Synthesizing Planar Rigid-Body Chains for Morphometric Applications

Abstract

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.

Design and Prototyping of a Shape-Changing Rigid-Body Human Foot in Gait

“…Practical devices synthesized using this methodology have thus far largely been limited to non-biological applications, such as morphing aircraft wings [38], automobile spoilers [33], and polymer extrusion dies [39]. It has previously been demonstrated, however, that the technique can be applied successfully to a variety of morphometric problems with biologically generated inputs [40]. After specifying V and W vectors, an initial population of p x q segment matrices is randomly generated.…”

“…Note that the joining of R type connections need not be performed at this stage of the synthesis process. It is advisable to join segments connected by R type connections after SMs have been optimized, as doing so beforehand has been demonstrated to significantly increase computation time without significantly affecting post-optimization results [40].…”