Analytic and Geometric Technique for the Singularity Analysis of Multi-Degree-of-Freedom Spherical Mechanisms

Mechanisms' instantaneous kinematics is modeled by linear and homogeneous mappings whose coefficient matrices are also meaningful to understand their static behavior through the virtual work principle. The analysis of these models is a mandatory step during design. The superposition principle can be used for building and studying linear and homogeneous models. Here, multi-degree-of-freedom (multi-DOF) spherical mechanisms are considered. Their instantaneous-kinematics model is written by exploiting instantaneous-pole-axes' (IPA) properties and the superposition principle. Then, this general model is analyzed and an exhaustive analytic and geometric technique to identify all their singular configurations is deduced. Eventually, the effectiveness of the deduced technique is shown with two relevant case studies.

Pole-Axis Based Singularity Analysis of Spherical Mechanisms

Instantaneous kinematics of complex multi-loop mechanisms is modeled by linear and homogeneous mappings whose coefficient matrices have also important static meanings. As a consequence, the analysis of these models is a mandatory step, during design, that can be implemented by using the superposition principle. Here, spherical mechanisms are considered. Their general instantaneous-kinematics model is written by exploiting the properties of the instantaneous pole axes and the superposition principle. Then, this general model is analyzed to deduce an exhaustive analytic and geometric technique for identifying all the singular configurations of these mechanisms.