Geometric Basics and Calculation Methods for the Design of a Technical Saddle Joint based on Owl Neck Vertebrae

Abstract

A saddle joint enables the movement of two components relative to each other primarily about two axes of rotation and, to a limited extent, in translational direction. This type of joint is primarily found in nature, for example in the human thumb, in the ossicles and the cervical spine of owls. Motivated by the high degree of the owls’ head mobility, the authors aim to make this high motion potential technically accessible by defining relevant design parameters and developing calculation methods for dimensioning the saddle joint components. First, an abstracted contact geometry model based on the owls’ saddle joints is de-fined. A method for calculating the kinematics of the joint as a function of the previously introduced design parameters of the contact is derived mathematically. Regarding the implementation in a design process, this model is used to calculate the restoring forces required to stabilize the joint parts as well as the actuator torque needed for a specific rotational movement around those axes. Furthermore, the rotational stiffness of a specific joint geometry is calculated as an important design criterion. In summary, the defined contact geometry, the kinematics, and the computable forces serve as basis for designing technical saddle joints in the future.