Variable-geometry extrusion die synthesis and morphometric analysis via planar, shape-changing rigid-body mechanisms


Bingjue Li

Date of Award


Degree Name

Ph.D. in Engineering


Department of Mechanical and Aerospace Engineering


Advisor: Andrew P. Murray


The presented work advances the kinematic synthesis methodology for planar, shape-changing rigid-body mechanisms. This methodology approximates a set of profile curves that represent the desired shapes with a single chain comprised of rigid links connected by revolute or prismatic joints. Two applications of the shape-changing chains are investigated. The first one is variable-geometry dies for polymer extrusion. The exit orifice of an extrusion die defines the cross-sectional shape of the extruded products. A die that alters its orifice shape during extrusion is capable of extruding products of varying cross section, which benefits the extrusion process by reducing the material waste and time cost. The second application is morphometric analysis. Morphometrics is the quantitative analysis for comparing a set of geometric representations of biological forms, including shape and size. Current forms of morphometrics require analyzing numerous variables. Rigid-body shape-change theory can be used as an alternate approach to analyzing morphometric problems. The primary advantage of the presented approach is that a modest number of physical parameters describes the shape and size change among a set of curves. The presented work addresses the constraints arising in the two applications and improves the methodology in the following aspects. First, new types of design profiles are implemented to accommodate the need in moveable die designs. Second, in order to reduce or eliminate the use of revolute joints in die designs which create leak path, the manner in which segments are connected can be specified a priori as either fused or by revolute joints. Third, algorithms for assembling the chain with revolute joints and aligning it with the target profiles while satisfying endpoint constraints for different types of profiles are presented. Fourth, a strategy for approximating profiles containing sharp corners or high-curvature regions is presented. Fifth, a new type of segments is introduced to address growth factor for morphometric applications. Other contributions of the presented work include a new algorithm for randomly generating an initial segment matrix, eliminating segments from the chain during optimization process, an alternate approach to determining matching error, shifting endpoint locations for closed profiles, and animating the morphing chain. The rigid-body shape-change methodology was applied to several die design and morphometric problems, and the results proved the capability of the presented technique in the applications investigated.


Extrusion process Equipment and supplies Design and construction, Joints (Engineering), Planing-machines, Shapes, Mechanical Engineering, Shapes, shape-changing mechanism, rigid-body mechanism, extrusion die, morphometrics

Rights Statement

Copyright 2017, author