J. Jesús Cervantes-Sánchez

On the workspace, assembly configurations and singularity curves of the RRRRR-type planar manipulator

Abstract In this paper, a broadly applicable approach for numerically obtaining the workspace and the singularity curves of a planar RRRRR-type manipulator is presented. The workspace generation is formulated as a direct kinematic problem involving only two branches which are mathematically defined and related with the manipulators assembly configurations. For solving that problem, the analytical solution of two simple quadratic equations is found. A simple existence criterion is also obtained to detect the set of points forming the manipulators workspace. On the other hand, the singularity curves are composed of sets of singular points. In order to obtain the singular points, the properties of the Jacobian matrix are used. The complete method has been implemented and tested, as illustrated with examples for different geometrical properties of the manipulator. For each of these examples, the corresponding singularity curves are graphically generated to obtain the practical manipulators workspace. This feature is a very powerful design tool which is indispensable in visualizing and analyzing the kinematic working capability of the manipulator.

On the kinematic design of the 5R planar, symmetric manipulator

A complete kinematic characterization of the 5R planar, symmetric manipulator, intended as a design aid, is proposed in this paper. The characterization scheme relies on the configuration of the Cartesian workspace plots (CWP), the Cartesian workspace singularity plots (CWSP), the joint workspace plots (JWP) and the joint workspace singularity plots (JWSP). These plots are given in terms of two nondimensional geometric parameters, λ and μ, that represent the lengths of the manipulator links; these parameters can be used to investigate the relationships between the link lengths of the manipulator and the underlying workspace and singularity distribution. The plots can be regarded as an atlas of the workspace and singularity distribution that should find applications in analysis and design.

A simplified approach for obtaining the workspace of a class of 2-dof planar parallel manipulators

This paper presents a method for generating the reachable workspace of a class of planar two-degree-of-freedom (dof) end-effector-type manipulators. This class is based on six planar linkages with five links and five joints, revolute and/or prismatic. A common set of two quadratic equations is presented that determine the workspace of all the class as a function of the input motions of the manipulator under study. The quadratic equations involve only the Cartesian coordinates (x,y) of the operation point. Thus, the formulation is governed by the analytical solution of a well known second order equation and the inverse kinematic problem is not required. Because of the simplicity of the involved equations, an algorithm can be easily implemented on a computer program. Examples of generated workspaces for all the class are given to illustrate the proposed approach.

An efficient multi-camera, multi-target scheme for the three-dimensional control of robots using uncalibrated vision

Abstract A vision-based control methodology is presented in this paper that can perform accurate, three-dimensional (3D), positioning and path-tracking tasks. Tested with the challenging manufacturing task of welding in an unstructured environment, the proposed methodology has proven to be highly reliable, consistently achieving terminal precision of 1 mm . A key limiting factor for this high precision is camera–space resolution per unit physical space. This paper also presents a means of preserving and even increasing this ratio over a large region of the robots workspace by using data from multiple vision sensors. In the experiments reported in this paper, a laser is used to facilitate the image processing aspect of the vision-based control strategy. The laser projects “laser spots” over the workpiece in order to gather information about the workpiece geometry. Previous applications of the control method were limited to considering only local, geometric information of the workpiece, close to the region where the robots tool is going to be placed. This paper presents a methodology to consider all available information about the geometry of the workpiece. This data is represented in a compact matrix format that is used within the algorithm to evaluate an optimal robot configuration. The proposed strategy processes and stores the information that comes from various vision sensors in an efficient manner. An important goal of the proposed methodology is to facilitate the use of industrial robots in unstructured environments. A graphical-user-interface (GUI) has been developed that simplifies the use of the robot/vision system. With this GUI, complex tasks such as welding can be successfully performed by users with limited experience in the control of robots and welding techniques.

A robust classification scheme for spherical 4R linkages

Introduced in this paper is a robust classification scheme for the 4R spherical linkage. The robustness is acquired by means of a systematic and detailed analysis of the relative motions existing between adjacent links. Thus, one can avoid the usual ambiguities encountered in type-identification procedures which have become somewhat standard. Moreover, it is shown that there are only 33 distinct types of 4R spherical linkages instead of 81, as it was reported elsewhere. Finally, an unambiguous terminology is proposed and several examples with numerical values of link lengths for each linkage type are also provided.

Optimization of Industrial, Vision-Based, Intuitively Generated Robot Point-Allocating Tasks Using Genetic Algorithms

Current industrial robot-programming methods require, depending on the task to be developed, an elevated degree of technical ability and time from a human operator, in order to obtain a precise, nonoptimal result. This correspondence paper presents a methodology used to generate an optimal sequence of robot configurations that enable a precise point-allocating task applicable, for instance, to spot-welding, drilling, or electronic component placement maneuvers. The optimization process starts from a nonoptimal, initial sequence designated intuitively by a human operator using an easy-to-use interface. In this correspondence paper, intuitive programming is considered as the process of defining, in a computer graphics environment and with a limited user knowledge of robotics or the industrial task, the sequence of motions that enable the execution of a complex industrial robotic maneuver. Such an initial sequence is later followed by a robot, very precisely, using a vision-based, calibration-free, robot control method. Further robot path optimization is performed with a genetic algorithm approach. An industrial robot, which is part of the experimental setup, was used in order to validate the proposed procedure.

A Comprehensive Theory of Type Synthesis of Fully Parallel Platforms

This contribution presents a comprehensive theory for the type synthesis of fully parallel platforms. The theory deals with both types of platforms, 6 D.O.F. parallel platforms and lower mobility platforms. The theory is based on an analysis of the subsets and subgroups of the Euclidean group, SE(3). It is likely that the theory can be also developed based on an analysis of the subspaces and subalgebras of the Lie algebra, se(3), of the Euclidean group, SE(3).Copyright

The differential calculus of screws: Theory, geometrical interpretation, and applications

Abstract This article presents a novel and original formula for the higher-order time derivatives, and also for the partial derivatives of screws, which are successively computed in terms of Lie products, thus leading to the automation of the differentiation process. Through the process and, due to the pure geometric nature of the derivation approach, an enlightening physical interpretation of several screw derivatives is accomplished. Important applications for the proposed formula include higher-order kinematic analysis of open and closed kinematic chains and also the kinematic synthesis of serial and parallel manipulators. More specifically, the existence of a natural relationship is shown between the differential calculus of screws and the Lie subalgebras associated with the expected finite displacements of the end effector of an open kinematic chain. In this regard, a simple and comprehensible methodology is obtained, which considerably reduces the abstraction level frequently required when one resorts to more abstract concepts, such as Lie groups or Lie subalgebras; thus keeping the required mathematical background to the extent that is strictly necessary for kinematic purposes. Furthermore, by following the approach proposed in this article, the elements of Lie subalgebra arise in a natural way — due to the corresponding changes in screws through time — and they also have the typical shape of the so-called ordered Lie products that characterize those screws that are compatible with the feasible joint displacements of an arbitrary serial manipulator. Finally, several application examples — involving typical, serial manipulators — are presented in order to prove the feasibility and validity of the proposed method.

New Considerations on the Theory of Type Synthesis of Fully Parallel Platforms

This contribution presents new considerations on the theory of type synthesis of fully parallel platforms. These considerations prove that the theory of type synthesis of fully parallel platforms can be dealt with by analyzing two types of fully parallel platforms, where the displacements of the moving platform generate a subgroup of the Euclidean group, SE(3), including in this type, 6DOF parallel platforms and lower mobility platforms or, more precisely, parallel platforms where the displacements of the moving platforms generate only a subset of the Euclidean group. The theory is based on an analysis of the subsets and subgroups of the Euclidean group, SE(3), and their intersections. The contribution shows that the different types of parallel platforms are determined by the intersections of the subgroups or subsets, of the Euclidean group, generated by the serial connecting chains or limbs of the parallel platform. From an analysis of the intersections of subgroups and subsets of the Euclidean group, this contribution presents three possibilities for the type synthesis of fully parallel platforms where the displacements of the moving platform generate a subgroup of the Euclidean group, and two possibilities for the type synthesis of fully parallel platforms where the displacements of the moving platforms generate only a subset of the Euclidean group. An example is provided for each one of these possibilities. Thus, once these possible types of synthesis are elucidated, the type synthesis of fully parallel platforms is just reduced to the synthesis of the serial connecting chains or limbs that generate the required subgroups or subsets of the Euclidean group.

A Numerically Robust Algorithm to Solve the Five-Pose Burmester Problem

Introduced in this paper is a robust algorithm to solve the five-pose planar Burmester problem. The proposed algorithm functions even in the presence of special conditions of the prescribed poses that lead to algorithmic singularities otherwise. In order to show the applicability and to validate the robustness of the proposed algorithm, some examples are included.Copyright