A novel mathematical formulation for predicting symmetric passive bipedal walking motion with unbalanced masses

• A bipedal walking algorithm is presented for curved feet and unequal masses.
• The effect of changing length/mass ratio's on stable walking process is studied.
• Results are expressed in terms of roll-over shape curvature and foot length values.
• The new insights are useful in the design of prosthetic as well as robotic feet.

Commercial prosthetic feet weigh about 25% of their equivalent physiological counterparts. The human body is able to overcome the walking asymmetry resulting from this mass imbalance by exerting more energy. It is hypothesised that the passive walking dynamics coupled with roll-over shapes has potential to suggest energy efficient walking solutions. A two link passive walking kinematic model has been proposed to study the gait pattern with unbalanced leg masses. An optimal roll-over shape for the prosthetic foot that minimises the asymmetry in the inter-leg angle and the step period is determined. The proposed mathematical formulation provides insights into the variation of step length and inter-leg angle with respect to the position and location of the centres for mass of both prosthetic and physiological legs.