Surface Robots based on S-Isothermic Surfaces

Surface robots can have many applications due to multiple degrees of freedom. Accordingly, many open research questions arise due to the limited number of realized cases and insufficient theory foundation. For a surface robot that performs deformations with shear deformation, the inner product calculation in a local coordinate system on the robot generally depends on the shear angle. However, the shear angle cannot be accurately measured, making it difficult to control the robot with coordinate transformation. We present herein a geometric robot with coordinates that are as locally orthogonal as possible. This robot is embodied by adding thickness to a special circle group, called the S-isothermic surface. We propose the utilization of inverse kinematics in S-isothermic-surface robots and demonstrate the results of actual realization.