Synthesizing Planar Rigid-Body Chains for Morphometric Applications

Morphometrics is a quantitative analysis to compare a set of geometric representations of forms, including shape and size. Analysis of shape variation is useful in systematics, evolutionary biology, biostratigraphy, and developmental biology. Distinguished by the data being analyzed, three forms of morphometrics are commonly recognized. Traditional morphometrics measures the lengths, ratios, angles, etc., of patterns of shape variations. Outline-based morphometrics analyzes the outlines of forms using open or closed curves. Landmark-based geometric morphometrics summarizes shapes in terms of the coordinates of anatomical landmarks. The three morphometric methods are able to capture the variation of forms exactly, but require analyzing numerous variables. As an alternative approach to morphometrics, this paper presents a kinematic synthesis methodology of planar rigid-body chains. This methodology approximates the set of profile curves that represent a series of shapes with a single chain comprised of rigid-body links connected by revolute or prismatic joints. The primary advantage of the presented approach is that a modest number of physical parameters describes the shape and size change between a set of curves. Three morphometric problems are investigated by applying the methodology of synthesizing planar rigid-body chains to match the prescribed shapes. The result validates that the presented methodology might be used as an alternative approach to the analysis of morphological forms.