For this kind of journal paper, the Introduction should not read like a list of components. It should lead the reader through a problem chain: why energy harvesting matters, why electromagnetic conversion is appropriate, why nonlinear and multistable dynamics are useful, and why your particular mechanism fills a gap.

A strong English Introduction can follow your six-step logic, but it should be written as a narrative rather than numbered declarations.

Recommended argument flow

1. Start from the need for mechanical energy harvesting

Begin with the growing need for long-term power supplies in small, low-power devices. Vibration-based energy harvesting is commonly framed as a promising route for addressing battery-capacity limitations in wearable and implantable electronics, particularly biomedical devices ^[3]. Mechanical energy harvesting is also relevant to distributed sensors, where frequent battery replacement can be impractical ^[4].

A good opening sentence could be:

The rapid development of low-power electronic devices, wearable systems and distributed sensing networks has intensified the demand for compact and sustainable power sources.

Then connect that need to ambient motion:

Vibration and motion energy harvesting provide a route to convert otherwise wasted mechanical energy into usable electrical power, reducing reliance on conventional batteries ^[3][4].

2. Explain why electromagnetic induction fits rotational motion

After establishing the need, narrow the scope to the transduction mechanism. Reviews of electromagnetic vibration energy harvesters note that these devices are especially attractive because they can capture kinetic energy in low-frequency ranges, making them more applicable to many real-world vibration environments ^[2]. Developments in low-power circuitry have also improved the feasibility of such harvesters ^[2].

For rotational systems, you can then cite specific precedents. Prior work has investigated pendulum-based embedded electromagnetic energy harvesters for extracting kinetic energy from rotating bodies ^[5], pendulum-based hybrid systems for multidirectional mechanical energy harvesting ^[6], asymmetric rotating-pendulum hybrid harvesters for wave-energy scenarios ^[7], and pendulum-based electromagnetic generators for harvesting energy from human walking motion ^[8].

The key point is not simply that electromagnetic harvesters exist. It is that rotational motion naturally produces relative motion between magnetic and coil elements, and the literature already shows practical interest in pendulum or rotation-based electromagnetic harvesting ^[5][6][7][8].

3. Use multistability as the nonlinear-dynamics bridge

Next, move from the transduction mechanism to the structural design. Multistable structures have been treated as a distinct class of energy-harvesting architecture alongside monostable, bistable, magnetic-plucking and hybrid piezoelectric–electromagnetic harvesters ^[1]. Multistable vibration energy harvesters have also been reviewed as a dedicated research topic, reflecting broader interest in using multiple potential wells and nonlinear responses to improve harvesting behaviour under complex excitations ^[20].

Be careful with the wording. The supplied sources support the claim that multistability is an important design route, but they do not by themselves prove that your specific system will necessarily produce higher power or wider bandwidth. A safe formulation is:

Multistable configurations provide additional stable equilibrium states and richer transition dynamics, offering a promising structural basis for regulating the dynamic response of energy harvesters ^[1][20].

Avoid overclaiming with phrases such as “multistability always improves output power” unless your own results prove it.

4. Position nonlinear inertia as the core research gap

This is the most important part of the Introduction. You want to introduce your proposed nonlinear inertia-based power enhancement method, especially its ability to increase output power and peak power.

The literature does contain relevant work on inertia-related enhancement. Inertial-amplifier mechanisms have been proposed for low-frequency vibration energy harvesting with cantilever piezoelectric harvesters, with studies showing that such mechanisms can provide strong inertial amplification under certain conditions ^[16]. Inertial amplification has also been studied as a performance-enhancement method for snap-through vibration energy harvesters under weak excitation ^[13].

However, based on the supplied rotational electromagnetic studies, it would be safer not to claim that the same idea has already been fully developed for your exact system. The available rotating or pendulum-based electromagnetic studies cover embedded rotating harvesters, multidirectional hybrid harvesting, wave-energy harvesting and human walking applications ^[5][6][7][8]. They do not, from the supplied evidence, establish a multistable rotational electromagnetic harvester whose power enhancement is explicitly built around a nonlinear inertia mechanism ^[5][6][7][8].

A strong gap statement would be:

Although inertia-related amplification has been explored in vibration energy harvesting ^[13][16], its use as a deliberate power-enhancement mechanism in multistable rotational electromagnetic energy harvesters remains insufficiently addressed in the literature considered here ^[5][6][7][8].

This wording is academically safer than saying “no previous study has done this,” unless you have completed a broader literature review.

5. Explain why a linkage mechanism is a suitable implementation

The linkage structure should be framed as your design choice and contribution. The supplied sources do not directly prove that linkage mechanisms are generally accepted as a way to freely tune nonlinear inertia terms in this exact class of harvester. Therefore, do not present that as a literature consensus.

Instead, write it as a design rationale that your own modelling and results will support:

To realise the proposed nonlinear inertia effect, this study introduces a linkage-based architecture. The geometric parameters of the linkage serve as design variables, enabling the nonlinear inertial terms and multistable restoring characteristics to be shaped within a unified mechanical framework.

This lets you claim what your design is intended to do without overstating prior evidence.

6. End the Introduction with clear contributions

The final paragraph should list the novelty in a concise way. For example:

• A multistable electromagnetic energy harvester is proposed for rotational-motion energy harvesting.
• A nonlinear inertia-based power enhancement strategy is introduced, with particular attention to increasing output power and peak power.
• A linkage mechanism is used to provide structural tunability of the system’s nonlinear terms.
• A dynamic model is developed to analyse the coupling between multistability, nonlinear inertia and electromagnetic output.
• If included in your paper, simulations and/or experiments are used to evaluate the effects of key structural parameters on response behaviour and electrical performance.

