Representations of multi-joint stiffness for prosthetic limb design

Human limbs have inherent spring-like properties that have been shown to be important for posture and movement control. When an amputated limb is augmented with a powered prosthesis, the stiffness properties of the resulting limb-prosthesis combination are an important aspect of the performance of the system. Limb stiffness properties are typically represented as stiffness ellipses or isopotential ellipses at the hand. Such representations are useful visual tools for studies of human limb mechanics and in the design and control of limb prostheses and robotics. However, these representations require the stiffness to be stable and symmetric. An often neglected term to the endpoint stiffness and the effects of the controllers of powered prostheses can both result in unstable conditions of the limb. Understanding the state and behaviour of the stiffness becomes difficult when the possibility of instability is introduced, particularly since the stiffness can no longer be represented as an ellipse. The current work introduces an alternate stiffness representation based on the Mohr’s circle used in stress analysis. Realistic examples demonstrate the benefits of this approach and an example shows that this instability can occur in situations that are within the capabilities of the human limb.