The JPL mobile robot ATHLETE is a platform with six serial chain legs ending in wheels. JSC Robonaut are modeled as kinematic chains. Boulton & Watt steam engine is studied as a system of rigid bodies connected by joints forming a kinematic chain. A model of the human skeleton as a kinematic chain allows positioning using forward and inverse kinematics.
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When analyzing parallel robots, the kinematic chain of each leg is analyzed individually and the tool frames are set equal to one another. This method is extensible to grasp analyses.
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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.
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6 Axis Articulated Robots from KUKA 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 may be part of a more complex robot. The links of such a manipulator are connected by joints allowing either rotational motion (such as in an articulated robot) or transnational (linear) displacement. The links of the manipulator can be considered to form a kinematic chain. The terminus of the kinematic chain of the manipulator is called the end effect or and it is analogous to the human hand.
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The speed ratio and mechanical advantage are defined so they yield the same number in an ideal linkage. A kinematic chain, in which one link is fixed or stationary, is called a mechanism,OED and a linkage designed to be stationary is called a structure.
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A model of the human skeleton as a kinematic chain allows positioning using inverse kinematics. Kinematic analysis is one of the first steps in the design of most industrial robots. Kinematic analysis allows the designer to obtain information on the position of each component within the mechanical system. This information is necessary for subsequent dynamic analysis along with control paths.
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For each joint of the kinematic chain, an origin point q and an axis of action are selected for the zero configuration, using the coordinate frame of the base. In the case of a prismatic joint, the axis of action v is the vector along which the joint extends; in the case of a revolute joint, the axis of action ω the vector normal to the rotation.
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It is also possible to think of the Bricard octahedron as a mechanical linkage consisting of the twelve edges, connected by flexible joints at the vertices, without the faces. Omitting the faces eliminates the self-crossings for many (but not all) positions of these octahedra. The resulting kinematic chain has one degree of freedom of motion, the same as the polyhedron from which it is derived..
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The constraint equations of a kinematic chain can be used in reverse to determine the dimensions of the links from a specification of the desired movement of the system. This is termed kinematic synthesis.R. S. Hartenberg and J. Denavit, 1964, Kinematic Synthesis of Linkages, McGraw-Hill, New York. Perhaps the most developed formulation of kinematic synthesis is for four-bar linkages, which is known as Burmester theory.
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Inverse kinematics is an example of the kinematic analysis of a constrained system of rigid bodies, or kinematic chain. The kinematic equations of a robot can be used to define the loop equations of a complex articulated system. These loop equations are non-linear constraints on the configuration parameters of the system. The independent parameters in these equations are known as the degrees of freedom of the system.
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An animated figure is modeled with a skeleton of rigid segments connected with joints, called a kinematic chain. The kinematics equations of the figure define the relationship between the joint angles of the figure and its pose or configuration. The forward kinematic animation problem uses the kinematics equations to determine the pose given the joint angles. The inverse kinematics problem computes the joint angles for a desired pose of the figure.
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It is also defined in context of the configuration space, task space and workspace of a robot. A specific type of linkage is the open kinematic chain, where a set of rigid links are connected at joints; a joint may provide one DOF (hinge/sliding), or two (cylindrical). Such chains occur commonly in robotics, biomechanics, and for satellites and other space structures. A human arm is considered to have seven DOFs.
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Featherstone's algorithm is a technique used for computing the effects of forces applied to a structure of joints and links (an "open kinematic chain") such as a skeleton used in ragdoll physics. The Featherstone's algorithm uses a reduced coordinate representation. This is in contrast to the more popular Lagrange multiplier method, which uses maximal coordinates. Brian Mirtich's PhD Thesis has a very clear and detailed description of the algorithm.
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Linkages may be constructed from open chains, closed chains, or a combination of open and closed chains. Each link in a chain is connected by a joint to one or more other links. Thus, a kinematic chain can be modeled as a graph in which the links are paths and the joints are vertices, which is called a linkage graph. The deployable mirror linkage is constructed from a series of rhombus or scissor linkages.
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Inertial motion capture systems are able to capture finger motions reading the rotation of each finger segment in 3D space. Applying these rotations to kinematic chain, the whole human hand can be tracked in real time, without occlusion and wireless. Hand inertial motion capture systems, like for example Synertial mocap gloves, are using tiny IMU based sensors, located on each finger segment. For most precise capture, at least 16 sensors have to be used.
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The Stanford arm, on display at Stanford University The Stanford arm is an industrial robot with six degrees of freedom, designed at Stanford University by Victor Scheinman in 1969Stanford Arm history. The Stanford arm is a serial manipulator whose kinematic chain consists of two revolute joints at the base, a prismatic joint, and a spherical joint. Because it includes several kinematic pairs, it is often used as an educational example in robot kinematics.
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Variable stroke engine (Autocar Handbook, Ninth edition) A mechanical linkage is an assembly of bodies connected to manage forces and movement. The movement of a body, or link, is studied using geometry so the link is considered to be rigid. The connections between links are modeled as providing ideal movement, pure rotation or sliding for example, and are called joints. A linkage modeled as a network of rigid links and ideal joints is called a kinematic chain.
