Designing shape changing mechanisms for planar and spatial applications

Date of Award


Degree Name

M.S. in Mechanical Engineering


Department of Mechanical and Aerospace Engineering


Advisor: Andrew P. Murray


Rigid-body shape changing mechanisms are a growing area of research due to their numerous practical uses. Rigid-body shape-change describes mechanisms comprised of rigid links connected with revolute and prismatic joints that are able to approximate a set of prescribed morphing" curves. Planar rigid-body shape-changing mechanisms are synthesized to achieve different positions within a common plane. Designing for spatial tasks, however, is an area of emerging research. This thesis addresses topics in both planar and spatial shape-changing devices. First, a practical application for planar shape-changing devices is developed through the design and testing of variable geometry dies for polymer extrusion. Second, a synthesis methodology for spatial shape-changing is developed for serial chains of spherical four-bar mechanisms that can achieve specified helices. Variable geometry dies enable the extrusion of plastic parts with a varying cross-section. Extrusion accounts for 40% of all manufactured plastic parts due to its relatively low-cost and high-production-rate. Conventional polymer extrusion technology, however, is limited to fixed dies that produce continuous plastic products of constant cross section defined by the die exit profile. A shape-changing die allows the cross-section of the extruded part to change over its length, thereby introducing the capacity to manufacture plastic faster and with lower tooling costs than injection molding. This thesis discusses design guidelines that were developed for movable die features including revolute and prismatic joint details, land length, and the management of die leakage. To assess these guidelines, multiple dies have been designed and constructed to include an arbitrary four-sided exit profile where changes were made to the internal angles and length of sides as the extruder was operating. Experimental studies were conducted by using different extruder line settings and time between die movements. Test results are presented that include shape repeatability and the relationship between extrudate profile and die exit geometry. A spatial shape-change application is then introduced with serial chains of spherical four-bar mechanisms. The chains are comprised of identical copies of the same four-bar mechanism by connecting the coupler of the prior spherical mechanism to the base link of the subsequent spherical mechanism. Although having a degree of freedom per mechanism, the design methodology is based upon identically actuating each mechanism. With these conditions, the kinematic synthesis task of matching periodically spaced points on up to five arbitrary helices may be achieved. Due to the constraints realized via the spherical equivalent of planar Burmester Theory, spherical mechanisms produce at most five prescribed orientations resulting in this maximum. The methodology introduces a companion helix to each design helix along which the intersection locations of each spherical mechanisms axes must lie. As the mechanisms are connected by rigid links, the distance between the intersection locations along the companion helices is a constant. An extension to the coupler matches the points along the design helices. An approach to mechanically reducing the chain of mechanisms to a single degree of freedom is also presented. Finally, an example shows the methodology applied to three design helices."


Smart materials, Polymers Extrusion, Plastics Extrusion, Mechanical Engineering, polymer extrusion, shape change, spherical four-bar mechanism, variable geometry die, polymer manufacturing, spatial curve matching, mechanical helix

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Copyright © 2014, author