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Robot Kinematics
Robot kinematics applies geometry to the study of the movement of multi-degree of freedom kinematic chains that form the structure of robotic systems. The emphasis on geometry means that the links of the robot are modeled as rigid bodies and its joints are assumed to provide pure rotation or translation. Robot kinematics studies the relationship between the dimensions and connectivity of kinematic chains and the position, velocity and acceleration of each of the links in the robotic system, in order to plan and control movement and to compute actuator forces and torques. The relationship between mass and inertia properties, motion, and the associated forces and torques is studied as part of robot dynamics. Kinematic equations A fundamental tool in robot kinematics is the kinematics equations of the kinematic chains that form the robot. These non-linear equations are used to map the joint parameters to the configuration of the robot system. Kinematics equations are also ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometry
Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called a ''List of geometers, geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point (geometry), point, line (geometry), line, plane (geometry), plane, distance, angle, surface (mathematics), surface, and curve, as fundamental concepts. Originally developed to model the physical world, geometry has applications in almost all sciences, and also in art, architecture, and other activities that are related to graphics. Geometry also has applications in areas of mathematics that are apparently unrelated. For example, methods of algebraic geometry are fundamental in Wiles's proof of Fermat's Last Theorem, Wiles's proof of Fermat's ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multibody System
Multibody system is the study of the dynamics (physics), dynamic behavior of interconnected rigid body, rigid or flexible body, flexible bodies, each of which may undergo large Translation (physics), translational and rotational displacements. Introduction The systematic treatment of the dynamic behavior of interconnected bodies has led to a large number of important multibody formalisms in the field of mechanics. The simplest bodies or elements of a multibody system were treated by Isaac Newton, Newton (free particle) and Leonhard Euler, Euler (rigid body). Euler introduced reaction forces between bodies. Later, a series of formalisms were derived, only to mention Joseph Louis Lagrange, Lagrange’s formalisms based on minimal coordinates and a second formulation that introduces constraints. Basically, the motion of bodies is described by their kinematic behavior. The Analytical dynamics, dynamic behavior results from the equilibrium of applied forces and the rate of change of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Virtual Work
In mechanics, virtual work arises in the application of the '' principle of least action'' to the study of forces and movement of a mechanical system. The work of a force acting on a particle as it moves along a displacement is different for different displacements. Among all the possible displacements that a particle may follow, called virtual displacements, one will minimize the action. This displacement is therefore the displacement followed by the particle according to the principle of least action. The work of a force on a particle along a virtual displacement is known as the virtual work. Historically, virtual work and the associated calculus of variations were formulated to analyze systems of rigid bodies, but they have also been developed for the study of the mechanics of deformable bodies. History The principle of virtual work had always been used in some form since antiquity in the study of statics. It was used by the Greeks, medieval Arabs and Latins, and R ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Angular Velocity
In physics, angular velocity (symbol or \vec, the lowercase Greek letter omega), also known as the angular frequency vector,(UP1) is a pseudovector representation of how the angular position or orientation of an object changes with time, i.e. how quickly an object rotates (spins or revolves) around an axis of rotation and how fast the axis itself changes direction. The magnitude of the pseudovector, \omega=\, \boldsymbol\, , represents the '' angular speed'' (or ''angular frequency''), the angular rate at which the object rotates (spins or revolves). The pseudovector direction \hat\boldsymbol=\boldsymbol/\omega is normal to the instantaneous plane of rotation or angular displacement. There are two types of angular velocity: * Orbital angular velocity refers to how fast a point object revolves about a fixed origin, i.e. the time rate of change of its angular position relative to the origin. * Spin angular velocity refers to how fast a rigid body rotates around a f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jacobian Matrix And Determinant
In vector calculus, the Jacobian matrix (, ) of a vector-valued function of several variables is the matrix of all its first-order partial derivatives. If this matrix is square, that is, if the number of variables equals the number of components of function values, then its determinant is called the Jacobian determinant. Both the matrix and (if applicable) the determinant are often referred to simply as the Jacobian. They are named after Carl Gustav Jacob Jacobi. The Jacobian matrix is the natural generalization to vector valued functions of several variables of the derivative and the differential of a usual function. This generalization includes generalizations of the inverse function theorem and the implicit function theorem, where the non-nullity of the derivative is replaced by the non-nullity of the Jacobian determinant, and the multiplicative inverse of the derivative is replaced by the inverse of the Jacobian matrix. The Jacobian determinant is fundamentally use ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Revolute Joint
A revolute joint (also called pin joint or hinge joint) is a one-Degrees of freedom (mechanics), degree-of-freedom kinematic pair used frequently in Mechanism (engineering), mechanisms and machines. The joint Constraint (classical mechanics), constrains the motion of two bodies to pure rotation along a common Rotation around a fixed axis, axis. The joint does not allow Sliding (motion), 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 (mechanical), bearing. It enforces a cylindrical contact area, which makes it a Kinematic pair#Lower_pair, lower kinematic pair, also called a full joint. However, If there is any Engineering tolerance, clearance between the pin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polynomial
