Drawing on screw theory and the virtual joint method, this paper presents a general and hierarchical approach for semianalytical stiffness modeling of parallel mechanisms. The stiffness model is built by two essential steps: 1) formulating the map between the stiffness matrices of platform and limbs using the duality of wrench and twist of the platform; and 2) formulating the map between stiffness matrices of a limb and a number of elastic elements in that limb using the duality of the wrench attributed to the limb and the twist of the endlink of that limb. By merging these two threads, the Cartesian stiffness matrix can be explicitly expressed in terms of the compliance matrices of joints and links. The proposed approach bridges the gap between two currently available approaches and is thereby very useful for evaluating stiffness over the entire workspace and investigating the influences of joint/link compliances on those of the platform in a quick and precise manner. A stiffness analysis for a 3-PRS parallel mechanism is presented as an example to illustrate the effectiveness of the proposed approach.

This paper presents a general and systematic approach to formulate the dimensionally homogeneous Jacobian, which is an important issue for the dexterity evaluation and dimensional synthesis off-degrees-of-freedom (DOF) (f≤ 6) parallel manipulators having mixed rotational and translational movement capabilities. By the utilization offindependent coordinates to describe the specified motion types of the platform, thef×fdimensionally homogeneous Jacobian is derived directly from the generalized Jacobian, provided that the manipulator has only one type of actuator. The condition number of the new Jacobian is then employed to evaluate the dexterity of two typical 3-DOF parallel manipulators as an illustration of the effectiveness of this approach.

This paper deals with the kinematic calibration of a 3-DOF parallel mechanism using a double-ball-bar (DBB) system. The mechanism forms the main body of a 5-DOF reconfigurable hybrid robot named TriVariant that is a modified version of the Tricept, achieved by integrating one of its three active limbs into the passive one. The first order error mapping function is formulated to link the measured data and the geometric source errors affecting the compensatable pose accuracy. Issues to enhance the accuracy and efficiency of the calibration are investigated. The results are employed to a prototype machine calibration

This paper deals with the finite element analysis (FEA) of two 5-DOF reconfigurable hybrid robots, the Tricept and the TriVariant, by means of ANSYS parametric design language (APDL). The research interests are focused on: (1) precise FEA formulation of different types of joints by setting of contact elements, and (2) the development of an effective modeling strategy for the rapid stiffness and natural frequencies estimation associated with different configurations. The computational results show that two robots are of similar static and dynamic performances provided that they have identical geometrical dimensions, elastical and inertial parameters

This paper deals with the tolerance design of a two-degree-of-freedom translational parallel robot module for high-speed pick-and-place operations. The module is an overconstrained parallel mechanism using two sets of parallelograms in each limb. A probabilistic model of the uncompensatable pose error is formulated, together with a compatibility condition to ensure the mobility of the robot. Based upon this model, optimization of the tolerances of the geometric source errors and joint clearances is conducted, subject to a set of appropriate constraints. Simulation and experimental results are given to demonstrate the effectiveness of this approach.

This paper deals with the conceptual design and dimensional synthesis of a 3-DOF parallel mechanism module which forms the main body of a newly invented 5-DOF reconfigurable hybrid robot named "TriVariant." The TriVariant is a modified version of the Tricept robot, achieved by integrating one of the three active limbs into the passive limb. The idea leading to the innovation of the module is systematically addressed. Its kinematic performance is optimized by minimizing a global and comprehensive conditioning index subject to a set of appropriate mechanical constraints. It is concluded that the proposed hybrid system is more cost-effective and has a competitive kinematic performance in comparison with the well-known Tricept robot.

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.