This paper studies the static rigidity behaviour of a parallel manipulator with legs modelled as elastic members under axial loading. Structurally, a parallel module is more rigid compared to a serial module and is expected to take heavier payloads. Therefore, a guidance for design of such parallel manipulators is needed which leads to maximum rigidity over the workspace. In the present work, the authors propose the concept of the flexibility ellipsoid for a parallel system. Various scalar measures of rigidity are formulated on the basis of the proposed ellipsoid. An algorithm, involving multiple objective nonlinear programming technique, is implemented to decide upon some important design parameters of a generalised six degrees of freedom Stewart platform type parallel manipulator. It is observed that irrespective of the other parameters, parallel manipulators with the legs pairwise joined at the top platform possess the highest rigidity. Moreover, there exists certain kinematic dimensions for which the designed parallel system is completely free from all sorts of singularity.

Developing 6-DOF isotropic manipulators using isotropic generators is simple and efficient, and isotropic generators can be employed to develop serial, redundant, or parallel isotropic manipulators. An isotropic generator consists of a reference point and six straight lines. The existing generators, however, have one common geometric constraint: the reference point is equidistant from the six straight lines. Some practical isotropic designs might not be obtained due to this constraint. This paper proposes methods for developing new isotropic generators. The generators thus developed are not subject to the constraint, and the new methods allow us to specify the location of the tool center point, the size of the platform or the base, or the shape of isotropic parallel manipulators. Many new generators are presented to develop 6-DOF parallel manipulators with different shapes or different types of kinematic chains.

In this paper, an optimal kinematic design method of a three translational DoFs parallel manipulator is presented. The design is based on the concept of performance chart, which can show the relationship between a criterion and design parameters graphically and globally. The normalization on the design parameters of the studied manipulator makes it possible that the design space, which is made up of the normalized parameters, is limited. The design space includes of all possible basic similarity manipulators (BSMs). As any one of the BSMs represents all of its similarity manipulators (SMs) in terms of performances, if one BSM is optimal, its SMs are optimized as well. The said optimal BSM is from the optimum region, which is the intersecting result of involved performance charts. In this paper, the related performance criteria are good-conditioning workspace (GCW), global conditioning index (GCI) and global stiffness index (GSI). As an applying example, a design result of the parallel manipulator with a desired task workspace is presented. The results of the paper are very useful for the design and application of a parallel manipulator.

In this paper, we are interested in finding the optimal shapeof a magnet. The criterion to maximize is the jump of theelectromagnetic field between two different configurations.We prove existence of an optimal shape into a natural classof domains. We introduce a quasi-Newton type algorithm whichmoves the boundary. This method is very efficient to improvean initial shape. We give some numerical results.