The authors present a general method for the automated singularity analysis of any mechanism at a given configuration. The procedure uses a base of the motion space. This is obtained from a velocity equation characterized by a geometric matrix. This special form of Jacobian matrix has some advantages for automatic implementation. This approach provides the degree of freedom associated with the singularity, uncontrolled motion, and kinematic dependencies. It also facilitates the choice of actuators and redundant devices. The method has been implemented in a computer program for kinematic analysis.

This paper looks at a method for the analysis of highly redundant multibody systems (e.g., in the case of cellular adaptive structures of variable geometry) in environments with obstacles. Our aim is to solve the inverse kinematics in successive positions of multibody systems, avoiding the obstacles in its work environment. The multibody systems are modeled via rod-type finite elements, both deformable and indeformable, and the coordinates of their nodes are chosen as variables. The obstacles are modeled via a mesh of points that exert repulsive forces on the nodes of the model of the multibody, in order to model the obstacle avoidance. Such forces have been chosen inversely proportional to the Nth power of the distance between the corresponding points of the obstacle and of the multibody system. The method is based on a potential function and on its minimization using the Lagrange Multiplier Method. The solution of the resulting equations is undertaken iteratively with the Newton-Raphson Method.