This work presents the mechanical design of 4 configurations of compliant fingers in order to address the need for commercially feasible prosthetic and robotic hands. The fingers consist of a single part and utilize a compliant mechanism to reduce the cost and control complexity. The geometric parameters of the compliant finger designs follow the Fibonacci series. The first and second compliant fingers have 2 joints and 2 degrees of freedom. The others have 3 joints and 3 degrees of freedom. The type of flexure hinges of the compliant finger are single and multiple nonsymmetrical circular hinges. The finite element method (FEM) was used to verify the range of motion of the joints in the compliant finger. In addition, the study defines the finger tip trajectory of these configurations. The multiple flexure hinges have minimum stress. This study presents affordable, single-element, compliant finger designs and their presumable hypothetical design variables are defined by the Fibonacci series. This method is faster and simpler than optimization. The study identifies the application of each finger design for either prosthetic or robotic purposes.