This paper presents a hybrid method for the optimum kinematic design of two-degree-of-freedom (2-DOF) parallel manipulators with mirror symmetrical geometry. By taking advantage of both local and global approaches, the proposed method can be implemented in two steps. In the first step, the optimal architecture, in terms of isotropy and the behavior of the direct Jacobian matrix, is achieved, resulting in a set of closed-form parametric relationships that enable the number of design variables to be reduced. In the second step, the workspace bounded by the specified conditioning index is generated, which allows only one design parameter to be determined by optimizing a comprehensive index in a rectangular workspace. The kinematic optimization of a revolute-jointed 2-DOF parallel robot has been taken as an example to illustrate the effectiveness of this approach.

This paper presents a mathematic proof for the identifiability of geometric parameters of 6-DOF parallel kinematic machines (PKM). Rank deficiency of the identification matrix is justified if the end-effector undergoes all possible degrees of freedom but only a set of position errors normal to a plane is measured. An approach is proposed to tackle this problem, which enables the full set of parameter errors to be identified by only using a minimum set of pose errors: 1) the "flatness" of a fictitious plane generated by the tip of endpoint sensor; 2) the "squareness" of two orthogonal axes; and 3) the orientation of the end-effector at the initial configuration. Consequently, the burden arisen from the orientation error measurement may be dramatically reduced. The proposed method is so general that it can also be used to handle the parameter identification problems of the PKM with fewer than six degrees of freedom.

Presents a simple yet comprehensive approach that enables the stiffness of a tripod-based parallel kinematic machine to be quickly estimated. The approach arises from the basic idea for the determination of the equivalent stiffness of a group of serially connected linear springs and can be implemented in two steps. In the first step, the machine structure is decomposed into two substructures associated with the machine frame and parallel mechanism. The stiffness models of these two substructures are formulated by means of the virtual work principle. This is followed by the second step that enables the stiffness model of the machine structure as a whole to be achieved via linear superposition. The three-dimensional representations of the machine stiffness within the usable workspace are depicted and the contributions of different component rigidities to the machine stiffness are discussed. The results are compared with those obtained through experiments.

In this paper, an effective approach to determine the carriage stroke of 6-PSS parallel manipulator is presented. The analytical expression of the position workspace boundary is formulated using differential geometry. This allows the closed form solution to the carriage stroke necessary to generate a cylindrical prescribed workspace to be determined.

A novel methodology to formulate the closed form solution to the orientation workspace of Gough-Stewart parallel manipulators is presented by using a fictitious four-bar spatial linkage model. The possible mechanical constraints are considered which include the strut length and the passive joint limitations. Several examples are given to illustrate the effectiveness of this approach.