Manipulating industrial robots. Coordinate systems and motion nomenclatures

2015 ◽  

2015 ◽  
Vol 11 (5) ◽  
pp. 10 ◽  
Author(s):  
Paulo Abreu ◽  
Manuel Romano Barbosa ◽  
António Mendes Lopes

This paper presents the use of a virtual lab for teaching industrial robots programming to university students. The virtual lab, that replicates the existing physical lab, is built using an industrial simulation software package, RobotStudio™. The capabilities of this tool are explored in order to complement the introduction of theoretical concepts with practical programming experience. In addition to illustrate the use of different coordinate systems in a robotic cell, a description of the tool center point calibration and examples of evaluating different moving strategies to cover a plane surface, are also presented.



Author(s):  
S.G. Pudovkina ◽  
◽  
A.I. Telegin

The problem of bulkiness of mathematical models of manipulative systems of industrial robots is solved. Here we consider formulas for calculating static reactions in joints and formulas for active forces that balance the forces of gravity acting on the manipulator's bodies in its stationary state. The manipulator can be in such a state when it is before capturing the object of manipulation and releasing it, or when it is performing some assembly operations, or it is during spot welding and in slow (quasi-static) arc-welding and painting processes. Aim. The aim is to derive general recur-rence and finite formulas for calculating the reaction forces in joints and their projections to the ax-es of the coordinate system rigidly connected with the selected body. Express the formulas of force projections in terms of guiding cosines and justify their optimality in terms of the minimum of arithmetic operations. Derive general inverse recurrence formulas for writing out the guide cosines of the axes associated with the moving bodies of the coordinate system with respect to the stationary coordinate system. Research methods. The methods of research relate to vector mechanics and sys-tems analysis, and the algorithmization of calculations by reducing them to the use of recurrent formulas. Results. A systematic analysis of general formulas, in which all possible regular expres-sions are highlighted which are corresponding unambiguously to the kinematic parameters of ma-nipulators, is performed. These regular expressions are used in software for analytical modeling of manipulator, in particular, for the analytical solution of problems of statics of a manipulator. The method of analytical verification of the prescribed formulas is described. The tasks of writing out optimal formulas for calculating the projections of static reaction forces in joints have been solved. And the tasks of writing out optimal formulas for calculating active forces in progressive joints of universal manipulators with six degrees of freedom, operating in Cartesian, cylindrical, spherical and angular coordinate systems, have been solved also. Analytical verification of the derived equations of stat-ics is performed. Examples of the reuse of the derived formulas for manipulators with the same kin-ematic schemes of their subsystems. Conclusion. Expressions of the equations of statics of manipu-lators through the guide cosines of the axes of the associated coordinate systems of their bodies al-low us to write these equations through the known parameters of body orientation. The recurrent formulas for calculating directional cosines allows to use recursive functions in their software im-plementation, i.e. to increase the computational efficiency of the software.



