A novel classification of planar four-bar linkages and its application to the mechanical analysis of animal systems.

A novel classification of planar four-bar linkages is presented based on the systematical variation of one, two or three bar lengths and studying the transmission properties (input-output curves) of the linkages. This classification is better suited to the study of biological systems than the classical Grashof-classification used in engineering as it considers the change of structural elements, in evolution for example, instead of evaluating the possibilities for the rotation of a particular bar. The mechanical features of a wide range of planar linkages in vertebrates, described by various authors, have been included in this classification. Examples are: skull-levation and jaw-protrusion mechanisms in fishes, reptiles and birds, the coral crushing apparatus of parrotfishes, and catapult-mechanisms in feeding pipefishes. Four-bar replacement mechanisms, e.g., crank-slider mechanisms in feeding systems of fishes and cam-mechanisms in mammalian limb-joints, and more complex linkages than four-bar ones, e.g., six-bar linkages and interconnected four-bar linkages in fish feeding mechanisms are also discussed. In this way, an overview is obtained of the applicability of planar linkage theory in animal mechanics to mechanical functioning and the effect of possible variations of bar lengths and working ranges in evolution. Four-bar system analysis often provides a rigorous method of simplifying the study of complex biological mechanisms. The acceptable width-range of necessary and undesired hysteresis ('play') in biological linkages is also discussed.