Compliance Parameterization and Optimization of Compliant Parallel Mechanisms

After developing the compliance/stiffness matrix of a compliant mechanism, the next step is to evaluate the performance of the compliant mechanism based on the developed compliance/stiffness matrix. Sometimes this requires either an explicit or implicit expressions of compliance/stiffness matrix with respect to design parameters of the compliant mechanism, which will lead to further compliance/stiffness parameterization and optimization. As a result, this chapter looks into the Compliance/Stiffness Parameterization and Optimization problems using ortho-planar springs, a typical type of compliant mechanisms. In this chapter, for the first time, the six-dimensional compliance characteristics of ortho-planar springs are investigated using a compliance-matrix based approach, and they are further validated with both finite element (FEM) simulation and experiments. The compliance matrix is developed by treating an ortho-planar spring as a parallel mechanism and is revealed to be diagonal. As a consequence, corresponding diagonal compliance elements are evaluated and analysed in forms of their ratios, revealing that an ortho-planar spring not only has a large linear out-of-plane compliance but also has a large rotational bending compliance. Both FEM simulation and experiments were then conducted to validate the developed compliance matrix. In the FEM simulation, a total number of 30 types of planar-spring models were examined, followed by experiments that examined the typical side-type and radial-type planar springs, presenting a good agreement between the experiment results and analytical models. Further, a planar-spring based continuum manipulator was developed to demonstrate the large-bending capability of its planar-spring modules.