# Design and Analysis of a Novel Variable Stiffness Joint Based on Leaf Springs
## 5 Conclusions  
This paper proposed a novel VSJ, inspired by the principle of the effective beam length of a leaf spring. The wide stiffness range and fast adjustment speed from a minimum level to near infinite was achieved through driving the specially designed disc via rotation only. With the help of the reconfiguration mechanism, the stiffness adjustment range and nominal elastic torque or load capacity of the VSJ can be easily expanded for a specific requirement without the disassembling and re-assembling of the actuators. Mathematical models of the VSJ were derived and verified through adequate simulation analysis. The simulation results proved the fast regulation speed and good tracking performance of the VSJ using a simple controller, which validated the simplicity of the design. One limitation of the proposed design is that the maximum deflection angle is not large enough, which is not conducive to reverse driving in human-robot interactions. However, this can be expanded in future studies via the structural optimization of joints and springs. The weight of the VSJ should also be further reduced via reasonable structural optimization before the upcoming prototype manufacturing. Following this, the physical prototype of the VSJ is expected to be applied to a flexible robot with multiple degrees of freedom. Consequently, advanced control algorithms should be designed for the VSJ in the expected human-robot interaction applications. Conceptualization, C.W. and Y.X. ; methodology, X.W. ; software, Y.G. ; validation, Y.G., Y.X. and L.W. ; formal analysis, Y.G. ; investigation, C.W. ; resources, Y.G. ; data curation, Y.G. ; writing--original draft preparation, Y.G. ; writing--review and editing, Y.X. ; visualization, Y.G. ; supervision, C.W. ; project administration, C.W. ; funding acquisition, Y.X. All authors have read and agreed to the published version of the manuscript. This research was supported by the Open Project of Henan Key Laboratory of Intelligent Manufacturing of Mechanical Equipment, Zhengzhou University of Light Industry (No. IM202312), the Doctoral Research Fund of Zhengzhou University of Light Industry (No. 2022 BSJ)JZK02), the Program for Science & Technology Innovation Talents in Universities of Henan Province (Grant No. 22 HASTIT023), and the National Natural Science Foundation of China (Grant No. 52075500). * [PERSON] et al. (2019) [PERSON]; [PERSON]; [PERSON]; [PERSON] Design and analysis of spring parallel variable stiffness actuator based on antagonistic principle. _Mech. Mach. Theory_**2019**, _140_, 44-58. [CrossRef]
* [PERSON] et al. (2015) [PERSON]; [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON]; [PERSON] [PERSON]; [PERSON]; [PERSON] [PERSON]; [PERSON]; et al. Variable stiffness actuators: The user's point of view. _Int. J. Robot. Res._**2015**, _34_, 727-743. [CrossRef]
* [PERSON] et al. (2020) [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] Varying mechanical compliance benefits energy efficiency of a knee joint actuator. _Mechatronics_**2020**, _66_, 102318. [CrossRef]
* [PERSON] (2016) [PERSON]; [PERSON] Modeling and benchmarking energy efficiency of Variable Stiffness Actuators on the example of the DLR FSI. In Proceedings of the 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Daejeon, Republic of Korea, 9-14 October 2016. * [PERSON] et al. (2017) [PERSON]; [PERSON]; [PERSON] Design of variable impedance actuator for knee joint of a portable human gait rehabilitation exoskeleton. _Mech. Mach. Theory_**2017**, _116_, 248-261. [CrossRef]
* [PERSON] et al. (2020) [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] A Lightweight Series Elastic Actuator with Variable Stiffness: Design, Modeling, and Evaluation. _IEEE/ASME Trans. Mechatron._**2020**, _28_, 3110-3119. [CrossRef]
* [PERSON] et al. (2021) [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Design and evaluation of a novel torque-controllable variable stiffness actuator with reconfigurability.