Stable operation of an elastic three-segmented leg - Seyfarth, A.; Günther, M.; Blickhan, R. (2000)
Quasi-elastic operation of joints in multi-segmented systems as they occur in the legs of humans, animals, and robots requires a careful tuning of leg properties and geometry if catastrophic counteracting operation of the joints should be avoided. A simple three-segment model has been used to investigate the segmental organisation of the leg during repulsive tasks like human running and jumping. The effective operation of the muscles crossing the knee and ankle joints is described in terms of rotational springs. Following issues were addressed in this study: (1) How can the joint torques be controlled to result in a spring-like leg operation? (2) How can rotational stiffnesses be adapted to leg segment geometry? (3) To what extend can unequal segment lengths and orientations be of advantage? It was found that (1) the three-segment leg tends to become unstable at a certain amount of bending expressed by a counter-rotation of the joints, (2) homogeneous bending requires to adapt rotational stiffnesses to the outer segment lengths, (3) nonlinear joint torque-displacement behaviour extends the range of stable leg bending and may result in an almost constant leg stiffness, (4) biarticular structures (like human m. gastrocnemius) and geometrical constraints (like heel strike) support homogeneous bending in both joints, (5) unequal segment lengths enable homogeneous bending if asymmetric nominal angles meet the asymmetry in leg geometry, and (6) a short foot supports the elastic control of almost stretched knee positions. Furthermore, general leg design strategies for animals and robots are discussed with respect to the range of safe leg operation.