Kenneth E. Richardson, Department of Mechanical Engineering
Introduction
The modeling of the human body is not an easy task. Designers of artificial organs and prosthetic devices have the unenviable goal of attempting to duplicate (or at least satisfactorily approximate) the motion and function of the greatest and most powerful machine on the face of the earth. Any new tool that could be used in such design would be valuable and useful. Compliant mechanism theory and design is one such tool.
The stated purpose of this project was to explore applications of compliant mechanisms in medicine and biomechanical design. Several medical fields were studied and analyzed, including surgical equipment, artificial organs, and prosthetics. The main focus of the project was on the design of a prosthetic foot for below-knee amputees using compliant techniques. A brief summary of compliant mechanisms and their use in design follows as well as the description and results of one approach to the compliant design of a prosthetic foot.
Compliant Mechanism Design
Compliant mechanisms represent a class of mechanical systems which make use of flexible or large-displacement elements, as opposed to the use of only rigid, non-flexible elements. The traditional mechanisms that are used almost universally in the manufacturing world today are called rigid-body mechanisms. They involve solid links connected by joints which allow relative motion between them. Compliant equivalents of such mechanisms replace the links and joints with a single piece of material having rigid and flexible parts.
The study of compliant mechanisms is a relatively new design and research field, but one that is increasing in importance due to their potential uses and their advantages over rigid-body mechanisms. One such advantage is resiliency, a property in which a flexible part returns to an original position after being displaced and released. Compliant mechanisms are usually lighter in weight and lower in cost than their rigid-body counterparts without sacrificing strength. Since compliant mechanisms are often built in one piece, manufacturing is simplified greatly as are modeling techniques. Also, in the absence of rigid-body joints, where machine parts continually rub against each other, there is a significant decrease in wear, backlash, noise, and need for lubrication.
A Prosthetic Foot Design
Compliant mechanisms are perfectly suited to mechanical models of the human body. The 206 bones of the human skeleton provide motion and mobility to the body by virtue of their motion relative to each other, like a very complex rigid-body mechanism. However, when the muscles, tendons, and cartilage that provide control for this motion are considered, a large amount of compliance and resiliency is evident for even simple movements. Even the “rigid” bones exhibit great flexibility as they respond to muscular control, making the body seem more similar to compliant mechanisms than to rigid-body mechanisms. Like a mechanical spring, the compliant elements of the human body absorb and release energy according to applied forces. This compliance and resiliency must be considered to gain an accurate understanding of the biomechanics of the body.
The human gait cycle exhibits and depends upon a large degree of compliant behavior in the lower extremities, particularly the ankle. This joint and the muscles of the leg respond to the forces that the ground exerts on the foot during each part of the gait cycle to maintain balance and control at each instant. In addition, the resiliency of the ankle ensures that the foot is prepared for the next stride by returning it to its “rest position”.
The ideal design of a prosthetic foot for a lower-limb amputee would be one that exactly matched each part of the human leg, foot, and ankle (the “original design”) with rigid and compliant links and joints. The obvious problems that would arise from such an attempt include the inability to control such a system (the human brain and nervous system cannot be duplicated) and the impossibility of matching man-made materials exactly to those of the body, such as a material that has the same strength and elastic properties as bone, for example. A simplified design must therefore be found which follows the original design as closely as possible.
For a simple analysis, a proposed design is as follows: a shaft attached to the amputated leg extends to the location of the ankle on the original leg. There it is connected to another length of material (the “foot”), which contacts the floor in two primary locations, the “heel” and the “ball” of the foot. A simple but measurable degree of compliance is added to the device by connecting the two parts with a curved metal piece, a part which approximates the resiliency of the ankle by resisting any deviation from its resting position. The curved member has the properties of (and may be modeled by) a mechanical spring.
For analysis, the device is represented by a mechanism having two rigid links (1 and 2) connected at a joint A. The compliant (curved) member connecting the two links is represented by a rigid link (link 3), a slider, and a spring, as shown. Note that the slider and link 3 are attached to the other links at precisely the same points as the curved member would be.