**5. Conclusions**

A nonlinear model of a pendulum is used to power the model of the piston through the lever. The system's dynamic response is analyzed, and the presented results show the system's effectiveness after a series of simulations at various parameter values. The numerical results show a good response of the scenario through the power transient from the pendulum to the piston. In addition, the system's response depends on the length of the pendulum that can be manipulated to achieve better performance. The presented results also show that the system can transfer energy with little human effort to do heavy work since the piston's mass is much bigger than the combined mass of the pendulum and the lever. A novelty is presented where a vertically excited pendulum with variable length is used instead of the conventional pendulum with constant length. In the proposed model, the system response shows a quasi-periodicity behavior and does not settle even after 50 s of simulation time. However, the quasi-periodicity behavior can be compensated when a regular external forcing is applied to the system. No control algorithm is included since the aim is to operate a system in rural and urban areas without electricity. However, the system can be constructed to include a control algorithm and transformed into a mechatronics system for any laboratories and industrial uses. Synchronization of the pendulum pump

and the human body could be considered a problem of biomechanics. Lastly, further dynamical analysis can be performed to investigate the system's behavior more, and more studies on fluid mechanics will add value to the overall system operation.

**Author Contributions:** Conceptualization, G.Y. and P.O.; Data curation, P.O. and J.A.; Formal analysis, G.Y. and P.O.; Funding acquisition, J.A.; Investigation, G.Y.; Methodology, G.Y.; Project administration, G.Y.; Resources, G.Y. and J.A.; Software, G.Y.; Supervision, P.O. and J.A.; Validation, G.Y. and P.O.; Visualization, G.Y.; Writing—original draft, G.Y. and P.O.; Writing—review and editing, G.Y. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by Narodowe Centrum Nauki Grant No. 2019/35/B/ST8/00980 (NCN Poland).

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

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** The first author Godiya Yakubu is the Doctoral Candidate in the Interdisciplinary Doctoral School at the Lodz University of Technology, Poland.

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

#### **Abbreviations**

The following abbreviations are used in this manuscript:

