Philippe Wenger

Kinematics and workspace analysis of a three-axis parallel manipulator: the Orthoglide

The paper addresses kinematic and geometrical aspects of the Orthoglide, a three-DOF parallel mechanism. This machine consists of three fixed linear joints, which are mounted orthogonally, three identical legs and a mobile platform, which moves in the Cartesian x-y-z space with fixed orientation. New solutions to solve inverse/direct kinematics are proposed, and we perform a detailed workspace and singularity analysis, taking into account specific joint limit constraints.

Kinematic analysis of a serial–parallel machine tool: The VERNE machine

Abstract The paper derives the inverse and the forward kinematic equations of a serial–parallel 5-axis machine tool: the VERNE machine. This machine is composed of a three-degree-of-freedom (DOF) parallel module and a two-DOF serial tilting table. The parallel module consists of a moving platform that is connected to a fixed base by three non-identical legs. These legs are connected in a way that the combined effects of the three legs leadver-constrained mechanism with complex motion. This motion is defined as a simultaneous combination of rotation and translation. In this paper we propose symbolical methods that able to calculate all kinematic solutions and identify the acceptable one by adding analytical constraint on the disposition of legs of the parallel module.

A new general formalism for the kinematic analysis of all nonredundant manipulators

The author presents a novel general formalism for analyzing the kinematics of robot manipulators with arbitrary nonredundant geometry. It is shown that the classical description of singularities in the joint space may become insufficient. The notion of characteristic surfaces which define a new partition of the joint space is introduced. Generalizing the motion of aspects and c-sheets, the characteristic surfaces permit characterization of the joint space uniqueness domains, in which there is one unique solution to the inverse kinematic problem. The mapping into the workspace of the uniqueness domains defines the regions of feasible continuous trajectories.<<ETX>>

AN EXHAUSTIVE STUDY OF THE WORKSPACE TOPOLOGIES OF ALL 3R ORTHOGONAL MANIPULATORS WITH GEOMETRIC SIMPLIFICATIONS

Abstract This paper proposes a classification of three-revolute orthogonal manipulators that have at least one of their DH parameters equal to zero. This classification is based on the topology of their workspace. The workspace is characterized in a half cross-section by the singular curves. The workspace topology is defined by the number of cusps and nodes that appear on these singular curves. The manipulators are classified into different types with similar kinematic properties. Each type is evaluated according to interesting kinematic properties such as, whether the workspace is fully reachable with four inverse kinematic solutions or not, the existence of voids, and the feasibility of continuous trajectories in the workspace. It is found that several orthogonal manipulators have a “well-connected” workspace, that is, their workspace is fully accessible with four inverse kinematic solutions and any continuous trajectory is feasible. This result is of interest for the design of alternative manipulator geometries.

Consistent Kinetostatic Indices for Planar 3-DOF Parallel Manipulators, Application to the Optimal Kinematic Inversion

This paper investigates the problem of defining a consistent kinetostatic performance index for symmetric planar 3-DOF parallel manipulators. The condition number of the Jacobian matrix is known to be an interesting index. But since the Jacobian matrix is dimensionally inhomogeneous, a normalizing length must be used. This paper proposes two distinct kinetostatic indices. The first one is defined as the reciprocal of the condition number of the Jacobian matrix normalized with a convenient characteristic length. The second index is defined by a geometric interpretation of the “distance” to singularity. The two indices are compared and applied to the kinematic inversion in the presence of redundancy.Copyright

Singular curves in the joint space and cusp points of 3-RPR parallel manipulators

This paper investigates the singular curves in the joint space of a family of planar parallel manipulators. It focuses on special points, referred to as cusp points, which may appear on these curves. Cusp points play an important role in the kinematic behavior of parallel manipulators since they make possible a nonsingular change of assembly mode. The purpose of this study is twofold. First, it exposes a method to compute joint space singular curves of 3-RPR planar parallel manipulators. Second, it presents an algorithm for detecting and computing all cusp points in the joint space of these same manipulators.

Workspace Analysis of the Orthoglide Using Interval Analysis

This paper addresses the workspace analysis of the orthoglide, a 3-DOF parallel mechanism designed for machining applications. This machine features three fixed parallel linear joints which are mounted orthogonally and a mobile platform which moves in the Cartesian x-y-z space with fixed orientation. The workspace analysis is conducted on the bases of prescribed kinetostatic performances. The interesting features of the orthoglide are a regular Cartesian workspace shape, uniform performances in all directions and good compactness. Interval analysis based methods for computing the dextrous workspace and the largest cube enclosed in this workspace are presented.

Self-Motions of General 3-RPR Planar Parallel Robots

We study the kinematic geometry of general 3-RPR planar parallel robots with actuated base joints. These robots, while largely overlooked, have simple direct kinematics and large singularity-free workspace. Furthermore, their kinematic geometry is the same as that of a newly developed parallel robot with SCARA-type motions. Starting from the direct and inverse kinematic model, the expressions for the singularity loci of 3-RPR planar parallel robots are determined. Then, the global behavior at all singularities is geometrically described by studying the degeneracy of the direct kinematic model. Special cases of self-motions are then examined and the degree of freedom gained in such special configurations is kinematically interpreted. Finally, a practical example is discussed and experimental validations performed on an actual robot prototype are presented.

The Isoconditioning Loci of Planar Three-DOF Parallel Manipulators

This paper deals with a special class of three-degree-of-freedom parallel manipulators. First, the singular configurations of the two Jacobian matrices are studied. The isotropic configurations are then found based on the characteristic length of this manipulator. The isoconditioning loci for the Jacobian matrices are plotted to define a global performance index allowing the comparison of the different working modes. The resulting index is compared with the Cartesian workspace surface and the average of the condition number.

The Kinematic Sensitivity of Robotic Manipulators to Joint Clearances

The paper deals with the kinematic sensitivity of robotic manipulators to joint clearances. First, an error prediction model applicable to both serial and parallel manipulators is developed. A clearance model associated with axisymmetrical joints, which are widely used in robotic manipulators, is also proposed. Then, two nonconvex quadratically constrained quadratic programs (QCQPs) are formulated in order to find the maximum reference-point position error and the maximum orientation error of the moving-platform for given joint clearances. Finally, the contributions of the paper are highlighted by means of two illustrative examples.Copyright