A complex solution framework for the kinetostatic synthesis of a compliant four-bar mechanism

This paper presents a systematic solution framework for the kinetostatic synthesis of compliant four-bar mechanisms. The goal of the kinetostatic synthesis is to find feasible compliant mechanism solutions for a given set of kinematic and force/energy specifications. Similar to the synthesis of rigid body linkages, we first classify kinetostatic synthesis problems into three major categories: function, motion and path generations. 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 these synthesis equations. When kinematic and static equations are decoupled, we solve first kinematic equations independently and then solve static equations for springs' stiffness. While they are coupled, we transform them into a polynomial form and solve them simultaneously with polynomial solvers. For this case a parameter continuation is devised to avoid computing for the junk solutions. At last, three representative examples are provided to demonstrate the solution process and verify the solution framework.