Kinetostatic Synthesis of Compliant Mechanisms with Numerical Continuation

Devising a systematic and most importantly a complete solution framework for the kinetostatic synthesis of compliant mechanisms with numerical continuation is the goal of this dissertation.;The goal of the kinetostatic synthesis is to find feasible compliant mechanism solutions for a given set of kinematic and force/energy specifications. The kinetostatic synthesis equations are derived by combining the kinematic synthesis and static equilibrium equations. We then propose a comprehensive framework based on polynomial solvers for obtaining solutions to the synthesis equations. When kinematic and static equations are decoupled, we solve first kinematic equations independently and then solve static equations for springs' stiffness. While coupled, we transform them into a polynomial form possibly using approximations and solve them simultaneously with polynomial solvers. The approximation error if there is any is expunged out in a later step using Newton-Raphson method. In addition, to exclude the unwanted and the degenerate solutions, we propose a constrained homotopy technique that empowers the classical continuation techniques to recognize and sift out such solutions in the numerical path tracking step.;As the applications, rigid slider-crank and fully compliant four-bar mechanisms are synthesized for common tasks such as function, motion and path generation.