Beside our arms, it is our hands that help us to perform tasks. At first glance, we seems to move our arms and use our hands naturally. On closer inspection, however, we find that both our arms and hands are redundant mechanisms which explains why our arms can approach an object using different postures and our hands can grasp the object with many feasible grasp configurations. Duplicating this phenomenon has led to many innovative designs of redundant arms as well as multifingered hands, and has sparked many useful analyses of these topics. This thesis presents a new approach to intelligent multifingered grasping and redundant arm manipulation. Methods proposed in this research yield a computationally efficient and physically meaningful model for the planning of grasp positions, the determination of squeezing finger forces and the visualization of the motions of redundant arms. Principles and concepts embedded in this analysis will help researchers to gain new insights toward better designs for hands and arms. The model developed in this thesis also provides mathematical justification for some of the motions of human arms and fingers. The main thrust of this analysis of multifingered grasping is the use of mechanical equivalent force/moment systems. These systems allow us to decompose each finger force into a normal and a tangential component. Using this decomposition of finger forces, we can visualize the contribution of each finger force by the resultant force and moment required to manipulate a grasped object. Additionally, the nature of this decomposition, which is one of the unique feature of our method, will allow intelligent utilization of touch sensors. The frictional constraints and the squeezing internal finger forces are elegantly taken into account through a computationally efficient algorithm for choosing grasp points. Our methods have also been extended into the grasp of solid objects. The second part of this thesis provides an efficient method for analyzing the inverse kinematic problem of redundant manipulators. Our method is based on fully using the directional properties of the columns of the Jacobian matrix which relates the joint velocities of the arm and the end effector velocities. Motions of a redundant manipulator are analyzed through its upper arm's motion and wrist's motion and the Jacobian matrix is partitioned accordingly. It is shown that the motion of the upper arm and the wrist can be evaluated separately and in parallel though this vectorized approach.