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Robotics Conventions
There are many conventions used in the robotics research field. This article summarises these conventions. Line representations Lines are very important in robotics because: * They model joint axes: a revolute joint makes any connected rigid body rotate about the line of its axis; a prismatic joint makes the connected rigid body translate along its axis line. * They model edges of the polyhedral objects used in many task planners or sensor processing modules. * They are needed for shortest distance calculation between robots and obstacles Non-minimal vector coordinates A line L(p,d) is completely defined by the ordered set of two vectors: * a point vector p, indicating the position of an arbitrary point on L * one free direction vector d, giving the line a direction as well as a sense. Each point x on the line is given a parameter value t that satisfies: x = p+td. The parameter t is unique once p and d are chosen. The representation L(p,d) is not minimal, because it uses six ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Revolute Joint
A revolute joint (also called pin joint or hinge joint) is a one- degree-of-freedom kinematic pair used frequently in mechanisms and machines. The joint constrains the motion of two bodies to pure rotation along a common axis. The joint does not allow translation, or sliding linear motion, a constraint not shown in the diagram. Almost all assemblies of multiple moving bodies include revolute joints in their designs. Revolute joints are used in numerous applications such as door hinges, mechanisms, and other uni-axial rotation devices. A revolute joint is usually made by a pin or knuckle joint, through a rotary bearing. It enforces a cylindrical contact area, which makes it a lower kinematic pair, also called a full joint. However, If there is any clearance between the pin and hole (as there must be for motion), so-called surface contact in the pin joint actually becomes line contact. The contact between the inner and outer cylindrical surfaces is usually assumed to be fr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prismatic Joint
A prismatic joint is a one- degree-of-freedom kinematic pair which constrains the motion of two bodies to sliding along a common axis, without rotation; for this reason it is often called a slider (as in the slider-crank linkage) or a sliding pair. They are often utilized in hydraulic and pneumatic cylinders. A prismatic joint can be formed with a polygonal cross-section to resist rotation. See for example the dovetail joint and linear bearings. See also * Cylindrical joint * Degrees of freedom (mechanics) * Kinematic pair * Kinematics * Mechanical joint * Revolute joint A revolute joint (also called pin joint or hinge joint) is a one- degree-of-freedom kinematic pair used frequently in mechanisms and machines. The joint constrains the motion of two bodies to pure rotation along a common axis. The joint does ... References Kinematics Rigid bodies {{classicalmechanics-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plücker Coordinates
In geometry, Plücker coordinates, introduced by Julius Plücker in the 19th century, are a way to assign six homogeneous coordinates to each line in projective 3-space, P3. Because they satisfy a quadratic constraint, they establish a one-to-one correspondence between the 4-dimensional space of lines in P3 and points on a quadric in P5 (projective 5-space). A predecessor and special case of Grassmann coordinates (which describe ''k''-dimensional linear subspaces, or ''flats'', in an ''n''-dimensional Euclidean space), Plücker coordinates arise naturally in geometric algebra. They have proved useful for computer graphics, and also can be extended to coordinates for the screws and wrenches in the theory of kinematics used for robot control. Geometric intuition A line L in 3-dimensional Euclidean space is determined by two distinct points that it contains, or by two distinct planes that contain it. Consider the first case, with points x=(x_1,x_2,x_3) and y=(y_1,y_2,y_3). The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Common Normal (robotics)
In robotics the common normal of two non-intersecting joint axes is a line perpendicular to both axes. The common normal can be used to characterize robot arm links, by using the "common normal distance" and the angle between the link axes in a plane perpendicular to the common normal. When two consecutive joint axes are parallel, the common normal is not unique and an arbitrary common normal may be used, usually one that passes through the center of a coordinate system.''Foundations of Robotics: Analysis and Control'' by Tsuneo Yoshikawa 1990 page 33 The common normal is widely used in the representation of the frames of reference for robot joints and links, and the selection of minimal representations with the Denavit–Hartenberg parameters. See also * Denavit–Hartenberg parameters * Forward kinematics * Robotic arm A robotic arm is a type of mechanical arm, usually programmable, with similar functions to a human arm; the arm may be the sum total of the mechanism or ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coordinate System
In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space. The order of the coordinates is significant, and they are sometimes identified by their position in an ordered tuple and sometimes by a letter, as in "the ''x''-coordinate". The coordinates are taken to be real numbers in elementary mathematics, but may be complex numbers or elements of a more abstract system such as a commutative ring. The use of a coordinate system allows problems in geometry to be translated into problems about numbers and ''vice versa''; this is the basis of analytic geometry. Common coordinate systems Number line The simplest example of a coordinate system is the identification of points on a line with real numbers using the ''number line''. In this system, an arbitrary point ''O'' (the ''origin'') is chosen on a given line. The coordinate of a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cartesian Coordinate System
A Cartesian coordinate system (, ) in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in the same unit of length. Each reference coordinate line is called a ''coordinate axis'' or just ''axis'' (plural ''axes'') of the system, and the point where they meet is its ''origin'', at ordered pair . The coordinates can also be defined as the positions of the perpendicular projections of the point onto the two axes, expressed as signed distances from the origin. One can use the same principle to specify the position of any point in three-dimensional space by three Cartesian coordinates, its signed distances to three mutually perpendicular planes (or, equivalently, by its perpendicular projection onto three mutually perpendicular lines). In general, ''n'' Cartesian coordinates (an element of real ''n''-space) specify the point in an ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Product Of Exponentials Formula
