The theory of reciprocal screws is used for the enumeration of the feasible limb structures of a class of 3-degree-of-freedom (DOF) rotational parallel manipulators. Geometric conditions for the moving platform to possess finite spherical motion are described. A table of feasible limbs that can be used for the construction of 3-DOF rotational parallel manipulators is developed.

This paper presents a comparison study of the well-conditioned workspace and stiffness properties of two 3-degree-of-freedom (DOF) parallel manipulators, one with three supporting limbs and the other with four supporting limbs. The inverse kinematics and Jacobian of these two mechanisms are analyzed. The well-conditioned workspace of each mechanism is maximized and the stiffness properties are determined. A comparison of the results indicates that the Tricept manipulator out performs the 3-UPU parallel manipulator.

This paper presents a comparison study of the well-conditioned workspace and stiffness properties of two 3 degree-of-freedom (DOF) parallel manipulators, one with three supporting limbs and the other with four supporting limbs. The inverse kinematics and Jacobian of these two mechanisms are analyzed. The well-conditioned workspace of each mechanism is maximized and the stiffness properties are determined. A comparison of the results indicates that the Tricept manipulator out performs the 3-UPU parallel manipulator.

Presents a comparison study of the well-conditioned workspace, stiffness and inertia properties of four 3 degree-of-freedom (DOF) translational parallel manipulators. The well-conditioned workspace of each architecture is maximized and plotted. The stiffness properties of these architectures are then determined. Finally, the inertia properties of these architectures are determined. The limb lengths are normalized to ensure a fair comparison. The results obtained provide a performance index for each of these architectures. The comparison study indicates that none of the architectures is superior to all others with respect to all performance measures. An architecture which suits certain specific performance requirements best should be chosen for an application. Hence this approach is expected to be useful for the conceptual design of hybrid kinematic machines.

Two optimization studies on the design of a three degree of freedom translational parallel platform are conducted and the results are compared. The objective function of the first study maximizes total volume of the manipulator workspace without regard to the quality of the workspace. The second study optimizes the total volume of well conditioned workspace by maximizing a global condition index. The global condition index is a function of the condition number of the Jacobian matrix, providing a means of measuring the amplification error between the actuators and the end effector. Both objective functions involve an integration over the workspace of the manipulator. This integral is approximated using the Monte Carlo method.

A novel 3-DOF parallel manipulator is presented that employs only revolute joints and constrains the manipulator output to translational motion. Closed-form solutions are developed for both the inverse and forward kinematics. The inverse kinematics produces four solutions for each leg of the manipulator. In general, the four solutions are realized in only two unique leg configurations. The forward kinematic solution is reduced to a quadratic equation. So that in general, there are two poses the manipulator can assume for a given set of input joint angles.

The principle of inertia match is extended from one-degree-of-freedom (DOF) systems to multi-DOF systems. Based on the concept of maximum acceleration capacity, a methodology for the determination of gear ratios in geared robotic mechanisms is developed. It is found that, in the optimum design, the mass inertia matrix of the input links reflected at the joint-space is equal to that of the major links, and the maximum acceleration capacity is independent of the gear train arrangement. Several two-DOF geared robotic mechanisms are used as design examples to illustrate the principle. Using this methodology, mechanisms can be designed to yield optimum dynamic performance.>

The orientational workspace of three-DOF (degree-of-freedom), four-jointed spherical wrist mechanisms was investigated. The workspace boundary equations were derived via geometric consideration. It is shown that, for wrist mechanisms with links 2 and 3 coupled, the workspace boundary consists of circles centered at a fixed axis of rotation, while, for mechanisms with links 1 and 2 coupled, the boundary consists of two branches of curves. The workspace is divided by inner and outer boundaries into regions of accessibility zero, two, and four. The criteria for full workspace design as well as for the maximum four-root region have been established.>

The concept of transmission lines for the topological synthesis of articulated gear mechanisms is introduced. It is shown that the structural matrix which relates input displacements to the joint angles of a multi-degree-of-freedom articulated gear mechanism can be derived using the concept of transmission lines. Applying the characteristics of the structural matrix, a new methodology for the topological synthesis of articulated gear mechanisms has been established. All the basic admissible structural matrices of three-degree-of-freedom geared robotic mechanisms have been enumerated to demonstrate the principle. Several arm and wrist mechanisms created are believed to be novel.>

The authors introduce th concept of transmission lines for kinematic analysis and synthesis of geared robotic mechanisms. It is shown that the structural matrix, which relates input displacements to the joint angles of a multi-degree-of-freedom geared robotic mechanism, can be derived using the concept of transmission lines. Applying the characteristics of the structural matrix, a methodology for structural synthesis of articulated mechanisms is established. All the basic admissible structural matrices of three-degree-of-freedom robotic mechanisms are enumerated to demonstrate the principle.>

A systematic approach is developed for the kinematic analysis of multi-degree-of-freedom robotic bevel-gear trains. The approach is based on the idea that the motion of a bevel-gear-type and effector can be described by an equivalent open-loop chain and that the relative rotation between every two adjacent links in the equivalent open-loop chain can be derived from a set of fundamental circuit equations and coaxial conditions. The theory is demonstrated by the kinematic analysis of two robotic wrists.>

A systematic approach has been developed for the kinematic analysis of multi-degree-of-freedom robotic bevel-gear trains. The approach is based on the idea that the motion of the end- effector can be described by an equivalent open-loop chain and that the relative rotations between every two adjacent links in the equivalent open-loop chain can be derived from a set of fundamental circuit equations. The theory is demonstrated by the kinematic analysis of a robotic wrist.