In mathematics, a polynomial is a Expression (mathematics), mathematical expression consisting of indeterminate (variable), indeterminates (also called variable (mathematics), variables) and coefficients, that involves only the operations of addition, subtraction, multiplication and exponentiation to nonnegative integer powers, and has a finite number of terms. An example of a polynomial of a single indeterminate is . An example with three indeterminates is . Polynomials appear in many areas of mathematics and science. For example, they are used to form polynomial equations, which encode a wide range of problems, from elementary word problem (mathematics education), word problems to complicated scientific problems; they are used to define polynomial functions, which appear in settings ranging from basic chemistry and physics to economics and social science; and they are used in calculus and numerical analysis to approximate other functions. In advanced mathematics, polynomials are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Humanoid Robot
A humanoid robot is a robot resembling the human body in shape. The design may be for functional purposes, such as interacting with human tools and environments and working alongside humans, for experimental purposes, such as the study of bipedal locomotion, or for other purposes. In general, humanoid robots have a torso, a head, two arms, and two legs, though some humanoid robots may replicate only part of the body. Androids are humanoid robots built to aesthetically resemble humans. History The concept of a humanoid robot originated in many different cultures around the world. Some of the earliest accounts of the idea of humanoid automata date to the 4th century BCE in Greek mythologies and various religious and philosophical texts from China. Physical prototypes of humanoid automata were later created in the Middle East, Italy, Japan, France and South Korea. Greece The Greek god of blacksmiths, Hephaestus, created several different humanoid automata in various myths. In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parallel Manipulator
A parallel manipulator is a mechanical system that uses several computer-controlled serial chains to support a single platform, or end-effector. Perhaps, the best known parallel manipulator is formed from six linear actuators that support a movable base for devices such as flight simulators. This device is called a Stewart platform or the Gough-Stewart platform in recognition of the engineers who first designed and used them. Also known as parallel robots, or generalized Stewart platforms (in the Stewart platform, the actuators are paired together on both the basis and the platform), these systems are articulated robots that use similar mechanisms for the movement of either the robot on its base, or one or more manipulator arms. Their 'parallel' distinction, as opposed to a serial manipulator, is that the end effector (or 'hand') of this linkage (or 'arm') is directly connected to its base by a number of (usually three or six) separate and independent linkages working simu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Serial Manipulator
Serial manipulators are the most common industrial robots and they are designed as a series of links connected by motor-actuated joints that extend from a base to an end-effector. Often they have an anthropomorphic arm structure described as having a "shoulder", an "elbow", and a "wrist". Serial robots usually have six joints, because it requires at least six degrees of freedom to place a manipulated object in an arbitrary position and orientation in the workspace of the robot. A popular application for serial robots in today's industry is the pick-and-place assembly robot, called a SCARA robot, which has four degrees of freedom. Structure In its most general form, a serial robot consists of a number of rigid links connected to joints. Simplicity considerations in manufacturing and control have led to robots with only revolute or prismatic joints and orthogonal, parallel and/or intersecting joint axes (instead of arbitrarily placed joint axes). Donald L. Pieper derived ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robot End Effector
An end effector is the device at the end of a robotic arm, designed to interact with the environment. The exact nature of this device depends on the application of the robot. In the strict definition, which originates from serial robotic manipulators, the end effector means the last link (or end) of the robot. At this endpoint, the tools are attached. In a wider sense, an end effector can be seen as the part of a robot that interacts with the work environment. This does not refer to the wheels of a mobile robot or the feet of a humanoid robot, which are not end effectors but rather part of a robot's mobility. End effectors may consist of a gripper or a tool. Grippers Categories When referring to robotic prehension there are four general categories of robot grippers: # Impactive: jaws or claws which physically grasp by direct impact upon the object. # Ingressive: pins, needles or hackles which physically penetrate the surface of the object (used in textile, carbon, and g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Animation
Computer animation is the process used for digitally generating Film, moving images. The more general term computer-generated imagery (CGI) encompasses both still images and moving images, while computer animation refers to moving images. Virtual cinematography, Modern computer animation usually uses 3D computer graphics. Computer animation is a digital successor to stop motion and traditional animation. Instead of a physical model or illustration, a digital equivalent is manipulated frame-by-frame. Also, computer-generated animations allow a single graphic artist to produce such content without using actors, expensive set pieces, or Theatrical property, props. To create the illusion of movement, an image is displayed on the computer monitor and repeatedly replaced by a new similar image but advanced slightly in time (usually at a rate of 24, 25, or 30 frames/second). This technique is identical to how the illusion of movement is achieved with television and Film, motion pictur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
