Compliant mechanisms achieve motion by utilizing deformation of elastic members. They offer many advantages over conventional rigid-body mechanisms such as elimination of friction or wear and tear. They also offer greater accuracy and can usually be fabricated as a single part, without the need for assembly. They are used in a wide variety of applications, particularly in the fields of robotics and precision engineering. However, the deformation of different parts of a compliant mechanism makes the analysis and design of such devices a challenge. This dissertation seeks to address the need for a design framework for compliant mechanisms.;Many compliant mechanisms use beam-like structures, or flexures. These elements are usually analyzed using beam theory, in the form of differential equations. In this work, a beam theory approximation combining shear, elongation and Poisson's effects is developed to improve the accuracy of our predictions. The beams are replaced by pseudo-rigid-body (PRB) models, which serve as a convenient tool for the analysis of compliant mechanisms. They are rigid-body approximations of compliant elements that replace the differential equations of beam theory with algebraic equations. PRB models can be developed for various types of compliant elements, and two new models are shown here for soft compliant joints and circular beams. The use of these models in design and analysis problems is also illustrated. A general method of representation and derivation of PRB models is presented, along with a list of various PRB models, to be used as part of a design framework. The reasons for the errors that creep into these models are also studied and guidelines suggested to eliminate them. The initial design of a mechanism for a specific application can be an arduous task, and this is also addressed using a new topology optimization process using PRB models.;The overarching goal of setting up this framework is to streamline the process of design of compliant mechanisms. Using PRB models speeds up the computation involved in design optimization, as opposed to solving differential equations from beam theory or high-fidelity Finite Element Analysis. Better knowledge of accuracy and complexity of the models can help the designer choose the optimal PRB model for a specific application. The parameter optimization framework and the list of PRB models will provide researchers with tools for deriving the values for a PRB model. The topology optimization technique is capable of deducing a feasible solution from a large pool of possible design solutions. This may be extended to shape optimization as well. There are many applications for such methods, some of which are shown here, including compliant robotic manipulators, micropsine grippers for space applications and micro-scale force sensors.
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