The Kinematic Synthesis of Spatial Six-bar Mechanisms

This dissertation provides a new methodology for the kinematic synthesis of spatial linkages constructed from six links and seven spatial joints, known as spatial six-bar linkages. Kinematic synthesis uses the required movement of components of the linkage to define geometric constraint equations that are solved to determine thes dimensions of the links, also known as dimensional synthesis. Here a new methodology for the dimensional synthesis spatial six-bar linkages is introduced that combines robotics with the kinematic synthesis of spatial constraints. The new methodology defines the task of the linkage in terms of the movement of a spatial three-link serial chain, which is then constrained to define the six-bar linkage. The focus is on three spatial chains constructed from revolute, or hinged joints, and prismatic, or sliding, joints. These chains are denoted as the RRR, the RPR, and the PRP spatial serial chains. The spatial six-bar linkage is obtained by finding points in the moving links that lie on a sphere, which means that they can be constrained by a link connecting two spherical, or ball joints, known as an SS dyad. The result of this research is the ability to design mechanical devices that provide new capabilities. This is demonstrated by the design of a new flapping wing mechanism that coordinates wing swing and wing pitch based on the RRR serial chain, the design of a new valve mechanism that coordinates rotational and sliding movement to seal and close a foam injection port based on the RPR serial chain, and the biomimetic deployment of a patagium, the skin flap of a flying squirrel, based on the PRP serial chain