1975 ◽  
Vol 26 ◽  
pp. 87-92
Author(s):  
P. L. Bender

AbstractFive important geodynamical quantities which are closely linked are: 1) motions of points on the Earth’s surface; 2)polar motion; 3) changes in UT1-UTC; 4) nutation; and 5) motion of the geocenter. For each of these we expect to achieve measurements in the near future which have an accuracy of 1 to 3 cm or 0.3 to 1 milliarcsec.From a metrological point of view, one can say simply: “Measure each quantity against whichever coordinate system you can make the most accurate measurements with respect to”. I believe that this statement should serve as a guiding principle for the recommendations of the colloquium. However, it also is important that the coordinate systems help to provide a clear separation between the different phenomena of interest, and correspond closely to the conceptual definitions in terms of which geophysicists think about the phenomena.In any discussion of angular motion in space, both a “body-fixed” system and a “space-fixed” system are used. Some relevant types of coordinate systems, reference directions, or reference points which have been considered are: 1) celestial systems based on optical star catalogs, distant galaxies, radio source catalogs, or the Moon and inner planets; 2) the Earth’s axis of rotation, which defines a line through the Earth as well as a celestial reference direction; 3) the geocenter; and 4) “quasi-Earth-fixed” coordinate systems.When a geophysicists discusses UT1 and polar motion, he usually is thinking of the angular motion of the main part of the mantle with respect to an inertial frame and to the direction of the spin axis. Since the velocities of relative motion in most of the mantle are expectd to be extremely small, even if “substantial” deep convection is occurring, the conceptual “quasi-Earth-fixed” reference frame seems well defined. Methods for realizing a close approximation to this frame fortunately exist. Hopefully, this colloquium will recommend procedures for establishing and maintaining such a system for use in geodynamics. Motion of points on the Earth’s surface and of the geocenter can be measured against such a system with the full accuracy of the new techniques.The situation with respect to celestial reference frames is different. The various measurement techniques give changes in the orientation of the Earth, relative to different systems, so that we would like to know the relative motions of the systems in order to compare the results. However, there does not appear to be a need for defining any new system. Subjective figures of merit for the various system dependon both the accuracy with which measurements can be made against them and the degree to which they can be related to inertial systems.The main coordinate system requirement related to the 5 geodynamic quantities discussed in this talk is thus for the establishment and maintenance of a “quasi-Earth-fixed” coordinate system which closely approximates the motion of the main part of the mantle. Changes in the orientation of this system with respect to the various celestial systems can be determined by both the new and the conventional techniques, provided that some knowledge of changes in the local vertical is available. Changes in the axis of rotation and in the geocenter with respect to this system also can be obtained, as well as measurements of nutation.



1975 ◽  
Vol 26 ◽  
pp. 21-26

An ideal definition of a reference coordinate system should meet the following general requirements:1. It should be as conceptually simple as possible, so its philosophy is well understood by the users.2. It should imply as few physical assumptions as possible. Wherever they are necessary, such assumptions should be of a very general character and, in particular, they should not be dependent upon astronomical and geophysical detailed theories.3. It should suggest a materialization that is dynamically stable and is accessible to observations with the required accuracy.



1975 ◽  
Vol 26 ◽  
pp. 395-407
Author(s):  
S. Henriksen

The first question to be answered, in seeking coordinate systems for geodynamics, is: what is geodynamics? The answer is, of course, that geodynamics is that part of geophysics which is concerned with movements of the Earth, as opposed to geostatics which is the physics of the stationary Earth. But as far as we know, there is no stationary Earth – epur sic monere. So geodynamics is actually coextensive with geophysics, and coordinate systems suitable for the one should be suitable for the other. At the present time, there are not many coordinate systems, if any, that can be identified with a static Earth. Certainly the only coordinate of aeronomic (atmospheric) interest is the height, and this is usually either as geodynamic height or as pressure. In oceanology, the most important coordinate is depth, and this, like heights in the atmosphere, is expressed as metric depth from mean sea level, as geodynamic depth, or as pressure. Only for the earth do we find “static” systems in use, ana even here there is real question as to whether the systems are dynamic or static. So it would seem that our answer to the question, of what kind, of coordinate systems are we seeking, must be that we are looking for the same systems as are used in geophysics, and these systems are dynamic in nature already – that is, their definition involvestime.



1975 ◽  
Vol 26 ◽  
pp. 293-295 ◽  
Author(s):  
I. Zhongolovitch

Considering the future development and general solution of the problem under consideration and also the high precision attainable by astronomical observations, the following procedure may be the most rational approach:1. On the main tectonic plates of the Earth’s crust, powerful movable radio telescopes should be mounted at the same points where standard optical instruments are installed. There should be two stations separated by a distance of about 6 to 8000 kilometers on each plate. Thus, we obtain a fundamental polyhedron embracing the whole Earth with about 10 to 12 apexes, and with its sides represented by VLBI.







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