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All possible Assur dyadic isomers (1), their simplified embodiment (2), and representative applications (3). In mechanical engineering, an Assur group is a kinematic chain with zero degree of mobility, which added or subtracted from a mechanism do not alter its original number of degrees of freedom. They have been first described by the Russian engineer (1878–1920) in 1914., The simplest of all Assur groups (also known as dyads) have two links and three joints, of which two are potential joints.
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Yves Guiard's research interests span stimulus-response compatibility and the speed/accuracy of trade-off aimed movement. He has designed and tested his novel models of interaction for mobile devices. He proposed a kinematic-chain model in 1987, but the model was only found useful by HCI researchers a decade later when two-handed interaction with the devices was started being researched. Guiard's HCI Research team at Télécom ParisTech is group is devoted to fundamental and applied research on Human Computer Interaction (HCI).
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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.
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An articulated robot with six DOF in a kinematic chain. A system with several bodies would have a combined DOF that is the sum of the DOFs of the bodies, less the internal constraints they may have on relative motion. A mechanism or linkage containing a number of connected rigid bodies may have more than the degrees of freedom for a single rigid body. Here the term degrees of freedom is used to describe the number of parameters needed to specify the spatial pose of a linkage.
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Forward vs. Inverse Kinematics In computer animation and robotics, inverse kinematics is the mathematical process of calculating the variable joint parameters needed to place the end of a kinematic chain, such as a robot manipulator or animation character's skeleton, in a given position and orientation relative to the start of the chain. Given joint parameters, the position and orientation of the chain's end, e.g. the hand of the character or robot, can typically be calculated directly using multiple applications of trigonometric formulas, a process known as forward kinematics.
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The Chebychev–Grübler–Kutzbach criterion determines the degree of freedom of a kinematic chain, that is, a coupling of rigid bodies by means of mechanical constraints. These devices are also called linkages. The Kutzbach criterion is also called the mobility formula, because it computes the number of parameters that define the configuration of a linkage from the number of links and joints and the degree of freedom at each joint. Interesting and useful linkages have been designed that violate the mobility formula by using special geometric features and dimensions to provide more mobility than predicted by this formula.
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In mechanical engineering, a kinematic chain is an assembly of rigid bodies connected by joints to provide constrained (or desired) motion that is the mathematical model for a mechanical system.Reuleaux, F., 1876 The Kinematics of Machinery, (trans. and annotated by A. B. W. Kennedy), reprinted by Dover, New York (1963) As in the familiar use of the word chain, the rigid bodies, or links, are constrained by their connections to other links. An example is the simple open chain formed by links connected in series, like the usual chain, which is the kinematic model for a typical robot manipulator.
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A movement requiring several axes thus requires a number of such joints. Unwanted flexibility or sloppiness in one joint causes a similar sloppiness in the arm, which may be amplified by the distance between the joint and the end- effectuor: there is no opportunity to brace one joint's movement against another. Their inevitable hysteresis and off-axis flexibility accumulates along the arm's kinematic chain; a precision serial manipulator is a compromise between precision, complexity, mass (of the manipulator and of the manipulated objects) and cost. On the other hand, with parallel manipulators, a high rigidity may be obtained with a small mass of the manipulator (relatively to the charge being manipulated).
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Reuleaux believed that machines could be abstracted into chains of elementary links called kinematic pairs. Constraints on the machine are described by constraints on each kinematic pair, and the sequence of movements of pairs produces a kinematic chain. He developed a compact symbolic notation to describe the topology of a very wide variety of mechanisms, and showed how it could be used to classify them and even lead to the invention of new useful mechanisms. At the expense of the German government, he directed the design and manufacture of over 300 beautiful models of simple mechanisms, such as the four-bar linkage and the crank.
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Once a vehicle's motions are known, they can be used to determine the constantly-changing viewpoint for computer-generated imagery of objects in the landscape such as buildings, so that these objects change in perspective while themselves not appearing to move as the vehicle- borne camera goes past them. The movement of a kinematic chain, whether it is a robot or an animated character, is modeled by the kinematics equations of the chain. These equations define the configuration of the chain in terms of its joint parameters. Forward kinematics uses the joint parameters to compute the configuration of the chain, and inverse kinematics reverses this calculation to determine the joint parameters that achieve a desired configuration.
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The degrees of freedom, or mobility, of a kinematic chain is the number of parameters that define the configuration of the chain.J. J. Uicker, G. R. Pennock, and J. E. Shigley, 2003, Theory of Machines and Mechanisms, Oxford University Press, New York. A system of n rigid bodies moving in space has 6n degrees of freedom measured relative to a fixed frame. This frame is included in the count of bodies, so that mobility does not depend on link that forms the fixed frame. This means the degree-of-freedom of this system is M = 6(N − 1), where N = n + 1 is the number of moving bodies plus the fixed body.
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