Se-Kyong Song

New methodology for the forward kinematics of 6-DOF parallel manipulators using tetrahedron configurations

This paper presents a new methodology of using tetrahedron configurations to determine the forward kinematics of 6-DOF parallel manipulators. The approach is introduced in a form of the tetrahedron proposition and theorem using the special characteristics tetrahedral geometry which are then applied to obtaining the kinematic solutions of two 6-DOF parallel manipulators such as those previously introduced by Hunt-Primrose (1993) and by the authors (2000). The proposed methodology has the advantage in greatly reducing the complexity of formulation and computational burden required by conventional methods for solving the forward kinematics. As a result, the methodology allows a significant simplification in the formulations and provides an easier means of obtaining the solution.

A tetrahedron approach for a unique closed-form solution of the forward kinematics of six-dof parallel mechanisms with multiconnected joints

This article presents a new formulation approach that uses tetrahedral geometry to determine a unique closed-form solution of the forward kinematics of six-dof parallel mechanisms with multiconnected joints. For six-dof parallel mechanisms that have been known to have eight solutions, the proposed formulation, called the Tetrahedron Approach, can find a unique closed-form solution of the forward kinematics using the three proposed Tetrahedron properties. While previous methods to solve the forward kinematics involve complicated algebraic manipulation of the matrix elements of the orientation of the moving platform, or closed-loop constraint equations between the moving and the base platforms, the Tetrahedron Approach piles up tetrahedrons sequentially to directly solve the forward kinematics. Hence, it allows significant abbreviation in the formulation and provides an easier systematic way of obtaining a unique closed-form solution.

Efficient formulation approach for the forward kinematics of the 3-6 Stewart-Gough Platform

Presents an approach to reduce the computational burden of solving the forward kinematics of the 3-6 (Stewart-Gough) Platform. The conventional forward kinematics has been formulated with trigonometric functions through many complicated steps. Based on tetrahedron geometry, the proposed formulation approach can allow intuitive derivation of the forward kinematics and considerable abbreviation of the number of calculations involved in the three constraint equations that must be calculated in the process of the forward kinematics. Consequently, the proposed formulation approach greatly reduces the computational burden. The feasibility and convergence of the formulation approach has been verified through a series of simulation results.

Efficient formulation approach for the forward kinematics of 3-6 parallel mechanisms

This paper presents a new formulation approach to obtain a simplified form of the forward kinematic solution that can reduce the computational burden involved in determining the solution of the forward kinematics of the 3-6 parallel mechanism with three connecting joints on the moving platform. The conventional forward kinematics of haptic devices with serial–parallel mechanisms is formulated through employing the Denavit–Hartenberg notation, and results in complicated formulation procedures and computational burden. In order to reduce these problems, this paper transforms the haptic devices into an equivalent kinematic model of the 3-6 Stewart–Gough platform. The conventional forward kinematics of the 3-6 platform is formulated with trigonometric functions through complicated steps and results in the computational burden. Thus we introduce the new formulation approach, based on tetrahedron geometry, in order to simplify the formulation of the forward kinematics and to reduce the computational burden. The proposed formulation approach can allow intuitive derivation and considerable abbreviation of the number of calculations involved in the forward kinematic solution. The feasibility and convergence of the formulation approach is verified through a series of simulations and experiments.

Kinematic feature analysis of a 6-degree-of-freedom in-parallel manipulator for micro-positioning surgical

This paper presents a kinematic analysis of the parallel manipulator developed for micro-positioning application that requires high control bandwidth and high precision. The manipulator is a class of in-parallel platforms with 3 PRPS (prismatic-revolute-prismatic-spherical) joints chain geometry. The main advantage of this manipulator, compared with the typical Stewart platform type, is the ability to produce pure motion. The purpose of this paper is to develop an efficient kinematic model which can be used for real-time control and to propose systematic design methods that considers the existence conditions of the forward kinematic solution, singularity, manipulability, and resistivity. A series of simulations was carried out to show the kinematic characteristics and performance of the mechanism. The proposed manipulator has potentials in a wide range of applications from micro-surgery robots to a highly dextrous wrist mechanism of assembly robots.