This paper presents a systematic methodology for solving the inverse dynamics of a Stewart-Gough manipulator. Based on the principle of virtual work and the concept of link Jacobian matrices, a methodology for deriving the dynamical equations of motion is developed. It is shown that the dynamics of the manipulator can be reduced to solving a system of six linear equations in six unknowns. A computational algorithm for solving the inverse dynamics of the manipulator is developed and several trajectories of the moving platform are simulated.

Solving the Inverse Dynamics of a Stewart-Gough Manipulator by the Principle of Virtual Work

In this paper, a systematic approach is developed for the structural synthesis of a class of four-degrees-of-freedom (4-DoF) and 5-DoF overconstrained parallel manipulators with identical serial limbs. The theory of screws and reciprocal screws is employed for the analysis of the geometric conditions that must be met by the limbs of such parallel manipulators. Limb structures that can be used for constructing 4-DoF or 5-DoF parallel manipulators are enumerated according to the reciprocity of the twist and wrench systems. The assembly conditions of a parallel manipulator built by using identical C- or F-limbs are discussed. Several 4-DoF and 5-DoF parallel manipulators are sketched as examples.

Structure Synthesis of a Class of 4-DoF and 5-DoF Parallel Manipulators with Identical Limb Structures

This paper presents the results of a detailed study of the singular configurations of 3-DOF planar parallel mechanisms with three identical legs. Only prismatic and revolute joints are considered. From the point of view of singularity analysis, there are ten different architectures. All of them are examined in a compact and systematic manner using planar screw theory. The nature of each possible singular configuration is discussed and the singularity loci for a constant orientation of the mobile platform are obtained. For some architectures, simplified designs with easy to determine singularities are identified.

Singularity Analysis of 3-DOF Planar Parallel Mechanisms via Screw Theory

http://www-percro.sssup.it/~antony/papers/mech_mach_th_2003.pdf

Dynamics of parallel manipulators by means of screw theory

This paper deals with the conceptual design and optimal dimensional synthesis of a novel 2-DOF translational parallel robot for pick-and-place operations. In a conceptual design phase, the conditions for generating such kinds of parallel robots are investigated, leading to the invention of a 2-D version of the Delta robot. Combining this robot with a 1-DOF feed mechanism, a hybrid robot can be created which is particularly suitable for transporting objects at very high speed in a plane plus a relatively slow or step-by-step, yet long distance motion, normal to the plane. The kinematic optimality of the 2-DOF translational parallel robot is achieved by minimizing a global and comprehensive conditioning index subject to a set of appropriate constraints. The application of this robot to the development of a device for quality inspection of rechargeable batteries is used to demonstrate its applicability.

Conceptual Design and Dimensional Synthesis of a Novel 2-DOF Translational Parallel Robot for Pick-and-Place Operations

A new approach for the dynamic analysis of parallel manipulators is presented in this paper. This approach is based on the principle of virtual work. The approach is firstly illustrated using a simple example, namely, a planar four-bar linkage. Then, the dynamic analysis of a spatial six-degree-of-freedom parallel manipulator with prismatic actuators (Gough–Stewart platform) is performed. Finally, a numerical example is given in order to illustrate the results. The approach proposed here can be applied to any type of planar and spatial parallel mechanism and leads to faster computational algorithms than the classical Newton–Euler approach when applied to these mechanisms.

A New Approach for the Dynamic Analysis of Parallel Manipulators

Static balancing of spatial three-degree-of-freedom parallel mechanisms

https://espace2.etsmtl.ca/4818/1/CK2001.pdf

Singularity loci of planar parallel manipulators with revolute actuators

Static balancing of spatial four-degree-of-freedom parallel mechanisms

This article addresses the kinematic modeling and the determination of the singularity loci of spatial five-degree-of-freedom parallel mechanisms with prismatic or revolute actuators. The architecture of the spatial five-degree-of-freedom parallel mechanisms is first introduced. Then, algorithms are derived for the solution of the inverse kinematic problem for the two types of mechanisms considered here. Two different methods are presented for the derivation of the velocity equations and the corresponding Jacobian matrices are derived. The numerical determination of the workspace boundaries is then briefly discussed. Finally, the determination of the singularity loci is performed, using the velocity equations, and examples are given to illustrate the results. It is shown that the vector formulation of the velocity equations leads to more efficient algorithms for the determination of the singularity loci. Spatial five-degree-of-freedom parallel mechanisms can be used in several robotic applications as well as in flight simulators. The kinematic analysis and the determination of the singularity loci are very important design issues. © 1997 John Wiley & Sons, Inc.

Jiegao Wang

Papers

A New Approach for the Dynamic Analysis of Parallel Manipulators

Static balancing of spatial three-degree-of-freedom parallel mechanisms

Singularity loci of planar parallel manipulators with revolute actuators

Static balancing of spatial four-degree-of-freedom parallel mechanisms

Kinematic analysis and singularity representation of spatial five‐degree‐of‐freedom parallel mechanisms