Functional and Mathematical Equivalence of Mechanisms: A Novel Approach to Integrating Synthesis and Design Analysis

The objective of our research is to produce classical engineering design analysis models in conjunction with the employment of function based synthesis techniques. As a part of this goal, we define a design approach to construct parametric design models from functional models. Such an approach allows a natural progression from functional product models, to synthesis, to analysis, and then to initial parameter specification. An empirical study is performed to gather product data from a jigsaw and a palm sander. Our method starts by creating a black box model and a functional model of a product. From the functional model, a critical flow and an associated function chain are identified. The next step is to express each component at a functional level. Following that, components are mapped to equations describing their performance and finally, functions are mapped to equations. We analyze product data that is collected following the above described steps and discover functional and mathematical similarities between a scotch yoke mechanism in a jigsaw and an eccentric cam in a palm sander; in this case, two mechanisms used to perform the same function. We derive general performance equations for functions based on the components that are functionally similar but differing in form.

Functional and Mathematical Equivalence of Mechanisms: A Novel Approach to Integrating Synthesis and Design Analysis Conference Paper