Some Results on Fixed and Best Proximity Points of Multivalued

This paper is devoted to investigate the fixed points and best proximity points of multivalued cyclic self-mappings on a set of subsets of complete metric spaces endowed with a partial order under a generalized contractive condition involving a Hausdorff distance. The existence and uniqueness of fixed points of both the cyclic self-mapping and its associate composite self-mappings on each of the subsets are investigated, if the subsets in the cyclic disposal are nonempty, bounded and of nonempty convex intersection. The obtained results are extended to the existence of unique best proximity points in uniformly convex Banach spaces.

Structural Synthesis of 3-DoF Spatial Fully Parallel Manipulators

In this paper, the architectures of three degrees of freedom (3-DoF) spatial, fully parallel manipulators (PMs), whose limbs are structurally identical, are obtained systematically. To do this, the methodology followed makes use of the concepts of the displacement group theory of rigid body motion. This theory works with so-called 'motion generators'. That is, every limb is a kinematic chain that produces a certain type of displacement in the mobile platform or end-effector. The laws of group algebra will determine the actual motion pattern of the end-effector. The structural synthesis is a combinatorial process of different kinematic chains' topologies employed in order to get all of the 3-DoF motion pattern possibilities in the end-effector of the fully parallel manipulator.