A kinematic mapping of planar displacements is used to derive generalized constraint equations having the form of ruled quadric surfaces in the image space. The forward kinematic problem for all three-legged, three-degree-of-freedom planar parallel manipulators thus reduces to determining the points of intersection of three of these constraint surfaces, one corresponding to each leg. The inverse kinematic solutions, though trivial, are implicit in the formulation of the constraint surface equations. Herein the forward kinematic solutions of planar parallel robots with arbitrary, mixed leg architecture are exposed completely, and in a unified way, for the first time.
In this paper the singular configurations of wrist-partitioned 6R serial robots in general, and the KUKA KR-15/2 industrial robot in particular, are analytically described and classified. While the results are not new, the insight provided by the geometric analysis for users of such robots is. Examining the problem in the joint axis parameter space, it is shown that when the end-effector reference point is taken to be the wrist centre the determinant of the associated Jacobian matrix splits into four factors, three of which can vanish. Two of the three potentially vanishing factors give a complete description of the positioning singularities and the remaining one a complete description of the orientation singularities, in turn providing a classification scheme. Configurations Singulières des Robots Sérielsà Poignet Sphérique et Six Couples Rotöides: une Perspective Géométrique pour les Utilisateurs Résumé Dans cet article les configurations singuliéres des robots sérielsà poignet sphérique et six couples rotöides en général, et celle du robot industriel KUKA KR-15/2 en particulier, sont analytiquement décrites et classifiées. Bien que les résultats ne soient pas nouveaux, la perspective fournie par l'analyse géométrique pour des utilisateurs de tels robots l'est. En examinant le problème dans l'espace commun de paramètre d'axe, on montre que quand le point de référence terminal est pris commeétant le centre du poignet le déterminant de la matrice associée du Jacobian se divise en quatre facteurs, dont trois peuvent disparaître. Deux des trois facteurs qui peuvent potentiellement disparaître donnent une description complète des singularités de positionnement et les autres une description complète des singularités d'orientation, fournissant ainsi une méthode de classification.
This paper addresses the problem of finding an approximation to the minimal element set of the objective space for the class of multiobjective deterministic finite horizon optimal control problems. The objective space is assumed to be partially ordered by a pointed convex cone containing the origin. The approximation procedure consists of a two-step discretization in time and state space. Following the first-order time discretization, the dynamic programming principle is used to find the multiobjective discrete dynamic programming equation equivalent to the resulting discrete multiobjective optimal control problem. The multiobjective discrete dynamic programming equation is finally discretized in the state space. The convergence of the approximation for both discretization steps is discussed.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.