Analysis and synthesis of interconnected hybrid mechanisms using Freedom and Constraint Topologies (FACT)

We introduce visualization-based methods to analyze and synthesize interconnected hybrid (ICH) systems. These systems consist of joints that are not strictly parallel nor serial to one another. We include two types of analysis methods – one that uses joint freedom spaces and another that uses joint constraint spaces. These methods leverage intuition to determine the mobility, under-constraint, over-constraint, transmission, and load paths of any mechanism. The analysis methods are an interpretation of previously established numerical approaches for ICH systems. To adapt the complexities of screw theory and matrix algebra, this work builds off the geometries and systematic rules of the Freedom and Constraint Topologies (FACT) design approach. The synthesis approach is a reversal of the freedom-based analysis method. This synthesis approach takes a designer from any set of desired transmissions to an ICH system capable of achieving them. Both the analysis and synthesis approaches are accompanied by an example compliant mechanism to illustrate their utility and limitations. These methods seek to facilitate the design of emerging mechanism classes, such as metamaterials, and extend the FACT design approach to include ICH systems.