Invertebrate paraxial locomotory appendages: design, deformation and control

Some principles governing the design of invertebrate paired propulsive appendages are discussed, with particular reference to the extent to which information encoded in their skeletal structure determines their instantaneous shape in locomotion. The hydrostatic paired fins of some cephalopods and marine gastropods, polychaete parapodia and onychophoran lobopodia rely entirely on musculature for shape control. The deformations of walking limbs, though still under muscular control, are strongly influenced by the nature and sequence of movement of the joints. Limbs adapted for walking in air are effectively point-loaded, and their rigid components need to resist axial forces as well as bending and torsional moments. Aquatic walking limbs have little axial loading, while swimming appendages and wings experience only bending and torsional moments, and can exploit these to assist in the deformations that are necessary to gain force asymmetry between half-strokes. Swimming appendages normally employ both muscles and drag, but the wings of insects lack internal muscles, and their changes in shape are largely complex aeroelastic responses to the constantly changing aerodynamic and inertial loads, moderated by muscles inserted at the base. For illustration, wings modelled as thin shells with flexible hinge-lines are used to investigate how transverse distal flexion, essential for controlling the angle of attack in the upstroke, is remotely controlled by the indirect flight muscles.