and profound mathematical tool for studying parallel mechanisms, and it has been used in evaluating the kinematic performance, type synthesis, and singularity analysis [21,22,23,24,25]
We introduce our analytical approach to elucidating singularity and its classifications, in which we consider motion/force transmissibility and constrainability in parallel robots on the basis of screw theory
Summary
Parallel robots, compared with their counterparts, have the potential to answer the increasing need for high stiffness, compactness, load-to-weight ratio, and so forth. The Jacobian matrix of a parallel robot was always derived to identify singularity; that is, Mathematical Problems in Engineering. We put forward an alternative viewpoint to the singularity in terms of the motion/force transmission and constraint properties of lower-mobility parallel robots. The indices used to evaluate the transmission and constraint performance of parallel robots have the potential to indicate the worst transmissibility and constrainability when they are equal to zero In such cases, the mechanism cannot transmit or constrain the underlying motions and forces, thereby resulting in singularities, which are discussed in this work.
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