The product of exponentials (POE) method is a robotics convention for mapping the links of a spatial kinematic chain. It is an alternative to Denavit–Hartenberg parameterization. While the latter method uses the minimal number of parameters to represent joint motions, the former method has a number of advantages: uniform treatment of prismatic and revolute joints, definition of only two reference frames, and an easy geometric interpretation from the use of screw axes for each joint. The POE method was introduced by Roger W. Brockett in 1984. Method The following method is used to determine the product of exponentials for a kinematic chain, with the goal of parameterizing an affine transformation matrix between the base and tool frames in terms of the joint angles \theta_1...\theta_N. Define "zero configuration" The first step is to select a "zero configuration" where all the joint angles are defined as being zero. The 4x4 matrix g_(0) describes the transformation from the b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Twist (screw Theory)
Screw theory is the algebraic calculation of pairs of vectors, such as forces and moments or angular and linear velocity, that arise in the kinematics and dynamics of rigid bodies. The mathematical framework was developed by Sir Robert Stawell Ball in 1876 for application in kinematics and statics of mechanisms (rigid body mechanics). Screw theory provides a mathematical formulation for the geometry of lines which is central to rigid body dynamics, where lines form the screw axes of spatial movement and the lines of action of forces. The pair of vectors that form the Plücker coordinates of a line define a unit screw, and general screws are obtained by multiplication by a pair of real numbers and addition of vectors. An important result of screw theory is that geometric calculations for points using vectors have parallel geometric calculations for lines obtained by replacing vectors with screws. This is termed the ''transfer principle.'' Screw theory has become ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Basic Robotics Topics
Robotics is the branch of technology that deals with the design, construction, operation, structural disposition, manufacture and application of robots. Robotics is related to the sciences of electronics, engineering, mechanics, and software. The word "robot" was introduced to the public by Czech writer Karel Čapek in his play R.U.R. (Rossum's Universal Robots), published in 1920. The term "robotics" was coined by Isaac Asimov in his 1941 science fiction short-story " Liar!"According to the ''Oxford English Dictionary,'' the term "robotics" was first used in the short story "Liar!" published in the May, 1941 issue of ''Astounding Science Fiction.'' Articles related to robotics include: 0–9 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z References External links {{Robotics Robotics Robotics Robotics is an interdisciplinary branch of computer s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Denavit–Hartenberg Parameters
In mechanical engineering, the Denavit–Hartenberg parameters (also called DH parameters) are the four parameters associated with a particular convention for attaching reference frames to the links of a spatial kinematic chain, or robot manipulator. Jacques Denavit and Richard Hartenberg introduced this convention in 1955 in order to standardize the coordinate frames for spatial linkages. Richard Paul demonstrated its value for the kinematic analysis of robotic systems in 1981. While many conventions for attaching reference frames have been developed, the Denavit–Hartenberg convention remains a popular approach. Denavit–Hartenberg convention A commonly used convention for selecting frames of reference in robotics applications is the Denavit and Hartenberg (D–H) convention which was introduced by Jacques Denavit and Richard S. Hartenberg. In this convention, coordinate frames are attached to the joints between two links such that one transformation is associated wi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arthur Cayley
Arthur Cayley (; 16 August 1821 – 26 January 1895) was a prolific United Kingdom of Great Britain and Ireland, British mathematician who worked mostly on algebra. He helped found the modern British school of pure mathematics. As a child, Cayley enjoyed solving complex maths problems for amusement. He entered Trinity College, Cambridge, where he excelled in Greek language, Greek, French language, French, German language, German, and Italian language, Italian, as well as mathematics. He worked as a lawyer for 14 years. He postulated the Cayley–Hamilton theorem—that every square matrix is a root of its own characteristic polynomial, and verified it for matrices of order 2 and 3. He was the first to define the concept of a group (mathematics), group in the modern way—as a set with a Binary function, binary operation satisfying certain laws. Formerly, when mathematicians spoke of "groups", they had meant permutation groups. Cayley tables and Cayley graphs as well as Cayle ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kenneth H
Kenneth is an English given name and surname. The name is an Anglicised form of two entirely different Gaelic personal names: ''Cainnech'' and '' Cináed''. The modern Gaelic form of ''Cainnech'' is ''Coinneach''; the name was derived from a byname meaning "handsome", "comely". A short form of ''Kenneth'' is '' Ken''. Etymology The second part of the name ''Cinaed'' is derived either from the Celtic ''*aidhu'', meaning "fire", or else Brittonic ''jʉ:ð'' meaning "lord". People :''(see also Ken (name) and Kenny)'' Places In the United States: * Kenneth, Indiana * Kenneth, Minnesota * Kenneth City, Florida In Scotland: * Inch Kenneth, an island off the west coast of the Isle of Mull Other * "What's the Frequency, Kenneth?", a song by R.E.M. * Hurricane Kenneth * Cyclone Kenneth Intense Tropical Cyclone Kenneth was the strongest tropical cyclone to make landfall in Mozambique since modern records began. The cyclone also caused significant damage in the Comoro Islands an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