Polished Introduction draft

The following version is written in a journal-paper style and can be adapted directly.

The rapid development of low-power electronic devices, wearable systems, implantable electronics and distributed sensing networks has created increasing demand for compact and sustainable power sources. Conventional batteries remain limited by finite capacity, replacement requirements and maintenance costs, particularly in applications where devices are embedded, distributed or difficult to access. Vibration-based and mechanical energy harvesting have therefore attracted considerable attention as alternative power-supply strategies, because they can convert ambient mechanical motion into usable electrical energy ^[3][4]. In parallel, advances in low-power circuitry have further improved the feasibility of vibration energy harvesters for practical applications ^[2].

Among the main electromechanical transduction mechanisms, electromagnetic induction is particularly suitable for harvesting low-frequency kinetic energy. Electromagnetic vibration energy harvesters are regarded as attractive because they can operate effectively in low-frequency ranges, which are common in many real-world ambient-vibration environments ^[2]. This feature makes electromagnetic conversion especially relevant for rotational and pendulum-type systems, where relative motion between magnetic and coil components can be generated by rotational dynamics. Previous studies have investigated pendulum-based embedded electromagnetic harvesters for rotating systems ^[5], hybrid pendulum systems for multidirectional mechanical energy harvesting ^[6], asymmetric rotating-pendulum hybrid harvesters for wave-energy applications ^[7], and pendulum-based electromagnetic generators for human walking motion ^[8]. These studies indicate that rotational motion combined with electromagnetic conversion provides a practical basis for mechanical energy harvesting in diverse scenarios ^[5][6][7][8].

In addition to the transduction mechanism, the dynamic structure of the harvester plays a crucial role in determining its response and energy-conversion performance. Nonlinear energy harvesters have been widely studied to overcome limitations associated with conventional linear resonant designs. In this context, multistable structures have emerged as an important class of energy-harvesting architecture. Existing reviews classify multistable harvesters alongside monostable, bistable, magnetic-plucking and hybrid piezoelectric–electromagnetic structures ^[1], and multistable vibration energy harvesters have been discussed as a dedicated research direction ^[20]. By introducing multiple stable equilibrium states, multistable systems can provide richer dynamic responses and create additional opportunities for response regulation under complex excitation conditions ^[1][20].

Building on this nonlinear design concept, this study proposes a nonlinear inertia-based power enhancement method for rotational electromagnetic energy harvesting. Inertia-related enhancement has been explored in vibration energy harvesting; for example, inertial-amplifier mechanisms have been proposed to improve low-frequency vibration energy harvesting performance ^[16], and inertial amplification has been studied as a performance-enhancement method for snap-through vibration energy harvesters ^[13]. However, within the rotational electromagnetic harvesting studies considered here, existing work mainly focuses on embedded pendulum harvesters, multidirectional hybrid systems, wave-energy harvesters and human-motion applications ^[5][6][7][8]. The deliberate use of nonlinear inertia as the central mechanism for enhancing output power, especially peak power, in a multistable rotational electromagnetic harvester remains insufficiently addressed by the supplied literature ^{[5][6][7][8][13][16]}.

To implement this concept, a linkage-based structure is introduced in the proposed harvester. The linkage geometry provides adjustable design parameters that can be used to shape the nonlinear inertial characteristics of the system and coordinate them with the multistable restoring mechanism. This architecture therefore offers a flexible mechanical platform for investigating how nonlinear inertia and multistability jointly affect rotational response and electromagnetic power generation. Based on this design, the present study develops a dynamic model of the proposed harvester and analyses the influence of key structural parameters on system response and electrical output.

The main contributions of this work are as follows. First, a multistable electromagnetic energy harvester is proposed for rotational-motion energy harvesting. Second, a nonlinear inertia-based power enhancement strategy is introduced to improve output power, with particular emphasis on peak-power amplification. Third, a linkage mechanism is adopted to realise tunable nonlinear inertial effects within the multistable harvester architecture. Finally, the dynamic behaviour and output performance of the proposed system are investigated through theoretical modelling and, where applicable, numerical or experimental validation.

Wording to avoid

Do not write:

No one has studied nonlinear inertia-based amplification before.

A safer version is:

Although inertial amplification has been investigated in vibration energy harvesting ^[13][16], its integration into a multistable rotational electromagnetic harvester as a peak-power enhancement mechanism remains insufficiently addressed in the supplied literature ^[5][6][7][8].

Do not write:

Multistability necessarily increases power and broadens bandwidth.

A safer version is:

Multistability provides a nonlinear dynamic framework with multiple stable states and richer response characteristics, which may be exploited for performance enhancement when appropriately designed ^[1][20].

Do not write:

Linkage structures are known to freely adjust all nonlinear terms.

A safer version is:

In the proposed design, the linkage parameters are used as structural variables to tune the nonlinear inertial characteristics of the system.

Bottom line

The strongest Introduction strategy is to make the first half literature-grounded and the second half contribution-driven. The literature can support the need for energy harvesting, the suitability of electromagnetic conversion for low-frequency motion, the relevance of rotational and pendulum-based harvesters, and the importance of multistable nonlinear structures ^{[1][2][3][4][5][6][7][8][20]}. Your distinctive claims should then be framed around what this paper proposes: a multistable rotational electromagnetic harvester using a linkage-enabled nonlinear inertia mechanism to enhance output power, especially peak power.