In small scale and more specifically in miniature robotics applications, compliant mechanisms are highly preferred because of their advantages such as, less moving parts, friction losses, assembly time and effort, but their biggest challenge need to be addressed which is fatigue failure under cyclic loads. As the first step of this work, a new miniature, foldable, quadruped robot, MinIAQ, was developed whose legs are individually controlled by custom motors and encoders. The locomotion mechanism used in this robot is based on a simple four bar mechanism that consists of flexure joints instead of ideal revolute joints. These joints allow a single degree of freedom rotation provided by the bending of flexure members. Even though they are much more efficient and easier to make in small scale, such compliant joints suffer from fatigue failure, if subjected to long period of cyclic loads. Moreover, flexure joints and their use in robotic applications have not been modeled before using large deflection beam theory methods, which results with a limited understanding of the robot kinematics using compliant joints. In this thesis, elliptic integral solution of nonlinear large deflections are used to model the flexure joints used in miniature compliant mechanisms. The elliptic integral kinematic solutions are verified with experimental and FEA results by using a simple leg mechanism. With varying the geometric parameters for this simple compliant mechanism, results obtained from elliptic integral solution and experiments are presented and discussed. Since flexure joints store strain energy throughout bending, they act as torsion springs. The elliptic integral kinematic solution takes this bending moment into account and the results yield accurate load capacity of the compliant mechanism. The necessary input torque to operate the compliant mechanism can also be predicted in a more accurate manner. Using the model developed, the stresses on a compliant joint can be calculated for any

mechanism. As a case study, an optimization is done for MinIAQ’s compliant joints based on its geometric parameters to withstand desired number of cycles before failure.