The workspace boundary of 6-DOF parallel manipulators is a two-dimensional surface consisting of many patches that can be obtained by solving different sets of four constraint equations. This paper proposes algorithms for finding the equations to generate each patch of the boundary. Methods involving a searching technique are first developed to generate some small subsets of the boundary. The obtained data are then used to predict the equations for generating the rest of the boundary.

We present the positional abilities of a humanoid manipulator based on an improved kinematical model of the human arm. This was synthesized from electro-optical measurements of healthy female and male subjects. The model possesses three joints: inner shoulder joint, outer shoulder joint and elbow joint. The first functions as the human sternoclavicular joint, the second functions as the human glenohumeral joint, and the last replicates the human humeroulnar rotation. There are three links included, the forearm and the upper arm link which are of a constant length, and the shoulder link which is expandable. Mathematical interrelations between the joint coordinates are also taken into consideration. We determined the reachability of a humanoid arm, treated its orienting redundancy in the shoulder complex and the positional redundancy in the shoulder-elbow complexes, and discussed optimum configurations in executing different tasks. The results are important for the design and control of humanoid robots, in medicine and sports.

In this paper an inverse concept idea is presented to determine the main configuration dimensional parameters of a novel 5-DOF parallel kinematic machine tool. By the new described orientation workspace, the motion of the passive joints on the moving platform can be expressed in the fixed coordinate analytically. Some relationships between the reachable workspace and the dimensional parameters of the parallel machine tool have been obtained with graphical representation.