Prosthetic hands are vital assistive devices that significantly enhance quality of life for individuals with upper limb amputations, enabling them to regain autonomy and perform essential daily activities. However, many existing prosthetic solutions are hindered by high costs, excessive weight, and complex actuation systems that limit accessibility and usability. This paper introduces a novel prosthetic hand design that addresses these limitations through a mechanically efficient and cost-effective approach. The proposed system employs five motors, one per finger, combined with a closed-loop chain linkage mechanism that transmits motion across joints of each finger. This eliminates a need for multiple actuators per finger, thereby reducing an overall weight, power consumption, and cost of the device. We present a complete design methodology, a mechanical architecture, and functional analysis of the prototype. The mechanical structure achieves finger flexion up to 125 degrees, distal interphalangeal (DIP) joint articulation up to 90 degrees, and wrist deviation of ±20 degrees, closely mimicking natural hand movement. The results demonstrate feasibility and advantages of the approach, offering a promising direction for developing affordable, efficient, and user-friendly prosthetic hands.