Pantomeshes: kinematics, synthesis, and applications of closed pantograph-style linkage systems.

Abstract

This research describes the kinematics, analysis, and synthesis of a pantomesh. A pantomesh is a patchwork assembly of pantograph elements (known elsewhere as scissor pairs or duplets) that obey certain mobility requirements. A pantomesh, as described in this thesis, has scissor-like elements connected to one another by spherical joints to allow a wide variety of motions. Previous pantograph-style linkages, such as the Hoberman Sphere, use special geometry restrictions and have elements joined with gussets, thereby limiting the variety of shapes possible. The thesis begins with examining the kinematics of pantomeshes and their constituent parts. First, the kinematics of the individual pantograph elements are detailed for further use. The mobility of a closed pantomesh is ensured by the mobility of its constituent pantopatches, two-wide by two-high sub-assemblies of pantograph elements that must be mobile themselves for the entire pantomesh to be mobile. A new method for mobility of spatial linkages is presented relating the use of polygonal elements. Next, two methods for pantomesh synthesis are presented. A graphical method is presented to use a computer-aided design system to create a mobile pantomesh that meets specified requirements. A computational method for synthesis is also presented, using a numerical optimization method to create pantomeshes to certain specifications. Practical considerations of manufacturing are considered in the discussion of multi-link spherical joints, including past work and new approaches. The new approaches include a compliant multi-link spherical joint and a crossed-tendon system that acts a a spherical joint. Finally, an application is presented: a new linkage which provides radial pressure for the purpose of stabilizing a human breast during cancer-related diagnosis and treatment procedures.