Six-Dimensional Compliance Analysis and Validation of Orthoplanar Springs

This paper for the first time investigates the six-dimensional compliance characteristics of orthoplanar springs using a compliance-matrix based approach, and validates them with both finite element (FEM) simulation and experiments. The compliance matrix is developed by treating an orthoplanar spring as a parallel mechanism and is revealed to be diagonal. As a consequence, corresponding diagonal compliance elements are evaluated and analyzed in forms of their ratios, revealing that an orthoplanar 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.