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

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

Preparation of Schr\"odinger cat states with cold ions beyond the Lamb-Dicke limit

A scheme for preparing Schr\"odinger cat (SC) states is proposed beyond the Lamb-Dicke limit in a Raman-$\Lambda$-type configuration. It is shown that SC states can be obtained more efficiently with our scheme than with the former ones.Comment: RevTex 9 pages, no figures and table

The description of the human knee as four-bar linkage

Purpose: We investigate the dependence of the kinematics of the human knee on its anatomy. The idea of describing the kinematics of the knee in the sagittal plane using four-bar linkage is almost as old as kinematics as an independent discipline. We start with a comparison of known four-bar linkage constructions. We then focus on the model by H. Nägerl which is applicable under form closure. Methods: We use geometry and analysis as the mathematical methods. The relevant geometrical parameters of the knee will be determined on the basis of the dimensions of the four-bar linkage. This leads to a system of nonlinear equations. Results: The four-bar linkage will be calculated from the limits of the constructively accessible parameters by means of a quadratic approximation. Conclusions: By adapting these requirements to the dimensions of the human knee, it will be possible to obtain valuable indications for the design of an endoprosthesis which imitates the kinematics of the natural knee

Characteristic points and cycles in planar kinematics with application to the human gait

Purpose: We present a novel method to process kinematical data typically coming from measurements of joints. This method will be illustrated through two examples. Methods: We adopt theoretical kinematics together with the principle of least action. We use motion and inverse motion for describing the whole experimental situation theoretically. Results: By using the principle of least action, the data contain information about inherent reference points, which we call characteristic points. These points are unique for direct and inverse motion. They may be viewed as centers of the fixed and moving reference systems. The respective actions of these characteristic points are analytically calculated. The sum of these actions defines the kinematical action. This sum is by design independent of the choice of reference system. The minimality of the kinematical action can be used again to select numerically one representative cycle in empirically given, approximately periodic motions. Finally, we illustrate the theoretical approach making use of two examples worked out, hinge movement and the sagittal component of the movement of a human leg during gait. Conclusions: This approach enables automatic cycle choices for evaluating large databases in order to compare and to distinguish empirically given movements. The procedure can be extended to three dimensional movements