# Small-angle perturbation method for moving platform orientation to avoid singularity of asymmetrical 3-RRR planner parallel manipulator

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## Abstract

To overcome the weakness of the present methods of singularity avoidance for 3-RRR planar parallel manipulator (PPM), a new method of avoiding singular points on planed paths in workspace via orientation perturbation to moving platforms is proposed. First, an inverse kinematics model of 3-RRR PPM is built. A discriminant matrix of type II singularity is specified and the mapping between determinant values of the matrix and points in workspace of 3-RRR PPM is defined as a singularity surface. Then, the planned path is regarded as a directrix and intersecting line between cylindrical surfaces (its generating line is parallel to the *z*-axis) and the singularity surface is defined as a singularity curve corresponding to a planned path. By determining the critical perturbation value of the moving platform’s orientation angle, the maximum value of the singularity curve corresponding to the planned path is no larger than 0 or its minimum value is no smaller than 0. Therefore, singular points on the planned path are avoided by changing the moving platform’s orientation angle without changing the planned path. Moreover, a numerical realization method is given; example and experiment verification indicates that singular points in the planned path can be avoided when perturbation to the moving platform’s orientation angle is no larger than 0.1745 rad. Therefore, the proposed method lays a solid foundation for singularity-free kinematics control based on inverse solutions.

## Keywords

3-RRR PPM Working mode Workspace Singularity avoidance Perturbation to the moving platform’s orientation## Notes

### Acknowledgments

The authors would like to thank the financial support of the National Natural Science Foundation of China (Grant No. 51305001) and the Major Natural Science Foundation of Anhui Provincial Universities (Grant No. KJ2017ZD14) for their financial support.

### Compliance with ethical standards

### Conflict of interest

The authors declare that there are no conflicts of interest regarding the publication of this paper.

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