# Instant Center Identification of Single-Loop Multi-DOF Planar Linkage Using Virtual Link
## 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; 31; 4; 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:  
1. Three types of instant centers are redefined and the instant center identification process graph is introduced. Compared to the traditional classification of instant center, the difference is that the new classification classifies the traditional secondary instant center into three refined types: new secondary instant center, A type third instant center and B type third instant center in view of the access. That is, the new classification is more accurate and detailed, which brings conveniences for further research about instant centers.
2. According to the instantaneous configuration of the linkage and definition of instant center, two criteria are presented and used to convert single-loop multi-DOF planar linkage into a two-loop virtual linkage by adding virtual links to acquire all the instant centers. Compared to the previous graphical methods, the proposed method has less operation than [PERSON]'s method and [PERSON]'s method facing the instant center identification of the simple planar linkage, such as single-loop five-bar planar linkage, and it has higher applicable rate than [PERSON]'s method. As for [PERSON]'s method, the proposed method does not need the analytical calculation. However, its disadvantage is that it must be programmed facing the instant center identification of the single-loop N-bar (N > 6) planar linkage. Moreover, the proposed method only works in the instantaneous configuration, for the continuous motion of planar linkage, it fails.
3. The instant centers of the single-loop five-bar, six-bar linkages with several prismatic joints are the first time to be located.
4. The proposed method provides a geometry loop insight to reveal the relationship between the formation of the instant center and the motion of single-loop multi-DOF planar linkage, and a new research idea for the study of instant centers.  
[PERSON], [PERSON] and [PERSON] conducted the numerical analyses and wrote the majority of the paper. [PERSON] supervised the findings and organized and structured the paper. [PERSON]-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.  
This paper has been supported by the Natural Science Foundation of China (No. 51975544) and the Natural Science Foundation of Hubei Province (No.2019 AAA071).  
The data in this study can be requested from the corresponding author.  
The first author would like to thank Academic Editors, [PERSON], [PERSON], Assistant Editor, [PERSON], and two anonymous referees, whose hard work improved the quality of the paper.  
The authors declare that they have no conflict of interest.