Six Dimensional Compliance Analysis of Ortho-Planar Springs for a Continuum Manipulator

Ortho-planar spring is a compact spring that generates the motion based on the deformation of flexure elements, and it has wide applications in the compliant robotic designs. Previous studies only investigate the out-of-plane compliance of ortho-planar spring and fewer work pays attention to its angular compliance. To address this issue, this paper provides an analytical method to study both the linear and angular compliance characteristics of ortho-planar spring for the first time. In the frame work of screw theory, the symbolic formula of platform’s compliance matrix was obtained based on the hybrid integration of beam elements. Subsequently non-dimensional geometric parameters were introduced to compare the compliance characteristics of planar spring, which revealed the ortho-planar spring also demonstrates large bending compliance. Numerical studies of angular compliance of planar spring were provided, and they showed good agreements with the finite element simulations in a large working range. Based on the numerical study, a physical prototype of one continuum structure assembled with planar springs was provided and it demonstrated a large flexibility compared to other previous designs, which suggests the ortho-planar spring has potential value in developing continuum manipulators in related medical surgery and biorobotic research fields.