**6. Conclusions**

Instant center can be used in spatial mechanisms [26,27], redundant mechanisms [28], real devices [30], and is even available in commercial packages. It is a basic kinematic property which helps analyze kinematics of the linkages [2–5,31], rigid-body synthesis [6], dynamics modeling [7], dynamic balancing analysis [29], and imperfect systems of real devices [30]. Based on coupled loop chain characteristic and definition of instant center, a virtual link method to identify instant centers of the single-loop multi-DOF planar linkage is proposed. The conclusions and advantages can be summarized as follows:


**Author Contributions:** L.N., H.D. and A.K. conducted the numerical analyses and wrote the majority of the paper. H.D. supervised the findings and organized and structured the paper. K.-L.T. reviewed the paper and given the constructive suggestion to improve the quality of the paper. All authors have read and agreed to the published version of the manuscript.

**Funding:** This paper has been supported by the Natural Science Foundation of China (No. 51975544) and the Natural Science Foundation of Hubei Province (No.2019AAA071).

**Data Availability Statement:** The data in this study can be requested from the corresponding author.

**Acknowledgments:** The first author would like to thank Academic Editors, Giuseppe Carbone, Med Amine Laribi, Assistant Editor, Erica Li, and two anonymous referees, whose hard work improved the quality of the paper.

**Conflicts of Interest:** The authors declare that they have no conflict of interest.
