Wheelchairs are widely used globally and are essential for providing autonomy and mobility to elderly and disabled people who have movement restrictions. Manual wheelchairs require operation through turning the wheels or pushing the wheelchair directly, thus posing mobility limitations for the user and caregiver. In contrast, electric wheelchairs, when used by the user, allow for improved flexibility by operating the wheelchair through a single control mechanism. However, the use of electric wheelchairs poses challenges in accessing areas with stairs and curbs, limiting the range of activity and thereby diminishing the quality of life for users and those reliant on electric wheelchairs. The electric wheelchair developed in this research incorporates a single motor for lightweight design. It uses a wheel travel variation actuator, eliminating the need for synchronization and allowing for low-power operation. This design reduces power loss from the caterpillar’s idling during wheel movement and includes the implementation of a pulley system. The optimal pulley belt length was calculated, and a deceleration device was installed inside the caterpillar, enabling a design that is compact, lightweight, and capable of high deceleration. On paved roads and flat terrain, the electric wheelchair is designed for high-speed travel using two pairs of front omni wheels and drive wheels. For terrains with stairs, speed bumps, unpaved roads, and unavoidable obstacles, the wheelchair is powered by caterpillars. The electric wheelchair developed through the research presented in this paper has verified the reliability of its transmission system through gear stress and deformation analysis. Additionally, an electric wheelchair based on the proposed concept was constructed to validate the drivability, safety, operability, and convenience of its driving unit. Furthermore, a user rode the constructed electric wheelchair to confirm that there were no issues with its drivability.