SUMMARYDuring flight, many insect wings undergo dramatic deformations that are controlled largely by the architecture of the wing. The pattern of supporting veins in wings varies widely among insect orders and families, but the functional significance of phylogenetic trends in wing venation remains unknown, and measurements of the mechanical properties of wings are rare. In this study, we address the relationship between venation pattern and wing flexibility by measuring the flexural stiffness of wings (in both the spanwise and chordwise directions) and quantifying wing venation in 16 insect species from six orders. These measurements show that spanwise flexural stiffness scales strongly with the cube of wing span, whereas chordwise flexural stiffness scales with the square of chord length. Wing size accounts for over 95% of the variability in measured flexural stiffness; the residuals of this relationship are small and uncorrelated with standardized independent contrasts of wing venation characters. In all species tested, spanwise flexural stiffness is 1-2 orders of magnitude larger than chordwise flexural stiffness. A finite element model of an insect wing demonstrates that leading edge veins are crucial in generating this spanwise-chordwise anisotropy.

Plants and animals that inhabit the intertidal zone of wave-swept shores are generally small relative to terrestrial or subtidal organisms. Various biological mechanisms have been proposed to account for this observation (competition, size-specific predation, food-limitation, etc.). However, these biological mechanisms are constrained to operate within the mechanical limitations imposed by the physical environment, and these limitations have never been thoroughly explored. We investigated the possibility that the observed limits to size in wave-swept organisms are due solely or in part to mechanical, rather than biological, factors.The total force imposed on an organism by breaking waves and postbreaking flows is due to both the water's velocity and its acceleration. The force due to velocity (a combined effect of drag and lift) increases in strict proportion to the organism's structural strength as the organism increases in size, and therefore cannot act as a mechanical limit to size. In contrast, the force due to the water's acceleration increases faster than the organism's structural strength as the organism grows, and thus constitutes a potential mechanical limit to its size. We incorporated this fact into a model that predicts the probability that an organism will be destroyed (by breakage or dislodgement) as a function of five parameters that can be measured empirically: (!) the organism's size, (2) the organism's structural strength, (3) the maximum water acceleration in each wave, (4) the maximum water velocity at the time of maximum acceleration in each wave, and (5) the probability of encountering waves with given flow parameters.The model was tested using a variety of organisms. For each, parameters 1-4 were measured or calculated; the probability of destruction, and the size-specific increment in this probability, were then predicted. For the limpets Collisella pelta and Notoacmaea scutum, the urchin Strongylocentrotus purpuratus, the mussel Mytilus californianus (when solitary), and the hydrocoral Millepora complanata, both the probability of destruction and the size-specific increase in the risk of destruction were determined to be substantial. It is conjectured that the size of individuals of these species may be limited as a result of mechanical factors, though the case of M. complanata is complicated by the possibility that breakage may act as a dispersal mechanism. In other cases (the snails Thais canaliculata, T. emarginata, and Littorina scutulata; the barnacle Semibalanus cariosus), the size-specific increment in the risk of destruction is small and the size limits imposed on these organisms are conjectured to be due to biological factors.Our model also provides an approach to examining many potential effects of environmental stress caused by flowing water. For example, these methods may be applied to studies of: (!) life-history parameters (e.g., size at first reproduction, age at first reproduction, timing of reproductive cycles, length of possible reproductive lifetime), (2) the effects of...

SUMMARYThe dynamic, three-dimensional shape of flapping insect wings may influence many aspects of flight performance. Insect wing deformations during flight are largely passive, and are controlled primarily by the architecture and material properties of the wing. Although many details of wing structure are well understood, the distribution of flexural stiffness in insect wings and its effects on wing bending are unknown. In this study, we developed a method of estimating spatial variation in flexural stiffness in both the spanwise and chordwise direction of insect wings. We measured displacement along the wing in response to a point force, and modeled flexural stiffness variation as a simple mathematical function capable of approximating this measured displacement. We used this method to estimate flexural stiffness variation in the hawkmoth Manduca sexta, and the dragonfly Aeshna multicolor. In both species, flexural stiffness declines sharply from the wing base to the tip, and from the leading edge to the trailing edge; this variation can be approximated by an exponential decline. The wings of M. sexta also display dorsal/ventral asymmetry in flexural stiffness and significant differences between males and females. Finite element models based on M. sexta forewings demonstrate that the measured spatial variation in flexural stiffness preserves rigidity in proximal regions of the wing,while transferring bending to the edges, where aerodynamic force production is most sensitive to subtle changes in shape.

Neuromechanics seeks to understand how muscles, sense organs, motor pattern generators, and brain interact to produce coordinated movement, not only in complex terrain but also when confronted with unexpected perturbations. Applications of neuromechanics include ameliorating human health problems (including prosthesis design and restoration of movement following brain or spinal cord injury), as well as the design, actuation and control of mobile robots. In animals, coordinated movement emerges from the interplay among descending output from the central nervous system, sensory input from body and environment, muscle dynamics, and the emergent dynamics of the whole animal. The inevitable coupling between neural information processing and the emergent mechanical behavior of animals is a central theme of neuromechanics. Fundamentally, motor control involves a series of transformations of information, from brain and spinal cord to muscles to body, and back to brain. The control problem revolves around the specific transfer functions that describe each transformation. The transfer functions depend on the rules of organization and operation that determine the dynamic behavior of each subsystem (i.e., central processing, force generation, emergent dynamics, and sensory processing). In this review, we (1) consider the contributions of muscles, (2) sensory processing, and (3) central networks to motor control, (4) provide examples to illustrate the interplay among brain, muscles, sense organs and the environment in the control of movement, and (5) describe advances in both robotics and neuromechanics that have emerged from application of biological principles in robotic design. Taken together, these studies demonstrate that (1) intrinsic properties of muscle contribute to dynamic stability and control of movement, particularly immediately after perturbations; (2) proprioceptive feedback reinforces these intrinsic self-stabilizing properties of muscle; (3) control systems must contend with inevitable time delays that can simplify or complicate control; and (4) like most animals under a variety of circumstances, some robots use a trial and error process to tune central feedforward control to emergent body dynamics.