**5. Conclusions**

A design proposal has been presented for a scalable and modular link, inspired by origami structures. The validation of the kinematics for both single and nested links has been successfully carried out. In the case of the nested link, the change in length of the link can be done by completely folding one of the single links or by doing a proportional folding on each single link.

A simple link prototype has been built and experimentally tested to validate its scalability and shape change. The model with three tendons actuated by a motor allows the folding of the origami structure while an internal spring generates the unfolding.

Compared to other platforms such as [21], which are manually controlled, in our study we included system modeling and controller tuning for automatic operation in position control of the prototype.

The single link prototype has been successfully controlled in position mode. The position control has been done with two control loops for the correct operation of the motor. The internal loop allows for the elimination of the dead zones of the motor with a velocity control and with the external loop the origami position is controlled. The internal loop has been designed and tested with two controllers, integer and fractional, where the single link has been tested for correct operation with and without payload.

The identification of the whole system was carried out considering these two control loops; otherwise, the direct identification of the system would have resulted in a nonlinear system, due to the saturation and the dead zone of the motor.

It is also important to remark that the rotational movement of the Kresling pattern can be seen as an advantage that allows the orientation of the platform. However, the rotation can be canceled by coupling two simple links with opposite rotation, if only a prismatic displacement is required.

Some of the main limitations of the system are due to the fact that it is a very low cost 3D printed prototype that needs the adjustment of the mechanical parts and the use of a better motor. However, despite these limitations, the prototype works properly and the design has been validated.

Future works include the improvement of the mechanical and actuation parts of the link and the introduction of distance and rotation sensors to enhance the position accuracy *h* and rotation angle *θ*, which are now obtained indirectly. Besides, the development of the three-dimensional joint to interconnect several links is one of our major objectives, which will allow us to implement and test modularity.

**Author Contributions:** Conceptualization, L.M.; methodology, L.M.; software, L.M. and J.M.; validation, L.M. and J.M.; investigation, L.M., C.A.M., and J.M.; resources, C.A.M. and C.B.; data curation, L.M. and J.M.; writing—original draft preparation, L.M. and J.M.; writing—review and editing, C.A.M.; supervision, C.A.M. and C.B.; project administration, C.A.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** The research leading to these results has received funding from the project Desarrollo de articulaciones blandas para aplicaciones robóticas, with reference IND2020/IND-1739, funded by the Comunidad Autónoma de Madrid (CAM) (Department of Education and Research), and from RoboCity2030-DIH-CM, Madrid Robotics Digital Innovation Hub (Robótica aplicada a la mejora de la calidad de vida de los ciudadanos, FaseIV; S2018/NMT-4331), funded by "Programas de Actividades I+D en la Comunidad de Madrid" and cofunded by Structural Funds of the EU.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented are available on request from the corresponding author.

**Conflicts of Interest:** There are no conflicts of interest to declare.
