The stabilization of man-made dynamic systems has been achieved by sensor-based state feedback control with high computational bandwidth, fast signal transmission speed, and stiff joints. In contrast, many biological systems can achieve similar or superior stable behavior with low computational bandwidth, slow signal transmission speed via the nervous system, and flexible joints. The concept of self-stabilization has recently been proposed and widely investigated to explain this phenomenon. Self-stabilization is defined as the ability to restore its original state after a disturbance without any feedback control. In this paper, the stabilizing function of a musculoskeletal system for arbitrary motion in the vertical plane is analytically investigated using Lyapunov stability criteria. Based on this investigation, the method of designing a new actuator that can assign a self-stabilizing function to a robotic arm is introduced and a self-stabilizing manipulator is physically realized. As a result, a theoretically predicted self-stabilizing function is experimentally verified and explains why a biological musculoskeletal system can be stabilized with feedforward control.