Lung-Wen Tsai

Kinematics and Optimization of a Spatial 3-UPU Parallel Manipulator

The structural characteristics associated with parallel manipulators are investigated. Using these characteristics a class of 3 degree-of-freedom parallel manipulators are enumerated. Several parallel manipulators with only translational degrees of freedom are identified and the 3-UPU parallel manipulator is chosen for design analysis and optimization. The kinematics of this 3-UPU parallel manipulator is studied. Two geometric conditions that lead to pure translational motion of the moving platform are described. Due to the simple kinematic structure, the inverse kinematics yields two equal and opposite limb lengths whereas the direct kinematics produces two possible manipulator postures with one being the mirror image of the other. The Jacobian matrix is derived and several singular conditions are discussed. Furthermore the conditions for existence of an isotropic point within the workspace are discussed and equations to compute the isotropic configurations of a 3-UPU manipulator are derived. Finally, we undertake architecture optimization and show that certain values of design variables maximize the global condition index of the 3-UPU manipulator.

Jacobian Analysis of Limited-DOF Parallel Manipulators

This paper presents a methodology for the Jacobian analysis of limited degrees-of-freedom (DOF) parallel manipulators. A limited-DOF parallel manipulator is a spatial parallel manipulator which has less than six degrees-of-freedom. It is shown that a 6X6 Jacobian matrix, which provides information about both architecture and constraint singularities, can be derived by making use of the theory of reciprocal screws. The 3-UPU and 3-RPS parallel manipulators are used as examples to demonstrate the methodology.

Design Optimization of a Cartesian Parallel Manipulator

This paper introduces a 3-DOF translational parallel manipulator called Cartesian Parallel Manipulator (CPM). The manipulator consists of a moving platform that is connected to a fixed base by three limbs. Each limb is made up of one prismatic and three revolute joints and all joint axes are parallel to one another. In this way, each limb provides two rotational constraints to the moving platform and the combined effects of the three limbs lead to an over-constrained mechanism with three translational degrees of freedom. The manipulator behaves like a conventional X-Y-Z Cartesian machine due to the orthogonal arrangement of the three limbs. Two actuation methods are analyzed. However, the rotary actuation method is discarded because of the existence of singularities within the workspace. For the linear actuation method, there exists a one-to-one correspondence between the input and output displacements of the manipulator. The effects of misalignment of linear actuators on the motion of the moving platform are discussed. Each limb structure is exposed to a bending moment induced by external forces exerted on the moving platform. In order to minimize the deflection at the joints caused by the bending moment, a method to maximize the stiffness is suggested. A numerical example of the optimal design is presented.

Kinematics of a novel three DOF translational platform

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.

Kinematic Analysis of 3-DOF Position Mechanisms for Use in Hybrid Kinematic Machines

This paper introduces a new kinematic architecture called the hybrid kinematic machine. A hybrid kinematic machine typically consists of a position mechanism and an orientation mechanism that can be arranged in series or in parallel to achieve the notion of modular and reconfigurable machining centers. To demonstrate the concept, four parallel manipulators with translational motion characteristics have been identified. The kinematics of these mechanisms are described. Then, the well-conditioned workspace of each mechanism is maximized, and the stiffness properties are mapped. A comparison of the workspace volume and stiffness properties of these four mechanisms indicates that the 3-RUU manipulator appears to be the best design among the four architectures.

Optimization of a three DOF translational platform for well-conditioned workspace

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 comparison study of two 3-DOF parallel manipulators: one with three and the other with four supporting legs

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.

The kinematics of spatial robotic bevel-gear trains

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. >

Evaluation of a Cartesian Parallel Manipulator

This paper describes a new 3-DOF translational parallel manipulator named a Cartesian Parallel Manipulator (CPM). The machine behaves like a conventional X-Y-Z Cartesian machine due to the orthogonal arrangement of the three supporting limbs. It is shown that there exists a one-to-one correspondence between the input and output of the manipulator. Three possible arrangements of the Z actuator are evaluated by stiffness mapping. A method for compensating actuator misalignment is described.

Synthesis and analysis of a new class of six-degree-of-freedom parallel minimanipulators

A new class of 6-degree-of-freedom (dof) parallel minimanipulators is introduced. The minimanipulators are designed to provide high resolution and high stiffness for fine position and force control in a hybrid serial-parallel manipulator system. Two-dof planar linkages and inextensible limbs are used to improve positional resolution and stiffness of the minimanipulators. The 2-dof linkages serve as drivers for the minimanipulators. The minimanipulators require only three inextensible limbs and, unlike most of the six-limbed parallel manipulators, their direct kinematics can be reduced to solving a polynomial in a single variable. In addition, by using three limbs instead of six other benefits such as lower possibility of mechanical interference between limbs can be realized. All of the minimanipulator actuators are base-mounted. As a result, higher payload capacity, smaller actuator sizes, and lower power dissipation can be obtained. In addition to the design discussion, kinematic analysis of the minimanipulators is also presented.