Second order analysis of the mobility of kinematic loops via acceleration compatibility analysis

This paper presents a method for the second order analysis of the mobility of a mechanism (i.e., the identification of the first order infinitesimal motions of the mechanism), based on the compatibility of the acceleration restrictions. This second order analysis allows one to numerically or analytically obtain the limitations of the movement of a mechanism in an uncertainty singular configuration imposed by curvature compatibility, and it can easily be extended to even higher order analysis. This method is quite interesting from the point of view of computational simplicity, due to the fact that most of the algorithm is based on the work required for the resolution of the usual acceleration problem. The applications of the method include correct determination of the second order approximation of the number of degrees of freedom of a mechanism given in an uncertainty singular configuration, including bifurcation point analysis (with branches of movement) increase of the convergence in position problems, detection and interpretation of kinematotropic mechanisms (also including its branches), accessible spaces, path planning and more.